Numerically satisfactory solutions of Kummer recurrence relations

NARCIS (Netherlands)

J. Segura (Javier); N.M. Temme (Nico)

2008-01-01

textabstractPairs of numerically satisfactory solutions as $n\\rightarrow \\infty$ for the three-term recurrence relations satisfied by the families of functions $_1\\mbox{F}_1(a+\\epsilon_1 n; b +\\epsilon_2 n;z)$, $\\epsilon_i \\in {\\mathbb Z}$, are given. It is proved that minimal solutions always

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

Treating network junctions in finite volume solution of transient gas flow models

Science.gov (United States)

Bermúdez, Alfredo; López, Xián; Vázquez-Cendón, M. Elena

2017-09-01

A finite volume scheme for the numerical solution of a non-isothermal non-adiabatic compressible flow model for gas transportation networks on non-flat topography is introduced. Unlike standard Euler equations, the model takes into account wall friction, variable height and heat transfer between the pipe and the environment which are source terms. The case of one single pipe was considered in a previous reference by the authors, [8], where a finite volume method with upwind discretization of the flux and source terms has been proposed in order to get a well-balanced scheme. The main goal of the present paper is to go a step further by considering a network of pipes. The main issue is the treatment of junctions for which container-like 2D finite volumes are introduced. The couplings between pipes (1D) and containers (2D) are carefully described and the conservation properties are analyzed. Numerical tests including real gas networks are solved showing the performance of the proposed methodology.

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

PrECast: An Efficient Crypto-Free Solution for Broadcast-Based Attacks in IPv4 Networks

Directory of Open Access Journals (Sweden)

Dalal Hanna

2018-05-01

Full Text Available Broadcasting is one of the essential features in the Internet Protocol Ver 4 (IPv4. Attackers often exploit this feature of the IP protocol to launch several attacks against a network or an individual host. Attackers may either be a part of a Local Area Network (LAN or outside a LAN to launch these attacks. There are numerous papers available in the literature to solve problems resulting from IP broadcasting. However, all these solutions target a specific problem that results from IP broadcasting. Furthermore, these solutions use either a computationally-intensive cryptographic scheme, the a priori relation between the host and the network or a modified protocol stack at every host. In this paper, we provide a seamless and transparent solution to eliminate IP broadcasting and thus eliminate all problems related to IP broadcasting. Our proposed solution is crypto-free and does not need any modification to the protocol stack.

Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays.

Science.gov (United States)

Li, Hongfei; Jiang, Haijun; Hu, Cheng

2016-03-01

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

The existence and global attractivity of almost periodic sequence solution of discrete-time neural networks

International Nuclear Information System (INIS)

Huang Zhenkun; Wang Xinghua; Gao Feng

2006-01-01

In this Letter, we discuss discrete-time analogue of a continuous-time cellular neural network. Sufficient conditions are obtained for the existence of a unique almost periodic sequence solution which is globally attractive. Our results demonstrate dynamics of the formulated discrete-time analogue as mathematical models for the continuous-time cellular neural network in almost periodic case. Finally, a computer simulation illustrates the suitability of our discrete-time analogue as numerical algorithms in simulating the continuous-time cellular neural network conveniently

Introduction to the numerical solutions of Markov chains

CERN Document Server

Stewart, Williams J

1994-01-01

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

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

2015-01-01

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Rotationally symmetric numerical solutions to the sine-Gordon equation

DEFF Research Database (Denmark)

Olsen, O. H.; Samuelsen, Mogens Rugholm

1981-01-01

We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...

On numerical solution of Burgers' equation by homotopy analysis method

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

Numerical experiments with neural networks

International Nuclear Information System (INIS)

Miranda, Enrique.

1990-01-01

Neural networks are highly idealized models which, in spite of their simplicity, reproduce some key features of the real brain. In this paper, they are introduced at a level adequate for an undergraduate computational physics course. Some relevant magnitudes are defined and evaluated numerically for the Hopfield model and a short term memory model. (Author)

Optimal resource allocation solutions for heterogeneous cognitive radio networks

Directory of Open Access Journals (Sweden)

Babatunde Awoyemi

2017-05-01

Full Text Available Cognitive radio networks (CRN are currently gaining immense recognition as the most-likely next-generation wireless communication paradigm, because of their enticing promise of mitigating the spectrum scarcity and/or underutilisation challenge. Indisputably, for this promise to ever materialise, CRN must of necessity devise appropriate mechanisms to judiciously allocate their rather scarce or limited resources (spectrum and others among their numerous users. ‘Resource allocation (RA in CRN', which essentially describes mechanisms that can effectively and optimally carry out such allocation, so as to achieve the utmost for the network, has therefore recently become an important research focus. However, in most research works on RA in CRN, a highly significant factor that describes a more realistic and practical consideration of CRN has been ignored (or only partially explored, i.e., the aspect of the heterogeneity of CRN. To address this important aspect, in this paper, RA models that incorporate the most essential concepts of heterogeneity, as applicable to CRN, are developed and the imports of such inclusion in the overall networking are investigated. Furthermore, to fully explore the relevance and implications of the various heterogeneous classifications to the RA formulations, weights are attached to the different classes and their effects on the network performance are studied. In solving the developed complex RA problems for heterogeneous CRN, a solution approach that examines and exploits the structure of the problem in achieving a less-complex reformulation, is extensively employed. This approach, as the results presented show, makes it possible to obtain optimal solutions to the rather difficult RA problems of heterogeneous CRN.

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

2015-01-01

Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

Automatic validation of numerical solutions

DEFF Research Database (Denmark)

Stauning, Ole

1997-01-01

This thesis is concerned with ``Automatic Validation of Numerical Solutions''. The basic theory of interval analysis and self-validating methods is introduced. The mean value enclosure is applied to discrete mappings for obtaining narrow enclosures of the iterates when applying these mappings...... differential equations, but in this thesis, we describe how to use the methods for enclosing iterates of discrete mappings, and then later use them for discretizing solutions of ordinary differential equations. The theory of automatic differentiation is introduced, and three methods for obtaining derivatives...... are described: The forward, the backward, and the Taylor expansion methods. The three methods have been implemented in the C++ program packages FADBAD/TADIFF. Some examples showing how to use the three metho ds are presented. A feature of FADBAD/TADIFF not present in other automatic differentiation packages...

SOME UNUSUAL SOLUTIONS FOR EUROPEAN NETWORKS

Directory of Open Access Journals (Sweden)

Vernescu V

2012-03-01

Full Text Available Authors present several non-conventional solutions unused in Europe which are, however, frequently adopted in some medium (M and low (L voltages (V networks from North-American and Australian countries, especially in low density areas of consumption in rural and urban distribution. The proposed solutions may assure diversified supply possibilities in our middle and South–Eastern regions, as regards modernizing and upgrading the distribution networks. The solutions try to propose to adapt our European practice to the North-American experience, aiming at developing more flexible, cheaper and safer supply of the consumers, both at MV and at LV networks. Several original solutions promoted in Romanian networks and their peculiarities are also described. The paper presents distribution schemes at medium voltage in connection with low voltage supply in different condition of neutral treatment at MV or LV. It also shows the measures to be adopted in order to diminish the investment expenses in low voltage at the supplied consumers. The technical condition of co-existence of OHEL at MV and LV on the same poles, without jeopardizing the LV equipment, is necessary. Among the solutions proposed, the authors also describe the unconventional one, consisting in the supply of isolated monophase consumer at MV by ground return and also the conditions necessary for sure and safe operation of this particularly connection. Finally, there are shown some conclusions about the necessity to assure imposed environmental conditions.

Spurious solutions in few-body equations. II. Numerical investigations

International Nuclear Information System (INIS)

Adhikari, S.K.

1979-01-01

A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations

Numerical solution of electrostatic problems of the accelerator project VICKSI

International Nuclear Information System (INIS)

Janetzki, U.

1975-03-01

In this work, the numerical solution to a few of the electrostatic problems is dealt with which have occured within the framework of the heavy ion accelerator project VICKSI. By means of these selected examples, the versatile applicability of the numerical method is to be demonstrated, and simultaneously assistance is given for the solution of similar problems. The numerical process for solving ion-optics problems consists generally of two steps. In the first step, the potential distribution for a given boundary value problem is iteratively calculated for the Laplace equation, and then the image characteristics of the electostatic lense are investigated using the Raytrace method. (orig./LH) [de

Efficient numerical solution to vacuum decay with many fields

Energy Technology Data Exchange (ETDEWEB)

Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin, E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: shlaer@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

2017-01-01

Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.

Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

International Nuclear Information System (INIS)

Pappas, George

2009-01-01

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R ISCO ), the rotation frequency and the epicyclic frequencies Ω ρ , Ω z . Finally we present some results of the comparison.

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

Energy Technology Data Exchange (ETDEWEB)

Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

2009-10-01

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.

Ocean wave prediction using numerical and neural network models

Digital Repository Service at National Institute of Oceanography (India)

Mandal, S.; Prabaharan, N.

This paper presents an overview of the development of the numerical wave prediction models and recently used neural networks for ocean wave hindcasting and forecasting. The numerical wave models express the physical concepts of the phenomena...

Numerical solution of distributed order fractional differential equations

Science.gov (United States)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Numerical solution of ordinary differential equations. For classical, relativistic and nano systems

International Nuclear Information System (INIS)

Greenspan, D.

2006-01-01

An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)

Numerical solutions of the Vlasov equation

International Nuclear Information System (INIS)

Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

1985-01-01

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

Reduced-Order Direct Numerical Simulation of Solute Transport in Porous Media

Science.gov (United States)

Mehmani, Yashar; Tchelepi, Hamdi

2017-11-01

Pore-scale models are an important tool for analyzing fluid dynamics in porous materials (e.g., rocks, soils, fuel cells). Current direct numerical simulation (DNS) techniques, while very accurate, are computationally prohibitive for sample sizes that are statistically representative of the porous structure. Reduced-order approaches such as pore-network models (PNM) aim to approximate the pore-space geometry and physics to remedy this problem. Predictions from current techniques, however, have not always been successful. This work focuses on single-phase transport of a passive solute under advection-dominated regimes and delineates the minimum set of approximations that consistently produce accurate PNM predictions. Novel network extraction (discretization) and particle simulation techniques are developed and compared to high-fidelity DNS simulations for a wide range of micromodel heterogeneities and a single sphere pack. Moreover, common modeling assumptions in the literature are analyzed and shown that they can lead to first-order errors under advection-dominated regimes. This work has implications for optimizing material design and operations in manufactured (electrodes) and natural (rocks) porous media pertaining to energy systems. This work was supported by the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B).

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Optical solutions for unbundled access network

Science.gov (United States)

Bacîş Vasile, Irina Bristena

2015-02-01

The unbundling technique requires finding solutions to guarantee the economic and technical performances imposed by the nature of the services that can be offered. One of the possible solutions is the optic one; choosing this solution is justified for the following reasons: it optimizes the use of the access network, which is the most expensive part of a network (about 50% of the total investment in telecommunications networks) while also being the least used (telephone traffic on the lines has a low cost); it increases the distance between the master station/central and the terminal of the subscriber; the development of the services offered to the subscribers is conditioned by the subscriber network. For broadband services there is a need for support for the introduction of high-speed transport. A proper identification of the factors that must be satisfied and a comprehensive financial evaluation of all resources involved, both the resources that are in the process of being bought as well as extensions are the main conditions that would lead to a correct choice. As there is no single optimal technology for all development scenarios, which can take into account all access systems, a successful implementation is always done by individual/particularized scenarios. The method used today for the selection of an optimal solution is based on statistics and analysis of the various, already implemented, solutions, and on the experience that was already gained; the main evaluation criterion and the most unbiased one is the ratio between the cost of the investment and the quality of service, while serving an as large as possible number of customers.

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

2008-04-14

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Numeral eddy current sensor modelling based on genetic neural network

International Nuclear Information System (INIS)

Yu Along

2008-01-01

This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced. In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network (GNN) according to measurement data. So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network. The nonlinear model has the advantages of strong robustness, on-line modelling and high precision. The maximum nonlinearity error can be reduced to 0.037% by using GNN. However, the maximum nonlinearity error is 0.075% using the least square method

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

Energy Technology Data Exchange (ETDEWEB)

Woods, Mark Christopher [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Holmes, Mark [Rensselaer Polytechnic Inst., Troy, NY (United States); Sailor, William C [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-07-01

A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

Multi-digit handwritten sindhi numerals recognition using som neural network

International Nuclear Information System (INIS)

Chandio, A.A.; Jalbani, A.H.; Awan, S.A.

2017-01-01

In this research paper a multi-digit Sindhi handwritten numerals recognition system using SOM Neural Network is presented. Handwritten digits recognition is one of the challenging tasks and a lot of research is being carried out since many years. A remarkable work has been done for recognition of isolated handwritten characters as well as digits in many languages like English, Arabic, Devanagari, Chinese, Urdu and Pashto. However, the literature reviewed does not show any remarkable work done for Sindhi numerals recognition. The recognition of Sindhi digits is a difficult task due to the various writing styles and different font sizes. Therefore, SOM (Self-Organizing Map), a NN (Neural Network) method is used which can recognize digits with various writing styles and different font sizes. Only one sample is required to train the network for each pair of multi-digit numerals. A database consisting of 4000 samples of multi-digits consisting only two digits from 10-50 and other matching numerals have been collected by 50 users and the experimental results of proposed method show that an accuracy of 86.89% is achieved. (author)

Solution of Milne problem by Laplace transformation with numerical inversion

International Nuclear Information System (INIS)

Campos Velho, H.F. de.

1987-12-01

The Milne problem for monoenergetic neutrons, by Laplace Transform of the neutron transport integral equation with numerical inversion of the transformed solution by gaussian quadrature, using the fatorization of the dispersion function. The resulted is solved compared its analitical solution. (author) [pt

Advanced approach to numerical forecasting using artificial neural networks

Directory of Open Access Journals (Sweden)

Michael Štencl

2009-01-01

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

New networking solutions support GEANT2

CERN Multimedia

2006-01-01

"Researchers across the globe are benefiting from new advanced networking solutions, deployed as part of the GEANT2. For the first time, scientists collaborating on the world's largest particle physics experiment, the Large Hadron Collider (LHC), now have access to point-to-point network connections between distributed research centres." (1 page)

Solutions to operate transmission and distribution gas networks

Directory of Open Access Journals (Sweden)

Neacsu Sorin

2017-01-01

Full Text Available In order to respect the actual and future regulations, besides SCADA, there is a need for further modern operating solutions for the transmission and distribution gas network. The paper presents the newest operating principles and modern software solutions that represent a considerable help to operate the transmission and distribution gas networks.

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Directory of Open Access Journals (Sweden)

Hai Zhang

2017-01-01

Full Text Available This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

Meurant, Gerard; Golub, Gene.

1982-02-01

This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

On mesh refinement and accuracy of numerical solutions

NARCIS (Netherlands)

Zhou, Hong; Peters, Maria; van Oosterom, Adriaan

1993-01-01

This paper investigates mesh refinement and its relation with the accuracy of the boundary element method (BEM) and the finite element method (FEM). TO this end an isotropic homogeneous spherical volume conductor, for which the analytical solution is available, wag used. The numerical results

The numerical solution of boundary value problems over an infinite domain

International Nuclear Information System (INIS)

Shepherd, M.; Skinner, R.

1976-01-01

A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail

Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2015-05-01

The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

Directory of Open Access Journals (Sweden)

Rahman Farnoosh

2014-07-01

Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.

A Framework to Implement IoT Network Performance Modelling Techniques for Network Solution Selection.

Science.gov (United States)

Delaney, Declan T; O'Hare, Gregory M P

2016-12-01

No single network solution for Internet of Things (IoT) networks can provide the required level of Quality of Service (QoS) for all applications in all environments. This leads to an increasing number of solutions created to fit particular scenarios. Given the increasing number and complexity of solutions available, it becomes difficult for an application developer to choose the solution which is best suited for an application. This article introduces a framework which autonomously chooses the best solution for the application given the current deployed environment. The framework utilises a performance model to predict the expected performance of a particular solution in a given environment. The framework can then choose an apt solution for the application from a set of available solutions. This article presents the framework with a set of models built using data collected from simulation. The modelling technique can determine with up to 85% accuracy the solution which performs the best for a particular performance metric given a set of solutions. The article highlights the fractured and disjointed practice currently in place for examining and comparing communication solutions and aims to open a discussion on harmonising testing procedures so that different solutions can be directly compared and offers a framework to achieve this within IoT networks.

A Framework to Implement IoT Network Performance Modelling Techniques for Network Solution Selection

Directory of Open Access Journals (Sweden)

Declan T. Delaney

2016-12-01

Full Text Available No single network solution for Internet of Things (IoT networks can provide the required level of Quality of Service (QoS for all applications in all environments. This leads to an increasing number of solutions created to fit particular scenarios. Given the increasing number and complexity of solutions available, it becomes difficult for an application developer to choose the solution which is best suited for an application. This article introduces a framework which autonomously chooses the best solution for the application given the current deployed environment. The framework utilises a performance model to predict the expected performance of a particular solution in a given environment. The framework can then choose an apt solution for the application from a set of available solutions. This article presents the framework with a set of models built using data collected from simulation. The modelling technique can determine with up to 85% accuracy the solution which performs the best for a particular performance metric given a set of solutions. The article highlights the fractured and disjointed practice currently in place for examining and comparing communication solutions and aims to open a discussion on harmonising testing procedures so that different solutions can be directly compared and offers a framework to achieve this within IoT networks.

Numerical solution of the resistive magnetohydrodynamic boundary-layer equations

International Nuclear Information System (INIS)

Glasser, A.H.; Jardin, S.C.; Tesauro, G.

1983-10-01

Three different techniques are presented for numerical solution of the equations governing the boundary layer of resistive magnetohydrodynamic tearing and interchange instabilities in toroidal geometry. Excellent agreement among these methods and with analytical results provides confidence in the correctness of the results. Solutions obtained in regimes where analytical medthods fail indicate a new scaling for the tearing mode as well as the existence of a new regime of stability

Numerical solution of the radionuclide transport equation

International Nuclear Information System (INIS)

Hadermann, J.; Roesel, F.

1983-11-01

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

Fast Deploy Radiation Monitoring Array Emergency Solution Based on GPS and Cellular Network

International Nuclear Information System (INIS)

Vax, E.; Broide, A.; Manor, A.; Marcus, E.; Seif, R.; Nir, J.; Kadmon, Y.; Sattinger, D.; Levinson, S.; Tal, N.

2004-01-01

Radiation monitoring of a possible contaminating source is highly important for safety and risk analysis. Since the monitoring must cover the whole contaminated area, the standard solution is to scatter an array of numerous fixed detectors in advance. The Fast Deploy Radiation Monitoring Array (FDRMA) is a solution that does not require coverage of the entire area. The FDRMA is a compact, world wide applicative, seamless and novel solution, designed for emergency cases. The system consists of GPS and IP cellular network, which make it mobile and therefore suitable for global use. The most significant advantage of the FDRMA system is minimizing the exposure time of the monitoring teams, while maintaining flexibility of the deployment area, as opposed to the Vehicle Monitoring System (VMS) [1] or the standard solution mentioned above. A detailed description of the proposed FDRMA system and its comparison to a fixed detectors' array is presented in this work

Numerical study of traveling-wave solutions for the Camassa-Holm equation

International Nuclear Information System (INIS)

Kalisch, Henrik; Lenells, Jonatan

2005-01-01

We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied

Numerical solutions of a three-point boundary value problem with an ...

African Journals Online (AJOL)

Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.

Numerical solution of the polymer system

Energy Technology Data Exchange (ETDEWEB)

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

1999-05-01

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

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

International Nuclear Information System (INIS)

Kalla, C; Klein, C

2012-01-01

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

Numerical Solution of Differential Algebraic Equations and Applications

DEFF Research Database (Denmark)

Thomsen, Per Grove

2005-01-01

These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...

Numerical solution of field theories using random walks

International Nuclear Information System (INIS)

Barnes, T.; Daniell, G.J.

1985-01-01

We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)

Numerical double layer solutions with ionization

International Nuclear Information System (INIS)

Andersson, D.; Soerensen, J.

1982-08-01

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

Network periodic solutions: patterns of phase-shift synchrony

International Nuclear Information System (INIS)

Golubitsky, Martin; Wang, Yunjiao; Romano, David

2012-01-01

We prove the rigid phase conjecture of Stewart and Parker. It then follows from previous results (of Stewart and Parker and our own) that rigid phase-shifts in periodic solutions on a transitive network are produced by a cyclic symmetry on a quotient network. More precisely, let X(t) = (x 1 (t), ..., x n (t)) be a hyperbolic T-periodic solution of an admissible system on an n-node network. Two nodes c and d are phase-related if there exists a phase-shift θ cd in [0, 1) such that x d (t) = x c (t + θ cd T). The conjecture states that if phase relations persist under all small admissible perturbations (that is, the phase relations are rigid), then for each pair of phase-related cells, their input signals are also phase-related to the same phase-shift. For a transitive network, rigid phase relations can also be described abstractly as a Z m permutation symmetry of a quotient network. We discuss how patterns of phase-shift synchrony lead to rigid synchrony, rigid phase synchrony, and rigid multirhythms, and we show that for each phase pattern there exists an admissible system with a periodic solution with that phase pattern. Finally, we generalize the results to nontransitive networks where we show that the symmetry that generates rigid phase-shifts occurs on an extension of a quotient network

Numerical solution of dynamic equilibrium models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

2013-01-01

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

Case studies in the numerical solution of oscillatory integrals

International Nuclear Information System (INIS)

Adam, G.

1992-06-01

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

Solutions manual to accompany An introduction to numerical methods and analysis

CERN Document Server

Epperson, James F

2014-01-01

A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp

Numerical simulation for gas-liquid two-phase flow in pipe networks

International Nuclear Information System (INIS)

Li Xiaoyan; Kuang Bo; Zhou Guoliang; Xu Jijun

1998-01-01

The complex pipe network characters can not directly presented in single phase flow, gas-liquid two phase flow pressure drop and void rate change model. Apply fluid network theory and computer numerical simulation technology to phase flow pipe networks carried out simulate and compute. Simulate result shows that flow resistance distribution is non-linear in two phase pipe network

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

Directory of Open Access Journals (Sweden)

Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

Numerical solution of conservation equations in the transient model for the system thermal - hydraulics in the Korsar computer code

International Nuclear Information System (INIS)

Yudov, Y.V.

2001-01-01

The functional part of the KORSAR computer code is based on the computational unit for the reactor system thermal-hydraulics and other thermal power systems with water cooling. The two-phase flow dynamics of the thermal-hydraulic network is modelled by KORSAR in one-dimensional two-fluid (non-equilibrium and nonhomogeneous) approximation with the same pressure of both phases. Each phase is characterized by parameters averaged over the channel sections, and described by the conservation equations for mass, energy and momentum. The KORSAR computer code relies upon a novel approach to mathematical modelling of two-phase dispersed-annular flows. This approach allows a two-fluid model to differentiate the effects of the liquid film and droplets in the gas core on the flow characteristics. A semi-implicit numerical scheme has been chosen for deriving discrete analogs the conservation equations in KORSAR. In the semi-implicit numerical scheme, solution of finite-difference equations is reduced to the problem of determining the pressure field at a new time level. For the one-channel case, the pressure field is found from the solution of a system of linear algebraic equations by using the tri-diagonal matrix method. In the branched network calculation, the matrix of coefficients in the equations describing the pressure field is no longer tri-diagonal but has a sparseness structure. In this case, the system of linear equations for the pressure field can be solved with any of the known classical methods. Such an approach is implemented in the existing best-estimate thermal-hydraulic computer codes (TRAC, RELAP5, etc.) For the KORSAR computer code, we have developed a new non-iterative method for calculating the pressure field in the network of any topology. This method is based on the tri-diagonal matrix method and performs well when solving the thermal-hydraulic network problems. (author)

Numerical solution of a reaction-diffusion equation

International Nuclear Information System (INIS)

Moyano, Edgardo A.; Scarpettini, Alberto F.

2000-01-01

The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2014-03-01

The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil

Directory of Open Access Journals (Sweden)

Kozel K

2013-04-01

Full Text Available The article presents results of a numerical solution of subsonic and transonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the NACA 0012 airfoil. Authors used Runge-Kutta method to numerically solve the flows around the NACA 0012 airfoil.

Numerical solutions of diffusive logistic equation

International Nuclear Information System (INIS)

Afrouzi, G.A.; Khademloo, S.

2007-01-01

In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

Joint physical and numerical modeling of water distribution networks.

Energy Technology Data Exchange (ETDEWEB)

Zimmerman, Adam; O' Hern, Timothy John; Orear, Leslie Jr.; Kajder, Karen C.; Webb, Stephen Walter; Cappelle, Malynda A.; Khalsa, Siri Sahib; Wright, Jerome L.; Sun, Amy Cha-Tien; Chwirka, J. Benjamin; Hartenberger, Joel David; McKenna, Sean Andrew; van Bloemen Waanders, Bart Gustaaf; McGrath, Lucas K.; Ho, Clifford Kuofei

2009-01-01

This report summarizes the experimental and modeling effort undertaken to understand solute mixing in a water distribution network conducted during the last year of a 3-year project. The experimental effort involves measurement of extent of mixing within different configurations of pipe networks, measurement of dynamic mixing in a single mixing tank, and measurement of dynamic solute mixing in a combined network-tank configuration. High resolution analysis of turbulence mixing is carried out via high speed photography as well as 3D finite-volume based Large Eddy Simulation turbulence models. Macroscopic mixing rules based on flow momentum balance are also explored, and in some cases, implemented in EPANET. A new version EPANET code was developed to yield better mixing predictions. The impact of a storage tank on pipe mixing in a combined pipe-tank network during diurnal fill-and-drain cycles is assessed. Preliminary comparison between dynamic pilot data and EPANET-BAM is also reported.

Evaluate the accuracy of the numerical solution of hydrogeological problems of mass transfer

Directory of Open Access Journals (Sweden)

Yevhrashkina G.P.

2014-12-01

Full Text Available In the hydrogeological task on quantifying pollution of aquifers the error are starting add up with moment organization of regime observation network as a source of information on the pollution of groundwater in order to evaluate migration options for future prognosis calculations. Optimum element regime observation network should consist of three drill holes on the groundwater flow at equal distances from one another and transversely to the flow of the three drill holes, and at equal distances. If the target of observation drill holes coincides with the stream line on which will then be decided by direct migration task, the error will be minimal. The theoretical basis and results of numerical experiments to assess the accuracy of direct predictive tasks planned migration of groundwater in the area of full water saturation. For the vadose zone, we consider problems of vertical salt transport moisture. All studies were performed by comparing the results of fundamental and approximate solutions in a wide range of characteristics of the processes, which are discussed in relation to ecological and hydrogeological conditions of mining regions on the example of the Western Donbass.

Stand-alone solutions, computer networks and extern communications

International Nuclear Information System (INIS)

Tarschisch, H.

1988-01-01

The advantages of local networks over stand-alone solutions are presented. Of the local networks (LAN), two are presently at the center of attention: the bus and the ring. ETHERNET and the IBM-Token-Ring are described as typical examples. Access to public networks, especially TELEPAC and ISDN, is discussed. 12 figs

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Directory of Open Access Journals (Sweden)

Kryštůfek P.

2014-03-01

Full Text Available The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

KAUST Repository

Pathmanathan, Pras

2010-06-01

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

KAUST Repository

Pathmanathan, Pras; Bernabeu, Miguel O.; Bordas, Rafel; Cooper, Jonathan; Garny, Alan; Pitt-Francis, Joe M.; Whiteley, Jonathan P.; Gavaghan, David J.

2010-01-01

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

LED-based Photometric Stereo: Modeling, Calibration and Numerical Solutions

DEFF Research Database (Denmark)

Quéau, Yvain; Durix, Bastien; Wu, Tao

2018-01-01

We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in pr...

Solution Algorithm for a New Bi-Level Discrete Network Design Problem

Directory of Open Access Journals (Sweden)

Qun Chen

2013-12-01

Full Text Available A new discrete network design problem (DNDP was pro-posed in this paper, where the variables can be a series of integers rather than just 0-1. The new DNDP can determine both capacity improvement grades of reconstruction roads and locations and capacity grades of newly added roads, and thus complies with the practical projects where road capacity can only be some discrete levels corresponding to the number of lanes of roads. This paper designed a solution algorithm combining branch-and-bound with Hooke-Jeeves algorithm, where feasible integer solutions are recorded in searching the process of Hooke-Jeeves algorithm, lend -ing itself to determine the upper bound of the upper-level problem. The thresholds for branch cutting and ending were set for earlier convergence. Numerical examples are given to demonstrate the efficiency of the proposed algorithm.

The simulation of solute transport: An approach free of numerical dispersion

International Nuclear Information System (INIS)

Carrera, J.; Melloni, G.

1987-01-01

The applicability of most algorithms for simulation of solute transport is limited either by instability or by numerical dispersion, as seen by a review of existing methods. A new approach is proposed that is free of these two problems. The method is based on the mixed Eulerian-Lagrangian formulation of the mass-transport problem, thus ensuring stability. Advection is simulated by a variation of reverse-particle tracking that avoids the accumulation of interpolation errors, thus preventing numerical dispersion. The algorithm has been implemented in a one-dimensional code. Excellent results are obtained, in comparison with an analytical solution. 36 refs., 14 figs., 1 tab

Performance analysis of numeric solutions applied to biokinetics of radionuclides

International Nuclear Information System (INIS)

Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva

2013-01-01

Biokinetics models for radionuclides applied to dosimetry problems are constantly reviewed by ICRP. The radionuclide trajectory could be represented by compartmental models, assuming constant transfer rates between compartments. A better understanding of physiological or biochemical phenomena, improve the comprehension of radionuclide behavior in the human body and, in general, more complex compartmental models are proposed, increasing the difficulty of obtaining the analytical solution for the system of first order differential equations. Even with constant transfer rates numerical solutions must be carefully implemented because of almost singular characteristic of the matrix of coefficients. In this work we compare numerical methods with different strategies for ICRP-78 models for Thorium-228 and Uranium-234. The impact of uncertainty in the parameters of the equations is also estimated for local and global truncation errors. (author)

Numerical solution of a model for a superconductor field problem

International Nuclear Information System (INIS)

Alsop, L.E.; Goodman, A.S.; Gustavson, F.G.; Miranker, W.L.

1979-01-01

A model of a magnetic field problem occurring in connection with Josephson junction devices is derived, and numerical solutions are obtained. The model is of mathematical interest, because the magnetic vector potential satisfies inhomogeneous Helmholtz equations in part of the region, i.e., the superconductors, and the Laplace equation elsewhere. Moreover, the inhomogeneities are the guage constants for the potential, which are different for each superconductor, and their magnitudes are proportional to the currents flowing in the superconductors. These constants are directly related to the self and mutual inductances of the superconducting elements in the device. The numerical solution is obtained by the iterative use of a fast Poisson solver. Chebyshev acceleration is used to reduce the number of iterations required to obtain a solution. A typical problem involves solving 100,000 simultaneous equations, which the algorithm used with this model does in 20 iterations, requiring three minutes of CPU time on an IBM VM/370/168. Excellent agreement is obtained between calculated and observed values for the inductances

On the numerical solution of fault trees

International Nuclear Information System (INIS)

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

2003-01-01

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

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

Science.gov (United States)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Numerical solutions of ordinary and partial differential equations in the frequency domain

International Nuclear Information System (INIS)

Hazi, G.; Por, G.

1997-01-01

Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

The Numerical Solution of an Abelian Ordinary Differential Equation ...

African Journals Online (AJOL)

In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...

Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery

International Nuclear Information System (INIS)

Ramirez-Marquez, Jose Emmanuel; Rocco S, Claudio M.

2009-01-01

This paper introduces an evolutionary optimization approach that can be readily applied to solve stochastic network interdiction problems (SNIP). The network interdiction problem solved considers the minimization of the cost associated with an interdiction strategy such that the maximum flow that can be transmitted between a source node and a sink node for a fixed network design is greater than or equal to a given reliability requirement. Furthermore, the model assumes that the nominal capacity of each network link and the cost associated with their interdiction can change from link to link and that such interdiction has a probability of being successful. This version of the SNIP is for the first time modeled as a capacitated network reliability problem allowing for the implementation of computation and solution techniques previously unavailable. The solution process is based on an evolutionary algorithm that implements: (1) Monte-Carlo simulation, to generate potential network interdiction strategies, (2) capacitated network reliability techniques to analyze strategies' source-sink flow reliability and, (3) an evolutionary optimization technique to define, in probabilistic terms, how likely a link is to appear in the final interdiction strategy. Examples for different sizes of networks are used throughout the paper to illustrate the approach

Secure Wireless Sensor Networks: Problems and Solutions

Directory of Open Access Journals (Sweden)

Fei Hu

2003-08-01

Full Text Available As sensor networks edge closer towards wide-spread deployment, security issues become a central concern. So far, the main research focus has been on making sensor networks feasible and useful, and less emphasis was placed on security. This paper analyzes security challenges in wireless sensor networks and summarizes key issues that should be solved for achieving the ad hoc security. It gives an overview of the current state of solutions on such key issues as secure routing, prevention of denial-of-service and key management service. We also present some secure methods to achieve security in wireless sensor networks. Finally we present our integrated approach to securing sensor networks.

Sensitivity of the solution of the Elder problem to density, velocity and numerical perturbations

Science.gov (United States)

Park, Chan-Hee; Aral, Mustafa M.

2007-06-01

In this paper the Elder problem is studied with the purpose of evaluating the inherent instabilities associated with the numerical solution of this problem. Our focus is first on the question of the existence of a unique numerical solution for this problem, and second on the grid density and fluid density requirements necessary for a unique numerical solution. In particular we have investigated the instability issues associated with the numerical solution of the Elder problem from the following perspectives: (i) physical instability issues associated with density differences; (ii) sensitivity of the numerical solution to idealization irregularities; and, (iii) the importance of a precise velocity field calculation and the association of this process with the grid density levels that is necessary to solve the Elder problem accurately. In the study discussed here we have used a finite element Galerkin model we have developed for solving density-dependent flow and transport problems, which will be identified as TechFlow. In our study, the numerical results of Frolkovič and de Schepper [Frolkovič, P. and H. de Schepper, 2001. Numerical modeling of convection dominated transport coupled with density-driven flow in porous media, Adv. Water Resour., 24, 63-72.] were replicated using the grid density employed in their work. We were also successful in duplicating the same result with a less dense grid but with more computational effort based on a global velocity estimation process we have adopted. Our results indicate that the global velocity estimation approach recommended by Yeh [Yeh, G.-T., 1981. On the computation of Darcian velocity and mass balance in finite element modelling of groundwater flow, Water Resour. Res., 17(5), 1529-1534.] allows the use of less dense grids while obtaining the same accuracy that can be achieved with denser grids. We have also observed that the regularity of the elements in the discretization of the solution domain does make a difference

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

Energy Technology Data Exchange (ETDEWEB)

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

1994-04-01

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

A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. (paper)

Dynamics of the east India coastal current. 2. Numerical solutions

Digital Repository Service at National Institute of Oceanography (India)

McCreary, J.P.; Han, W.; Shankar, D.; Shetye, S.R.

A linear, continuously stratified model is used to investigate the dynamics of the East India Coastal Current (EICC). Solutions are found numerically in a basin that resembles the Indian Ocean basin north of 29 degrees S, and they are forced...

CSR Fields: Direct Numerical Solution of the Maxwell's Equation

International Nuclear Information System (INIS)

Novokhatski, Alexander

2011-01-01

We discuss the properties of the coherent electromagnetic fields of a very short, ultra-relativistic bunch in a rectangular vacuum chamber inside a bending magnet. The analysis is based on the results of a direct numerical solution of Maxwell's equations together with Newton's equations. We use a new dispersion-free time-domain algorithm which employs a more efficient use of finite element mesh techniques and hence produces self-consistent and stable solutions for very short bunches. We investigate the fine structure of the CSR fields including coherent edge radiation. This approach should be useful in the study of existing and future concepts of particle accelerators and ultrafast coherent light sources. The coherent synchrotron radiation (CSR) fields have a strong action on the beam dynamics of very short bunches, which are moving in the bends of all kinds of magnetic elements. They are responsible for additional energy loss and energy spread; micro bunching and beam emittance growth. These fields may bound the efficiency of damping rings, electron-positron colliders and ultrafast coherent light sources, where high peak currents and very short bunches are envisioned. This is relevant to most high-brightness beam applications. On the other hand these fields together with transition radiation fields can be used for beam diagnostics or even as a powerful resource of THz radiation. A history of the study of CSR and a good collection of references can be found in (1). Electromagnetic theory suggests several methods on how to calculate CSR fields. The most popular method is to use Lienard-Wiechert potentials. Other approach is to solve numerically the approximate equations, which are a Schrodinger type equation. These numerical methods are described in (2). We suggest that a direct solution of Maxwell's equations together with Newton's equations can describe the detailed structure of the CSR fields (3).

WaterNet: The NASA Water Cycle Solutions Network

Science.gov (United States)

Houser, P. R.; Belvedere, D. R.; Pozzi, W. H.; Imam, B.; Schiffer, R.; Lawford, R.; Schlosser, C. A.; Gupta, H.; Welty, C.; Vorosmarty, C.; Matthews, D.

2007-12-01

Water is essential to life and directly impacts and constrains society's welfare, progress, and sustainable growth, and is continuously being transformed by climate change, erosion, pollution, and engineering practices. The water cycle is a critical resource for industry, agriculture, natural ecosystems, fisheries, aquaculture, hydroelectric power, recreation, and water supply, and is central to drought, flood, transportation-aviation, and disease hazards. It is therefore a national priority to use advancements in scientific observations and knowledge to develop solutions to the water challenges faced by society. NASA's unique role is to use its view from space to improve water and energy cycle monitoring and prediction. NASA has collected substantial water cycle information and knowledge that must be transitioned to develop solutions for all twelve National Priority Application (NPA) areas. NASA cannot achieve this goal alone -it must establish collaborations and interoperability with existing networks and nodes of research organizations, operational agencies, science communities, and private industry. Therefore, WaterNet: The NASA Water Cycle Solutions Network goal is to improve and optimize the sustained ability of water cycle researchers, stakeholders, organizations and networks to interact, identify, harness, and extend NASA research results to augment decision support tools and meet national needs. WaterNet is a catalyst for discovery and sharing of creative solutions to water problems. It serves as a creative, discovery process that is the entry-path for a research-to-solutions systems engineering NASA framework, with the end result to ultimately improve decision support.

Buoyancy-driven chaotic regimes during solute dispersion in pore networks

International Nuclear Information System (INIS)

Tsakiroglou, C.D.; Theodoropoulou, M.A.; Karoutsos, V.

2005-01-01

In an attempt to investigate gravity effects on solute dispersion at the scale of a pore network, single source-solute transport visualization experiments are performed on glass-etched pore networks of varying morphology and degree of pore-scale heterogeneities. The (lighter) low solute concentration aqueous solution flows steadily through the porous medium and the (heavier) high solute concentration solution is injected at a very low and constant flow rate through an inner port. The transient evolution of the solute concentration distribution over various regions of the pore network is determined at different scales by capturing and video-recording snapshots of the dispersion on PC, measuring automatically the spatial variation of the color intensity of the solution, and transforming the color intensities to solute concentrations. Without the action of gravity, the steady-state dispersion regime changes with Peclet (Pe) number, and the longitudinal and transverse dispersivities are estimated by fitting the experimental datasets to approximate analytic solutions of the advection-dispersion equation. Under the action of gravity, multiple of steady-state solute dispersion regimes is developed at each Pe value, and lobe-shaped instabilities of the solute concentration are observed across the pore network, as the downward flow of the denser (higher solute concentration) fluid is counterbalanced by the upward flow of the less dense (lower solute concentration) fluid. The steady-state dispersion regimes may be periodic, quasi-periodic or chaotic depending on the system parameters. The nature of the transient fluctuations of the average solute concentration is analyzed by identifying the periodicity of the fluctuations, determining the autocorrelation function and the statistical moments of the time series, and inspecting the FFT (fast Fourier transform) power spectra. It is found that the mixing zone tends to be stabilized at higher values of the Peclet (Pe) number

Numerical solution of High-kappa model of superconductivity

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

Comparing numerical methods for the solutions of the Chen system

International Nuclear Information System (INIS)

Noorani, M.S.M.; Hashim, I.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.

2007-01-01

In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

Directory of Open Access Journals (Sweden)

Bolandtalat A.

2016-01-01

Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks

Science.gov (United States)

Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.

2013-12-01

Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus

A numerical solution of the coupled proton-H atom transport equations for the proton aurora

International Nuclear Information System (INIS)

Basu, B.; Jasperse, J.R.; Grossbard, N.J.

1990-01-01

A numerical code has been developed to solve the coupled proton-H atom linear transport equations for the proton aurora. The transport equations have been simplified by using plane-parallel geometry and the forward-scattering approximations only. Otherwise, the equations and their numerical solutions are exact. Results are presented for the particle fluxes and the energy deposition rates, and they are compared with the previous analytical results that were obtained by using additional simplifying approximations. It is found that although the analytical solutions for the particle fluxes differ somewhat from the numerical solutions, the energy deposition rates calculated by the two methods agree to within a few percent. The accurate particle fluxes given by the numerical code are useful for accurate calculation of the characteristic quantities of the proton aurora, such as the ionization rates and the emission rates

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Science.gov (United States)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Analysis of numerical solutions for Bateman equations; Analise de solucoes numericas para as equacoes de Bateman

Energy Technology Data Exchange (ETDEWEB)

Loch, Guilherme G.; Bevilacqua, Joyce S., E-mail: guiloch@ime.usp.br, E-mail: joyce@ime.usp.br [Universidade de Sao Paulo (IME/USP), Sao Paulo, SP (Brazil). Departamento de Matematica Aplicada. Instituto de Matematica e Estatistica; Hiromoto, Goro; Rodrigues Junior, Orlando, E-mail: rodrijr@ipen.br, E-mail: hiromoto@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN-CNEN/SP), Sao Paulo, SP (Brazil)

2013-07-01

The implementation of stable and efficient numerical methods for solving problems involving nuclear transmutation and radioactive decay chains is the main scope of this work. The physical processes associated with irradiations of samples in particle accelerators, or the burning spent nuclear fuel in reactors, or simply the natural decay chains, can be represented by a set of first order ordinary differential equations with constant coefficients, for instance, the decay radioactive constants of each nuclide in the chain. Bateman proposed an analytical solution for a particular case of a linear chain with n nuclides decaying in series and with different decay constants. For more complex and realistic applications, the construction of analytical solutions is not viable and the introduction of numerical techniques is imperative. However, depending on the magnitudes of the decay radioactive constants, the matrix of coefficients could be almost singular, generating unstable and non convergent numerical solutions. In this work, different numerical strategies for solving systems of differential equations were implemented, the Runge-Kutta 4-4, Adams Predictor-Corrector (PC2) and the Rosenbrock algorithm, this last one more specific for stiff equations. Consistency, convergence and stability of the numerical solutions are studied and the performance of the methods is analyzed for the case of the natural decay chain of Uranium-235 comparing numerical with analytical solutions. (author)

Numerical solution of the full potential equation using a chimera grid approach

Science.gov (United States)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Numerical solution of the ekpyrotic scenario in the moduli space approximation

International Nuclear Information System (INIS)

Soerensen, Torquil MacDonald

2005-01-01

A numerical solution to the equations of motion for the ekpyrotic bulk brane scenario in the moduli space approximation is presented. The visible universe brane has positive tension, and we use a potential that goes to zero exponentially at large distance, and also goes to zero at small distance. In the case considered, no bulk brane, visible brane collision occurs in the solution. This property and the general behavior of the solution is qualitatively the same when the visible brane tension is negative, and for many different parameter choices

A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

International Nuclear Information System (INIS)

Adam, G.

1979-01-01

A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

A coupled 3D-1D numerical monodomain solver for cardiac electrical activation in the myocardium with detailed Purkinje network

Science.gov (United States)

Vergara, Christian; Lange, Matthias; Palamara, Simone; Lassila, Toni; Frangi, Alejandro F.; Quarteroni, Alfio

2016-03-01

We present a model for the electrophysiology in the heart to handle the electrical propagation through the Purkinje system and in the myocardium, with two-way coupling at the Purkinje-muscle junctions. In both the subproblems the monodomain model is considered, whereas at the junctions a resistor element is included that induces an orthodromic propagation delay from the Purkinje network towards the heart muscle. We prove a sufficient condition for convergence of a fixed-point iterative algorithm to the numerical solution of the coupled problem. Numerical comparison of activation patterns is made with two different combinations of models for the coupled Purkinje network/myocardium system, the eikonal/eikonal and the monodomain/monodomain models. Test cases are investigated for both physiological and pathological activation of a model left ventricle. Finally, we prove the reliability of the monodomain/monodomain coupling on a realistic scenario. Our results underlie the importance of using physiologically realistic Purkinje-trees with propagation solved using the monodomain model for simulating cardiac activation.

special algorithm for the numerical solution of system of initial value ...

African Journals Online (AJOL)

Nwokem et al.

Science World Journal Vol 12(No 4) 2017 ... Over the years, several researchers have considered the collocation method as a way of generating numerical solutions to ... study problems in mathematics, engineering, computer science and.

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

Full Text Available An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

Numerical solution of modified differential equations based on symmetry preservation.

Science.gov (United States)

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

Polyanin, A. D.; Sorokin, V. G.

2017-12-01

The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions

Directory of Open Access Journals (Sweden)

Marina Popolizio

2018-01-01

Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.

ATHENA [Advanced Thermal Hydraulic Energy Network Analyzer] solutions to developmental assessment problems

International Nuclear Information System (INIS)

Carlson, K.E.; Ransom, V.H.; Roth, P.A.

1987-03-01

The ATHENA (Advanced Thermal Hydraulic Energy Network Analyzer) code has been developed to perform transient simulation of the thermal hydraulic systems that may be found in fusion reactors, space reactors, and other advanced systems. As an assessment of current capability the code was applied to a number of physical problems, both conceptual and actual experiments. Results indicate that the numerical solution to the basic conservation equations is technically sound, and that generally good agreement can be obtained when modeling relevant hydrodynamic experiments. The assessment also demonstrates basic fusion system modeling capability and verifies compatibility of the code with both CDC and CRAY mainframes. Areas where improvements could be made include constitutive modeling, which describes the interfacial exchange term. 13 refs., 84 figs

Adaptive cyclically dominating game on co-evolving networks: numerical and analytic results

Science.gov (United States)

Choi, Chi Wun; Xu, Chen; Hui, Pak Ming

2017-10-01

A co-evolving and adaptive Rock (R)-Paper (P)-Scissors (S) game (ARPS) in which an agent uses one of three cyclically dominating strategies is proposed and studied numerically and analytically. An agent takes adaptive actions to achieve a neighborhood to his advantage by rewiring a dissatisfying link with a probability p or switching strategy with a probability 1 - p. Numerical results revealed two phases in the steady state. An active phase for p pc has three separate clusters of agents using only R, P, and S, respectively with terminated adaptive actions. A mean-field theory based on the link densities in co-evolving network is formulated and the trinomial closure scheme is applied to obtain analytical solutions. The analytic results agree with simulation results on ARPS well. In addition, the different probabilities of winning, losing, and drawing a game among the agents are identified as the origin of the small discrepancy between analytic and simulation results. As a result of the adaptive actions, agents of higher degrees are often those being taken advantage of. Agents with a smaller (larger) degree than the mean degree have a higher (smaller) probability of winning than losing. The results are informative for future attempts on formulating more accurate theories.

Stochastic solution of population balance equations for reactor networks

International Nuclear Information System (INIS)

Menz, William J.; Akroyd, Jethro; Kraft, Markus

2014-01-01

This work presents a sequential modular approach to solve a generic network of reactors with a population balance model using a stochastic numerical method. Full-coupling to the gas-phase is achieved through operator-splitting. The convergence of the stochastic particle algorithm in test networks is evaluated as a function of network size, recycle fraction and numerical parameters. These test cases are used to identify methods through which systematic and statistical error may be reduced, including by use of stochastic weighted algorithms. The optimal algorithm was subsequently used to solve a one-dimensional example of silicon nanoparticle synthesis using a multivariate particle model. This example demonstrated the power of stochastic methods in resolving particle structure by investigating the transient and spatial evolution of primary polydispersity, degree of sintering and TEM-style images. Highlights: •An algorithm is presented to solve reactor networks with a population balance model. •A stochastic method is used to solve the population balance equations. •The convergence and efficiency of the reported algorithms are evaluated. •The algorithm is applied to simulate silicon nanoparticle synthesis in a 1D reactor. •Particle structure is reported as a function of reactor length and time

Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

Directory of Open Access Journals (Sweden)

F. Hosseini Shekarabi

2016-03-01

Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.

Numerical solution for heave of expansive soils

International Nuclear Information System (INIS)

Sadrnezhad, S. A.

1999-01-01

A numerical solution for heave prediction is developed within the context theories for both saturated and unsaturated soil behaviors. Basically, lowering the potential level of compressing on a saturated layer will cause heaving due to water absorption. This water absorption is in an opposite way, similar to water dissipation as what happens during unloading in consolidation process. However, in unsaturated layers any change of the stability of potential energy level will cause the tendency of change in particle interconnection forces. So, any change by either distressing or the variation of moisture ratio will lead to soil heave. In this paper a finite element solution is employed for predicting the heave in saturated soil similar to unloading in consolidation. Also, in the case of unsaturated soil, equivalent soil suction as negative pore water pressures in applied to soil elements as equivalent nodal forces. To show the potential of this method, test results were com pated with those obtained from computations. These comparisons show that the presented method is capable of predicting the heave phenomenon quite well

Backend solutions for AA in the MUSE network supporting FMC

NARCIS (Netherlands)

Neerbos, A.N.R. van; Prins, M.; Melander, B.; Pimilla Larrucea, I.; Thakur, M.J.; Fredricx, F.

2007-01-01

The European MUSE project investigated fixed-mobile convergence from the perspective of an unbundled fixed network. A major part of the work consisted of finding solutions for the authentication and authorisation of users who roam from their home network to a visited network. This paper shows how AA

Power-Aware Routing and Network Design with Bundled Links: Solutions and Analysis

Directory of Open Access Journals (Sweden)

Rosario G. Garroppo

2013-01-01

Full Text Available The paper deeply analyzes a novel network-wide power management problem, called Power-Aware Routing and Network Design with Bundled Links (PARND-BL, which is able to take into account both the relationship between the power consumption and the traffic throughput of the nodes and to power off both the chassis and even the single Physical Interface Card (PIC composing each link. The solutions of the PARND-BL model have been analyzed by taking into account different aspects associated with the actual applicability in real network scenarios: (i the time for obtaining the solution, (ii the deployed network topology and the resulting topology provided by the solution, (iii the power behavior of the network elements, (iv the traffic load, (v the QoS requirement, and (vi the number of paths to route each traffic demand. Among the most interesting and novel results, our analysis shows that the strategy of minimizing the number of powered-on network elements through the traffic consolidation does not always produce power savings, and the solution of this kind of problems, in some cases, can lead to spliting a single traffic demand into a high number of paths.

The numerical solution of ICRF fields in axisymmetric mirrors

International Nuclear Information System (INIS)

Phillips, M.W.; Todd, A.M.M.

1986-01-01

The numerics of a numerical code called GARFIELD (Grumman Aerospace RF fIELD code) designed to calculate the three-dimensional structure of ICRF fields in axisymmetric mirrors is presented. The code solves the electromagnetic wave equation for the electric field using a cold plasma dispersion relation with a small collision term to simulate absorption. The full wave solution including E.B is computed. The fields are Fourier analyzed in the poloidal direction and solved on a grid in the axial and radial directions. A two-dimensional equilibrium can be used as the source of equilibrium data. This allows us to extend previous studies of ICRF wave propagation and absorption in mirrors to include the effect of axial variation of the magnetic field and density. (orig.)

Almost Periodic Solution for Memristive Neural Networks with Time-Varying Delays

Directory of Open Access Journals (Sweden)

Huaiqin Wu

2013-01-01

Full Text Available This paper is concerned with the dynamical stability analysis for almost periodic solution of memristive neural networks with time-varying delays. Under the framework of Filippov solutions, by applying the inequality analysis techniques, the existence and asymptotically almost periodic behavior of solutions are discussed. Based on the differential inclusions theory and Lyapunov functional approach, the stability issues of almost periodic solution are investigated, and a sufficient condition for the existence, uniqueness, and global exponential stability of the almost periodic solution is established. Moreover, as a special case, the condition which ensures the global exponential stability of a unique periodic solution is also presented for the considered memristive neural networks. Two examples are given to illustrate the validity of the theoretical results.

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

Science.gov (United States)

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

Storage Solutions for Power Quality Problems in Cyprus Electricity Distribution Network

Directory of Open Access Journals (Sweden)

Andreas Poullikkas

2014-01-01

Full Text Available In this work, a prediction of the effects of introducing energy storage systems on the network stability of the distribution network of Cyprus and a comparison in terms of cost with a traditional solution is carried out. In particular, for solving possible overvoltage problems, several scenarios of storage units' installation are used and compared with the alternative solution of extra cable connection between the node with the lowest voltage and the node with the highest voltage of the distribution network. For the comparison, a case study of a typical LV distribution feeder in the power system of Cyprus is used. The results indicated that the performance indicator of each solution depends on the type, the size and the position of installation of the storage unit. Also, as more storage units are installed the better the performance indicator and the more attractive is the investment in storage units to solve power quality problems in the distribution network. In the case where the technical requirements in voltage limitations according to distribution regulations are satisfied with one storage unit, the installation of an additional storage unit will only increase the final cost. The best solution, however, still remains the alternative solution of extra cable connection between the node with the lowest voltage and the node with the highest voltage of the distribution network, due to the lower investment costs compared to that of the storage units.

Numerical solution of modified fokker-planck equation with poissonian input

Czech Academy of Sciences Publication Activity Database

Náprstek, Jiří; Král, Radomil

2010-01-01

Roč. 17, 3/4 (2010), s. 251-268 ISSN 1802-1484 R&D Projects: GA AV ČR(CZ) IAA200710805; GA ČR(CZ) GA103/09/0094 Institutional research plan: CEZ:AV0Z20710524 Keywords : Fokker-Planck equation * poisson ian exciation * numerical solution * transition effects Subject RIV: JN - Civil Engineering

Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions

OpenAIRE

Karkar , Sami; Vergez , Christophe; Cochelin , Bruno

2012-01-01

International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a set of equations is modified when one (or several) parameter of these equations are allowed to vary. Several physical models (clarinet, saxophone, and violin) are formulated as nonlinear dynamical systems, whose periodic solution...

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

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Elmira Ashpazzadeh

2018-04-01

Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Numerical benchmarking of SPEEDUP trademark against point kinetics solutions

International Nuclear Information System (INIS)

Gregory, M.V.

1993-02-01

SPEEDUP trademark is a state-of-the-art, dynamic, chemical process modeling package offered by Aspen Technology. In anticipation of new customers' needs for new analytical tools to support the site's waste management activities, SRTC has secured a multiple-user license to SPEEDUP trademark. In order to verify both the installation and mathematical correctness of the algorithms in SPEEDUP trademark, we have performed several numerical benchmarking calculations. These calculations are the first steps in establishing an on-site quality assurance pedigree for SPEEDUP trademark. The benchmark calculations consisted of SPEEDUP trademark Version 5.3L representations of five neutron kinetics benchmarks (each a mathematically stiff system of seven coupled ordinary differential equations), whose exact solutions are documented in the open literature. In all cases, SPEEDUP trademark solutions to be in excellent agreement with the reference solutions. A minor peculiarity in dealing with a non-existent discontinuity in the OPERATION section of the model made itself evident

Analytical Solutions for Rumor Spreading Dynamical Model in a Social Network

Science.gov (United States)

Fallahpour, R.; Chakouvari, S.; Askari, H.

2015-03-01

In this paper, Laplace Adomian decomposition method is utilized for evaluating of spreading model of rumor. Firstly, a succinct review is constructed on the subject of using analytical methods such as Adomian decomposion method, Variational iteration method and Homotopy Analysis method for epidemic models and biomathematics. In continue a spreading model of rumor with consideration of forgetting mechanism is assumed and subsequently LADM is exerted for solving of it. By means of the aforementioned method, a general solution is achieved for this problem which can be readily employed for assessing of rumor model without exerting any computer program. In addition, obtained consequences for this problem are discussed for different cases and parameters. Furthermore, it is shown the method is so straightforward and fruitful for analyzing equations which have complicated terms same as rumor model. By employing numerical methods, it is revealed LADM is so powerful and accurate for eliciting solutions of this model. Eventually, it is concluded that this method is so appropriate for this problem and it can provide researchers a very powerful vehicle for scrutinizing rumor models in diverse kinds of social networks such as Facebook, YouTube, Flickr, LinkedIn and Tuitor.

A note on numerical solution of a parabolic-Schrödinger equation

Science.gov (United States)

Ozdemir, Yildirim; Alp, Mustafa

2016-08-01

In the present study, a nonlocal boundary value problem for a parabolic-Schrödinger equation is considered. The stability estimates for the solution of the given problem is established. The first and second order of difference schemes are presented for approximately solving a specific nonlocal boundary problem. The theoretical statements for the solution of these difference schemes are supported by the result of numerical examples.

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

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Pimenov Vladimir G.

2017-09-01

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

Random ordinary differential equations and their numerical solution

CERN Document Server

Han, Xiaoying

2017-01-01

This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).   RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems.  They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor ...

Six-dimensional localized black holes: Numerical solutions

International Nuclear Information System (INIS)

Kudoh, Hideaki

2004-01-01

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes

Cyclic deformation-induced solute transport in tissue scaffolds with computer designed, interconnected, pore networks: experiments and simulations.

Science.gov (United States)

Den Buijs, Jorn Op; Dragomir-Daescu, Dan; Ritman, Erik L

2009-08-01

Nutrient supply and waste removal in porous tissue engineering scaffolds decrease from the periphery to the center, leading to limited depth of ingrowth of new tissue into the scaffold. However, as many tissues experience cyclic physiological strains, this may provide a mechanism to enhance solute transport in vivo before vascularization of the scaffold. The hypothesis of this study was that pore cross-sectional geometry and interconnectivity are of major importance for the effectiveness of cyclic deformation-induced solute transport. Transparent elastic polyurethane scaffolds, with computer-programmed design of pore networks in the form of interconnected channels, were fabricated using a 3D printing and injection molding technique. The scaffold pores were loaded with a colored tracer for optical contrast, cyclically compressed with deformations of 10 and 15% of the original undeformed height at 1.0 Hz. Digital imaging was used to quantify the spatial distribution of the tracer concentration within the pores. Numerical simulations of a fluid-structure interaction model of deformation-induced solute transport were compared to the experimental data. The results of experiments and modeling agreed well and showed that pore interconnectivity heavily influences deformation-induced solute transport. Pore cross-sectional geometry appears to be of less relative importance in interconnected pore networks. Validated computer models of solute transport can be used to design optimal scaffold pore geometries that will enhance the convective transport of nutrients inside the scaffold and the removal of waste, thus improving the cell survivability deep inside the scaffold.

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

International Nuclear Information System (INIS)

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

2015-01-01

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

Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

Directory of Open Access Journals (Sweden)

De-Gang Wang

2012-01-01

Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

The Numerical Solution of the Equilibrium Problem for a Stretchable Elastic Beam

Science.gov (United States)

Mehdiyeva, G. Y.; Aliyev, A. Y.

2017-08-01

The boundary value problem under consideration describes the equilibrium of an elastic beam that is stretched or contracted by specified forces. The left end of the beam is free of load, and the right end is rigidly lapped. To solve the problem numerically, an appropriate difference problem is constructed. Solving the difference problem, we obtain an approximate solution of the problem. We estimate the approximate solution of the stated problem.

Criteria for the reliability of numerical approximations to the solution of fluid flow problems

International Nuclear Information System (INIS)

Foias, C.

1986-01-01

The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs

Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model

Directory of Open Access Journals (Sweden)

Nikola V. Georgiev

2003-01-01

Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.

A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation

Directory of Open Access Journals (Sweden)

Hakon A. Hoel

2007-07-01

Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.

Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available We consider a simplified bidirectional associated memory (BAM neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.

Development of numerical solution techniques in the KIKO3D code

International Nuclear Information System (INIS)

Panka, Istvan; Kereszturi, Andras; Hegedus, Csaba

2005-01-01

The paper describes the numerical methods applied in KIKO3D three-dimensional reactor dynamics code and present a new, more effective method (Bi-CGSTAB) for accelerating the large sparse matrix equation solution. The convergence characteristics were investigated in a given macro time step of a Control Rod Ejection transient. The results obtained by the old GMRES and new Bi-CGSTAB methods are compared. It is concluded that the real relative errors of the solutions obtained by GMRES or Bi - CGSTAB algorithms are in fact closer together than the estimated relative errors. The KIKO3D-Bi-CGSTAB method converges safely and it is 7-12 % faster than the old KIKO3D-GMRES solution (Authors)

Security Analysis of a Software Defined Wide Area Network Solution

OpenAIRE

Rajendran, Ashok

2016-01-01

Enterprise wide area network (WAN) is a private network that connects the computers and other devices across an organisation's branch locations and the data centers. It forms the backbone of enterprise communication. Currently, multiprotocol label switching (MPLS) is commonly used to provide this service. As a recent alternative to MPLS, software-dened wide area networking (SD-WAN) solutions are being introduced as an IP based cloud-networking service for enterprises. SD-WAN virtualizes the n...

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed hybrid finite element solution

NARCIS (Netherlands)

Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.R.J.

2007-01-01

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues.

Evaluation of Persian Professional Web Social Networks\\\\\\' Features, to Provide a Suitable Solution for Optimization of These Networks in Iran

Directory of Open Access Journals (Sweden)

Nadjla Hariri

2013-03-01

Full Text Available This study aimed to determine the status of Persian professional web social networks' features and provide a suitable solution for optimization of these networks in Iran. The research methods were library research and evaluative method, and study population consisted of 10 Persian professional web social networks. In this study, for data collection, a check list of social networks important tools and features was used. According to the results, “Cloob”, “IR Experts” and “Doreh” were the most compatible networks with the criteria of social networks. Finally, some solutions were presented for optimization of capabilities of Persian professional web social networks.

Numerical solution for identification of feedback coefficients in nuclear reactors

International Nuclear Information System (INIS)

Ebizuka, Yoshie; Sakai, Hideo

1975-01-01

Quasilinearization technique was studied to determine the Kinetic parameters of nuclear reactors. The method of solution was generalized to the determination of the parameters contained in a nonlinear system with nonlinear boundary conditions. A computer program, SNR-3, was developed to solve the resulting nonlinear two-point boundary value equations with generalized boundary conditions. In this paper, the problem formulation and the method of solution are explained for a general type of time dependent problem. A flow chart shows the procedure of numerical solution. The method was then applied to the determination of the critical factor and the reactivity feedback coefficients of reactors to investigate the accuracy and the applicability of the present method. The results showed that the present method was considerably successful, but that the random observation error effected the results of the identification. (Aoki, K.)

Game Theoretic Problems in Network Economics and Mechanism Design Solutions

CERN Document Server

Narahari, Y; Narayanam, Ramasuri; Prakash, Hastagiri

2009-01-01

Explores game theoretic modeling and mechanism design for problem solving in Internet and network economics. This monograph contains an exposition of representative game theoretic problems in three different network economics situations and a systematic exploration of mechanism design solutions to these problems.

A numerical solution to the radial equation of the tidal wave propagation

International Nuclear Information System (INIS)

Makarious, S.H.

1981-08-01

The tidal wave function y(x) is a solution to an inhomogeneous, linear, second-order differential equation with variable coefficient. Numerical values for the height-dependence terms, in the observed tides, have been utilized in finding y(x) as a solution to an initial-value problem. Complex Fast Fourier Transform technique is also used to obtain the solution in a complex form. Based on a realistic temperature structure, the atmosphere - below 110 km - has been divided into layers with distinct characteristics, and thus the technique of propagation in stratified media has been applied. The reduced homogeneous equation assumes the form of Helmholtz equation and with initial conditions the general solution is obtained. (author)

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

International Nuclear Information System (INIS)

Wehner, M.F.

1983-01-01

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

A numerical method for finding sign-changing solutions of superlinear Dirichlet problems

Energy Technology Data Exchange (ETDEWEB)

Neuberger, J.M.

1996-12-31

In a recent result it was shown via a variational argument that a class of superlinear elliptic boundary value problems has at least three nontrivial solutions, a pair of one sign and one which sign changes exactly once. These three and all other nontrivial solutions are saddle points of an action functional, and are characterized as local minima of that functional restricted to a codimension one submanifold of the Hilbert space H-0-1-2, or an appropriate higher codimension subset of that manifold. In this paper, we present a numerical Sobolev steepest descent algorithm for finding these three solutions.

A New Method to Solve Numeric Solution of Nonlinear Dynamic System

Directory of Open Access Journals (Sweden)

Min Hu

2016-01-01

Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

Optimization of multicast optical networks with genetic algorithm

Science.gov (United States)

Lv, Bo; Mao, Xiangqiao; Zhang, Feng; Qin, Xi; Lu, Dan; Chen, Ming; Chen, Yong; Cao, Jihong; Jian, Shuisheng

2007-11-01

In this letter, aiming to obtain the best multicast performance of optical network in which the video conference information is carried by specified wavelength, we extend the solutions of matrix games with the network coding theory and devise a new method to solve the complex problems of multicast network switching. In addition, an experimental optical network has been testified with best switching strategies by employing the novel numerical solution designed with an effective way of genetic algorithm. The result shows that optimal solutions with genetic algorithm are accordance with the ones with the traditional fictitious play method.

Reusable Object-Oriented Solutions for Numerical Simulation of PDEs in a High Performance Environment

Directory of Open Access Journals (Sweden)

Andrea Lani

2006-01-01

Full Text Available Object-oriented platforms developed for the numerical solution of PDEs must combine flexibility and reusability, in order to ease the integration of new functionalities and algorithms. While designing similar frameworks, a built-in support for high performance should be provided and enforced transparently, especially in parallel simulations. The paper presents solutions developed to effectively tackle these and other more specific problems (data handling and storage, implementation of physical models and numerical methods that have arisen in the development of COOLFluiD, an environment for PDE solvers. Particular attention is devoted to describe a data storage facility, highly suitable for both serial and parallel computing, and to discuss the application of two design patterns, Perspective and Method-Command-Strategy, that support extensibility and run-time flexibility in the implementation of physical models and generic numerical algorithms respectively.

A Mass Conservative Numerical Solution for Two-Phase Flow in Porous Media With Application to Unsaturated Flow

DEFF Research Database (Denmark)

Celia, Michael A.; Binning, Philip John

1992-01-01

that the algorithm produces solutions that are essentially mass conservative and oscillation free, even in the presence of steep infiltrating fronts. When the algorithm is applied to the case of air and water flow in unsaturated soils, numerical results confirm the conditions under which Richards's equation is valid....... Numerical results also demonstrate the potential importance of air phase advection when considering contaminant transport in unsaturated soils. Comparison to several other numerical algorithms shows that the modified Picard approach offers robust, mass conservative solutions to the general equations...

Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

Directory of Open Access Journals (Sweden)

Henrique Silva Furtado

2009-09-01

Full Text Available Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid-liquid interface thickness (2λ of 8 nanometers reproduced the solute (Cu equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007] was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification, indicating the necessity for new and more acute experimental data.

A numerical procedure for transient free surface seepage through fracture networks

Science.gov (United States)

Jiang, Qinghui; Ye, Zuyang; Zhou, Chuangbing

2014-11-01

A parabolic variational inequality (PVI) formulation is presented for the transient free surface seepage problem defined for a whole fracture network. Because the seepage faces are specified as Signorini-type conditions, the PVI formulation can effectively eliminate the singularity of spillpoints that evolve with time. By introducing a continuous penalty function to replace the original Heaviside function, a finite element procedure based on the PVI formulation is developed to predict the transient free surface response in the fracture network. The effects of the penalty parameter on the solution precision are analyzed. A relative error formula for evaluating the flow losses at steady state caused by the penalty parameter is obtained. To validate the proposed method, three typical examples are solved. The solutions for the first example are compared with the experimental results. The results from the last two examples further demonstrate that the orientation, extent and density of fractures significantly affect the free surface seepage behavior in the fracture network.

Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem

Directory of Open Access Journals (Sweden)

Won-Tak Hong

2016-01-01

Full Text Available We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1 as well as oscillating singularities (of type rαsin⁡(ϵlog⁡r. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.

Efficient Numerical Solution of Coupled Radial Differential Equations in Multichannel Scattering Problems

International Nuclear Information System (INIS)

Houfek, Karel

2008-01-01

Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.

New numerical method for iterative or perturbative solution of quantum field theory

International Nuclear Information System (INIS)

Hahn, S.C.; Guralnik, G.S.

1999-01-01

A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

Topological derivatives of eigenvalues and neural networks in identification of imperfections

International Nuclear Information System (INIS)

Grzanek, M; Nowakowski, A; Sokolowski, J

2008-01-01

Numerical method for identification of imperfections is devised for elliptic spectral problems. The neural networks are employed for numerical solution. The topological derivatives of eigenvalues are used in the learning procedure of the neural networks. The topological derivatives of eigenvalues are determined by the methods of asymptotic analysis in singularly perturbed geometrical domains. The convergence of the numerical method in a probabilistic setting is analysed. The method is presented for the identification of small singular perturbations of the boundary of geometrical domain, however the framework is general and can be used for numerical solutions of inverse problems in the presence of small imperfections in the interior of the domain. Some numerical results are given for elliptic spectral problem in two spatial dimensions.

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

Science.gov (United States)

Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

2002-01-01

We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

Numerical treatment of elliptic BVP with several solutions and of MHD equilibrium problems

International Nuclear Information System (INIS)

Meyer-Spasche, R.

1975-12-01

It is found out empirically that Newton iteration and difference methods are very suitable for the numerical treatment of elliptic boundary value problems (Lu)(x) = f(x,u(x)) in D c R 2 , u/deltaD = g having several solutions. Some convergence theorems for these methods are presented. Some notable numerical examples are given, including bifurcation diagrams, which are interesting in themselves and show also the applicability of the methods developed. (orig./WB) [de

Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil

Directory of Open Access Journals (Sweden)

Slouka Martin

2016-01-01

Full Text Available This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.

Numerical solutions of differential equations of an ionization chamber

International Nuclear Information System (INIS)

Novkovic, D.; Tomasevic, M.; Subotic, K.; Manic, S.

1998-01-01

A system of reduced differential equations generally valid for plane-parallel, cylindrical, and spherical ionization chambers filled with air, which is appropriate for numerical solution, has been derived. The system has been solved for all three geometries. The comparison of the calculated results of Armstrong and Tate, for plane-parallel ionization chambers, and Sprinkle and Tate, for spherical ionization chambers, with the present calculations has shown a good agreement. The calculated values for ionization chambers filled with CO 2 were also in good agreement with the experimental data of Moriuchi et al (author)

Numerical solution of plasma fluid equations using locally refined grids

International Nuclear Information System (INIS)

Colella, P.

1997-01-01

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results

Stability of small-amplitude periodic solutions near Hopf bifurcations in time-delayed fully-connected PLL networks

Science.gov (United States)

Ferruzzo Correa, Diego P.; Bueno, Átila M.; Castilho Piqueira, José R.

2017-04-01

In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a two-dimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results.

Multi-stability and almost periodic solutions of a class of recurrent neural networks

International Nuclear Information System (INIS)

Liu Yiguang; You Zhisheng

2007-01-01

This paper studies multi-stability, existence of almost periodic solutions of a class of recurrent neural networks with bounded activation functions. After introducing a sufficient condition insuring multi-stability, many criteria guaranteeing existence of almost periodic solutions are derived using Mawhin's coincidence degree theory. All the criteria are constructed without assuming the activation functions are smooth, monotonic or Lipschitz continuous, and that the networks contains periodic variables (such as periodic coefficients, periodic inputs or periodic activation functions), so all criteria can be easily extended to fit many concrete forms of neural networks such as Hopfield neural networks, or cellular neural networks, etc. Finally, all kinds of simulations are employed to illustrate the criteria

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

Science.gov (United States)

Felici, Helene M.; Drela, Mark

1993-01-01

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

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

Science.gov (United States)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

Science.gov (United States)

Ceccobello, C.; Farinelli, R.; Titarchuk, L.

2014-01-01

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

Science.gov (United States)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

New numerical solutions of three-dimensional compressible hydrodynamic convection. [in stars

Science.gov (United States)

Hossain, Murshed; Mullan, D. J.

1990-01-01

Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.

The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2015-01-01

Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

Directory of Open Access Journals (Sweden)

Valášek J.

2016-01-01

Full Text Available The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE is used. The whole problem is solved by the finite element method (FEM based solver. Results of numerical experiments with different boundary conditions are presented.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

Science.gov (United States)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Numerical Modeling for the Solute Uptake from Groundwater by Plants-Plant Uptake Package

OpenAIRE

El-Sayed, Amr A.

2006-01-01

A numerical model is presented to describe solute transport in groundwater coupled to sorption by plant roots, translocation into plant stems, and finally evapotranspiration. The conceptual model takes into account both Root Concentration Factor, RCF, and Transpiration Stream Concentration Factor, TSCF for chemicals which are a function of Kow. A similar technique used to simulate the solute transport in groundwater to simulate sorption and plant uptake is used. The mathematical equation is s...

An MPCC Formulation and Its Smooth Solution Algorithm for Continuous Network Design Problem

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Guangmin Wang

2017-12-01

Full Text Available Continuous network design problem (CNDP is searching for a transportation network configuration to minimize the sum of the total system travel time and the investment cost of link capacity expansions by considering that the travellers follow a traditional Wardrop user equilibrium (UE to choose their routes. In this paper, the CNDP model can be formulated as mathematical programs with complementarity constraints (MPCC by describing UE as a non-linear complementarity problem (NCP. To address the difficulty resulting from complementarity constraints in MPCC, they are substituted by the Fischer-Burmeister (FB function, which can be smoothed by the introduction of the smoothing parameter. Therefore, the MPCC can be transformed into a well-behaved non-linear program (NLP by replacing the complementarity constraints with a smooth equation. Consequently, the solver such as LINDOGLOBAL in GAMS can be used to solve the smooth approximate NLP to obtain the solution to MPCC for modelling CNDP. The numerical experiments on the example from the literature demonstrate that the proposed algorithm is feasible.

Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

2014-01-01

Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

Global stability and existence of periodic solutions of discrete delayed cellular neural networks

International Nuclear Information System (INIS)

Li Yongkun

2004-01-01

We use the continuation theorem of coincidence degree theory and Lyapunov functions to study the existence and stability of periodic solutions for the discrete cellular neural networks (CNNs) with delays xi(n+1)=xi(n)e-bi(n)h+θi(h)-bar j=1maij(n)fj(xj(n))+θi(h)-bar j=1mbij(n)fj(xj(n- τij(n)))+θi(h)Ii(n),i=1,2,...,m. We obtain some sufficient conditions to ensure that for the networks there exists a unique periodic solution, and all its solutions converge to such a periodic solution

Numerical Modeling Tools for the Prediction of Solution Migration Applicable to Mining Site

International Nuclear Information System (INIS)

Martell, M.; Vaughn, P.

1999-01-01

Mining has always had an important influence on cultures and traditions of communities around the globe and throughout history. Today, because mining legislation places heavy emphasis on environmental protection, there is great interest in having a comprehensive understanding of ancient mining and mining sites. Multi-disciplinary approaches (i.e., Pb isotopes as tracers) are being used to explore the distribution of metals in natural environments. Another successful approach is to model solution migration numerically. A proven method to simulate solution migration in natural rock salt has been applied to project through time for 10,000 years the system performance and solution concentrations surrounding a proposed nuclear waste repository. This capability is readily adaptable to simulate solution migration around mining

A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

Directory of Open Access Journals (Sweden)

Qicheng Meng

2016-04-01

Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.

Social networks a real solution for students' future jobs

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Lorena Bătăgan

2015-11-01

Full Text Available This study examines if social networks represent a real solution for students' future jobs. The authors use for their analysis data provided by the students from Faculty of Economic Cybernetics, Statistics and Informatics (ECSI ‒ The Bucharest University of Economic Studies and by professional networking websites like Facebook and LinkedIn. In this paper there are highlighted the level of using social networks and students’ perception on the use of social networks in their activities. The paper focuses on students’ interest in using social networks for securing future jobs. The results of research underlined the idea that for higher education there is an opportunity to facilitate the access of students to social networks in two ways: by developing or enhancing students’ knowledge on how to use social networks and as part of that effort, by educating students about how they can promote their skills. The main idea is that the use of large amounts of data generated by social networks accelerates students' integration within working environment and their employment.

Approximate solutions of dual fuzzy polynomials by feed-back neural networks

Directory of Open Access Journals (Sweden)

Ahmad Jafarian

2012-11-01

Full Text Available Recently, artificial neural networks (ANNs have been extensively studied and used in different areas such as pattern recognition, associative memory, combinatorial optimization, etc. In this paper, we investigate the ability of fuzzy neural networks to approximate solution of a dual fuzzy polynomial of the form $a_{1}x+ ...+a_{n}x^n =b_{1}x+ ...+b_{n}x^n+d,$ where $a_{j},b_{j},d epsilon E^1 (for j=1,...,n.$ Since the operation of fuzzy neural networks is based on Zadeh's extension principle. For this scope we train a fuzzified neural network by back-propagation-type learning algorithm which has five layer where connection weights are crisp numbers. This neural network can get a crisp input signal and then calculates its corresponding fuzzy output. Presented method can give a real approximate solution for given polynomial by using a cost function which is defined for the level sets of fuzzy output and target output. The simulation results are presented to demonstrate the efficiency and effectiveness of the proposed approach.

Numerical modeling of solute transport in deformable unsaturated layered soil

Directory of Open Access Journals (Sweden)

Sheng Wu

2017-07-01

Full Text Available The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.

Periodic oscillatory solution in delayed competitive-cooperative neural networks: A decomposition approach

International Nuclear Information System (INIS)

Yuan Kun; Cao Jinde

2006-01-01

In this paper, the problems of exponential convergence and the exponential stability of the periodic solution for a general class of non-autonomous competitive-cooperative neural networks are analyzed via the decomposition approach. The idea is to divide the connection weights into inhibitory or excitatory types and thereby to embed a competitive-cooperative delayed neural network into an augmented cooperative delay system through a symmetric transformation. Some simple necessary and sufficient conditions are derived to ensure the componentwise exponential convergence and the exponential stability of the periodic solution of the considered neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice

Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.

Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions.

Science.gov (United States)

Lötstedt, Erik; Jentschura, Ulrich D

2009-02-01

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip.

Directory of Open Access Journals (Sweden)

Cong Hu

Full Text Available We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO, which incorporates Levy flights into multi-verse optimizer (MVO algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC. Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed.

An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications

Directory of Open Access Journals (Sweden)

Petráš Ivo

2011-01-01

Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.

Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation

International Nuclear Information System (INIS)

Wei, T; Qin, H H; Shi, R

2008-01-01

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method

Temperature prediction in a coal fired boiler with a fixed bed by fuzzy logic based on numerical solution

International Nuclear Information System (INIS)

Biyikoglu, A.; Akcayol, M.A.; Oezdemir, V.; Sivrioglu, M.

2005-01-01

In this study, steady state combustion in boilers with a fixed bed has been investigated. Temperature distributions in the combustion chamber of a coal fired boiler with a fixed bed are predicted using fuzzy logic based on data obtained from the numerical solution method for various coal and air feeding rates. The numerical solution method and the discretization of the governing equations of two dimensional turbulent flow in the combustion chamber and one dimensional coal combustion in the fixed bed are explained. Control Volume and Finite Difference Methods are used in the discretization of the equations in the combustion chamber and in the fixed bed, respectively. Results are presented as contours within the solution domain and compared with numerical ones. Comparison of the results shows that the difference between the numerical solution and fuzzy logic prediction throughout the computational domain is less than 1.5%. The statistical coefficient of multiple determinations for the investigated cases is about 0.9993 to 0.9998. This accuracy degree is acceptable in predicting the temperature values. So, it can be concluded that fuzzy logic provides a feasible method for defining the system properties

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Solved problems in classical mechanics analytical and numerical solutions with comments

CERN Document Server

de Lange, O L

2010-01-01

Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

KAUST Repository

Frohne, Jö rg; Heister, Timo; Bangerth, Wolfgang

2015-01-01

© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

KAUST Repository

Frohne, Jörg

2015-08-06

© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

Computer-Aided Numerical Inversion of Laplace Transform

Directory of Open Access Journals (Sweden)

Umesh Kumar

2000-01-01

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

TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

International Nuclear Information System (INIS)

Walters, W.F.

1983-01-01

A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy

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

OpenAIRE

GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

2016-01-01

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

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

Science.gov (United States)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Babylonian Resistor Networks

Science.gov (United States)

Mungan, Carl E.; Lipscombe, Trevor C.

2012-01-01

The ancient Babylonians had an iterative technique for numerically approximating the values of square roots. Their method can be physically implemented using series and parallel resistor networks. A recursive formula for the equivalent resistance R[subscript eq] is developed and converted into a nonrecursive solution for circuits using…

So ware-Defined Network Solutions for Science Scenarios: Performance Testing Framework and Measurements

Energy Technology Data Exchange (ETDEWEB)

Settlemyer, Bradley [Los Alamos National Laboratory (LANL); Kettimuthu, R. [Argonne National Laboratory (ANL); Boley, Josh [Argonne National Laboratory (ANL); Katramatos, Dimitrios [Brookhaven National Laboratory (BNL); Rao, Nageswara S. [ORNL; Sen, Satyabrata [ORNL; Liu, Qiang [ORNL

2018-01-01

High-performance scientific work flows utilize supercomputers, scientific instruments, and large storage systems. Their executions require fast setup of a small number of dedicated network connections across the geographically distributed facility sites. We present Software-Defined Network (SDN) solutions consisting of site daemons that use dpctl, Floodlight, ONOS, or OpenDaylight controllers to set up these connections. The development of these SDN solutions could be quite disruptive to the infrastructure, while requiring a close coordination among multiple sites; in addition, the large number of possible controller and device combinations to investigate could make the infrastructure unavailable to regular users for extended periods of time. In response, we develop a Virtual Science Network Environment (VSNE) using virtual machines, Mininet, and custom scripts that support the development, testing, and evaluation of SDN solutions, without the constraints and expenses of multi-site physical infrastructures; furthermore, the chosen solutions can be directly transferred to production deployments. By complementing VSNE with a physical testbed, we conduct targeted performance tests of various SDN solutions to help choose the best candidates. In addition, we propose a switching response method to assess the setup times and throughput performances of different SDN solutions, and present experimental results that show their advantages and limitations.

assessment of concentration of air pollutants using analytical and numerical solution of the atmospheric diffusion equation

International Nuclear Information System (INIS)

Esmail, S.F.H.

2011-01-01

The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.

Unification of Information Security Policies for Network Security Solutions

Directory of Open Access Journals (Sweden)

D.S. Chernyavskiy

2012-03-01

Full Text Available Diversity of command languages on network security solutions’ (NSS interfaces causes problems in a process of information security policy (ISP deployment. Unified model for security policy representation and implementation in NSS could aid to avoid such problems and consequently enhance efficiency of the process. The proposed solution is Unified language for network security policy (ULNSP. The language is based on formal languages theory, and being coupled with its translator, ULNSP makes it possible to formalize and implement ISP independently of particular NSS.

Application of a space-time CE/SE (Conversation Element/Solution Element) method to the numerical solution of chromatographic separation processes

DEFF Research Database (Denmark)

including convection-difmsion-reaction PDEs are numerically solved using the two methods on the same spatial grid. Even though the CE/SE method uses a simple stencil structure and is developed on a simple mathematical basis (i.e., Gauss' divergence theorem), accurate and computationally-efficient solutions...

Intracortical stiffness of mid-diaphysis femur bovine bone: lacunar-canalicular based homogenization numerical solutions and microhardness measurements.

Science.gov (United States)

Hage, Ilige S; Hamade, Ramsey F

2017-09-01

Microscale lacunar-canalicular (L-C) porosity is a major contributor to intracortical bone stiffness variability. In this work, such variability is investigated experimentally using micro hardness indentation tests and numerically using a homogenization scheme. Cross sectional rings of cortical bones are cut from the middle tubular part of bovine femur long bone at mid-diaphysis. A series of light microscopy images are taken along a line emanating from the cross-section center starting from the ring's interior (endosteum) ring surface toward the ring's exterior (periosteum) ring surface. For each image in the line, computer vision analysis of porosity is conducted employing an image segmentation methodology based on pulse coupled neural networks (PCNN) recently developed by the authors. Determined are size and shape of each of the lacunar-canalicular (L-C) cortical micro constituents: lacunae, canaliculi, and Haversian canals. Consequently, it was possible to segment and quantify the geometrical attributes of all individual segmented pores leading to accurate determination of derived geometrical measures such as L-C cortical pores' total porosity (pore volume fraction), (elliptical) aspect ratio, orientation, location, and number of pores in secondary and primary osteons. Porosity was found to be unevenly (but linearly) distributed along the interior and exterior regions of the intracortical bone. The segmented L-C porosity data is passed to a numerical microscale-based homogenization scheme, also recently developed by the authors, that analyses a composite made up of lamella matrix punctuated by multi-inclusions and returns corresponding values for longitudinal and transverse Young's modulus (matrix stiffness) for these micro-sized spatial locations. Hence, intracortical stiffness variability is numerically quantified using a combination of computer vision program and numerical homogenization code. These numerically found stiffness values of the homogenization

A note on numerical solution to the problem of criticality

International Nuclear Information System (INIS)

Kyncl, J.

2002-01-01

The contribution deals with numerical solution to the problem of criticality for neutron transport equation by the external source iteration method. Especially, the speed of convergence is examined. It is shown that if neutron absorption in the medium considered is high and if the space region occupied by the medium is large then a slow convergence of the iterations can be expected. This expectation is confirmed by results to CB4 benchmark obtained by MCNP code. Besides the results presented some questions concerning applications of them to criticality calculations are pointed out (Author)

Use of Green's functions in the numerical solution of two-point boundary value problems

Science.gov (United States)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

Convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks

Science.gov (United States)

Long, Yin; Zhang, Xiao-Jun; Wang, Kui

2018-05-01

In this paper, convergence and approximate calculation of average degree under different network sizes for decreasing random birth-and-death networks (RBDNs) are studied. First, we find and demonstrate that the average degree is convergent in the form of power law. Meanwhile, we discover that the ratios of the back items to front items of convergent reminder are independent of network link number for large network size, and we theoretically prove that the limit of the ratio is a constant. Moreover, since it is difficult to calculate the analytical solution of the average degree for large network sizes, we adopt numerical method to obtain approximate expression of the average degree to approximate its analytical solution. Finally, simulations are presented to verify our theoretical results.

Design of analog networks in the control theory formulation. Part 2: Numerical results

OpenAIRE

Zemliak, A. M.

2005-01-01

The paper presents numerical results of design of nonlinear electronic networks based on the problem formulation in terms of the control theory. Several examples illustrate the prospects of the approach suggested in the first part of the work.

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

Science.gov (United States)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

Buffer Sizing in Wireless Networks: Challenges, Solutions, and Opportunities

KAUST Repository

Showail, Ahmad

2016-04-01

Buffer sizing is an important network configuration parameter that impacts the Quality of Service (QoS) characteristics of data traffic. With falling memory costs and the fallacy that \\'more is better\\', network devices are being overprovisioned with large bu ers. This may increase queueing delays experienced by a packet and subsequently impact stability of core protocols such as TCP. The problem has been studied extensively for wired networks. However, there is little work addressing the unique challenges of wireless environment such as time-varying channel capacity, variable packet inter-service time, and packet aggregation, among others. In this paper we discuss these challenges, classify the current state-of-the-art solutions, discuss their limitations, and provide directions for future research in the area.

Control and Optimization of Network in Networked Control System

Directory of Open Access Journals (Sweden)

Wang Zhiwen

2014-01-01

Full Text Available In order to avoid quality of performance (QoP degradation resulting from quality of service (QoS, the solution to network congestion from the point of control theory, which marks departure of our results from the existing methods, is proposed in this paper. The congestion and bandwidth are regarded as state and control variables, respectively; then, the linear time-invariant (LTI model between congestion state and bandwidth of network is established. Consequently, linear quadratic method is used to eliminate the network congestion by allocating bandwidth dynamically. At last, numerical simulation results are given to illustrate the effectiveness of this modeling approach.

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2007-01-01

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

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

Science.gov (United States)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

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

Numerical solution of ordinary differential equations

CERN Document Server

Fox, L

1987-01-01

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

Activity in the fronto-parietal network indicates numerical inductive reasoning beyond calculation: An fMRI study combined with a cognitive model.

Science.gov (United States)

Liang, Peipeng; Jia, Xiuqin; Taatgen, Niels A; Borst, Jelmer P; Li, Kuncheng

2016-05-19

Numerical inductive reasoning refers to the process of identifying and extrapolating the rule involved in numeric materials. It is associated with calculation, and shares the common activation of the fronto-parietal regions with calculation, which suggests that numerical inductive reasoning may correspond to a general calculation process. However, compared with calculation, rule identification is critical and unique to reasoning. Previous studies have established the central role of the fronto-parietal network for relational integration during rule identification in numerical inductive reasoning. The current question of interest is whether numerical inductive reasoning exclusively corresponds to calculation or operates beyond calculation, and whether it is possible to distinguish between them based on the activity pattern in the fronto-parietal network. To directly address this issue, three types of problems were created: numerical inductive reasoning, calculation, and perceptual judgment. Our results showed that the fronto-parietal network was more active in numerical inductive reasoning which requires more exchanges between intermediate representations and long-term declarative knowledge during rule identification. These results survived even after controlling for the covariates of response time and error rate. A computational cognitive model was developed using the cognitive architecture ACT-R to account for the behavioral results and brain activity in the fronto-parietal network.

Numerical solution of the Schroedinger equation with a polynomial potential

International Nuclear Information System (INIS)

Campoy, G.; Palma, A.

1986-01-01

A numerical method for solving the Schroedinger equation for a potential expressed as a polynomial is proposed. The basic assumption relies on the asymptotic properties of the solution of this equation. It is possible to obtain the energies and the stationary state functions simultaneously. They analyze, in particular, the cases of the quartic anharmonic oscillator and a hydrogen atom perturbed by a quadratic term, obtaining its energy eigenvalues for some values of the perturbation parameter. Together with the Hellmann-Feynman theorem, they use their algorithm to calculate expectation values of x'' for arbitrary positive values of n. 4 tables

Long-time behavior in numerical solutions of certain dynamical systems

International Nuclear Information System (INIS)

Vazquez, L.

1987-01-01

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

Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

Directory of Open Access Journals (Sweden)

Roman Cherniha

2016-06-01

Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

Directory of Open Access Journals (Sweden)

Markou A.A.

2018-03-01

Full Text Available Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

Science.gov (United States)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute

LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION

Directory of Open Access Journals (Sweden)

Decio Levi

2013-10-01

Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.

Existence and exponential stability of almost periodic solution for Hopfield-type neural networks with impulse

International Nuclear Information System (INIS)

Zhang Huiying; Xia Yonghui

2008-01-01

In this paper, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for bidirectional associative memory Hopfield-type neural networks with impulse. The approaches are based on contraction principle and Gronwall-Bellman's inequality. This paper is considering the almost periodic solution for impulsive Hopfield-type neural networks

Vehicular ad hoc networks standards, solutions, and research

CERN Document Server

Molinaro, Antonella; Scopigno, Riccardo

2015-01-01

This book presents vehicular ad-hoc networks (VANETs) from the their onset, gradually going into technical details, providing a clear understanding of both theoretical foundations and more practical investigation. The editors gathered top-ranking authors to provide comprehensiveness and timely content; the invited authors were carefully selected from a list of who’s who in the respective field of interest: there are as many from Academia as from Standardization and Industry sectors from around the world. The covered topics are organized around five Parts starting from an historical overview of vehicular communications and standardization/harmonization activities (Part I), then progressing to the theoretical foundations of VANETs and a description of the day-one standard-compliant solutions (Part II), hence going into details of vehicular networking and security (Part III) and to the tools to study VANETs, from mobility and channel models, to network simulators and field trial methodologies (Part IV), and fi...

Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

Science.gov (United States)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations

International Nuclear Information System (INIS)

Nakayama, T.; Yakubo, K.; Orbach, R.L.

1994-01-01

This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems

Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta

Directory of Open Access Journals (Sweden)

Andresa Pescador

2016-04-01

Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.

A mass conservative numerical solution of vertical water flow and mass transport equations in unsaturated porous media

International Nuclear Information System (INIS)

Lim, S.C.; Lee, K.J.

1993-01-01

The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)

Notes on a PDE system for biological network formation

KAUST Repository

Haskovec, Jan

2016-01-22

We present new analytical and numerical results for the elliptic–parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks. The model describes the pressure field using a Darcy’s type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. The analytical part extends the results of Haskovec et al. (2015) regarding the existence of weak and mild solutions to the whole range of meaningful relaxation exponents. Moreover, we prove finite time extinction or break-down of solutions in the spatially one-dimensional setting for certain ranges of the relaxation exponent. We also construct stationary solutions for the case of vanishing diffusion and critical value of the relaxation exponent, using a variational formulation and a penalty method. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on mixed finite elements and study the qualitative properties of network structures for various parameter values. Furthermore, we indicate numerically that some analytical results proved for the spatially one-dimensional setting are likely to be valid also in several space dimensions.

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

Energy Technology Data Exchange (ETDEWEB)

Rajamaeki, M. [VTT Energy (Finland)

1997-07-01

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

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

International Nuclear Information System (INIS)

Rajamaeki, M.

1997-01-01

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

Different nonideality relationships, different databases and their effects on modeling precipitation from concentrated solutions using numerical speciation codes

Energy Technology Data Exchange (ETDEWEB)

Brown, L.F.; Ebinger, M.H.

1996-08-01

Four simple precipitation problems are solved to examine the use of numerical equilibrium codes. The study emphasizes concentrated solutions, assumes both ideal and nonideal solutions, and employs different databases and different activity-coefficient relationships. The study uses the EQ3/6 numerical speciation codes. The results show satisfactory material balances and agreement between solubility products calculated from free-energy relationships and those calculated from concentrations and activity coefficients. Precipitates show slightly higher solubilities when the solutions are regarded as nonideal than when considered ideal, agreeing with theory. When a substance may precipitate from a solution dilute in the precipitating substance, a code may or may not predict precipitation, depending on the database or activity-coefficient relationship used. In a problem involving a two-component precipitation, there are only small differences in the precipitate mass and composition between the ideal and nonideal solution calculations. Analysis of this result indicates that this may be a frequent occurrence. An analytical approach is derived for judging whether this phenomenon will occur in any real or postulated precipitation situation. The discussion looks at applications of this approach. In the solutes remaining after the precipitations, there seems to be little consistency in the calculated concentrations and activity coefficients. They do not appear to depend in any coherent manner on the database or activity-coefficient relationship used. These results reinforce warnings in the literature about perfunctory or mechanical use of numerical speciation codes.

Dynamically Adapted Mesh Construction for the Efficient Numerical Solution of a Singular Perturbed Reaction-diffusion-advection Equation

Directory of Open Access Journals (Sweden)

Dmitry V. Lukyanenko

2017-01-01

Full Text Available This  work develops  a theory  of the  asymptotic-numerical investigation of the  moving fronts  in reaction-diffusion-advection models.  By considering  the  numerical  solution  of the  singularly perturbed Burgers’s  equation  we discuss a method  of dynamically  adapted mesh  construction that is able to significantly  improve  the  numerical  solution  of this  type of equations.  For  the  construction we use a priori information that is based  on the  asymptotic analysis  of the  problem.  In  particular, we take  into account the information about  the speed of the transition layer, its width  and structure. Our algorithms  are able to reduce significantly complexity and enhance stability of the numerical  calculations in comparison  with classical approaches for solving this class of problems.  The numerical  experiment is presented to demonstrate the effectiveness of the proposed  method.The article  is published  in the authors’  wording. 

Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

Directory of Open Access Journals (Sweden)

SURE KÖME

2014-12-01

Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

Promoting Wired Links in Wireless Mesh Networks: An Efficient Engineering Solution

Science.gov (United States)

Barekatain, Behrang; Raahemifar, Kaamran; Ariza Quintana, Alfonso; Triviño Cabrera, Alicia

2015-01-01

Wireless Mesh Networks (WMNs) cannot completely guarantee good performance of traffic sources such as video streaming. To improve the network performance, this study proposes an efficient engineering solution named Wireless-to-Ethernet-Mesh-Portal-Passageway (WEMPP) that allows effective use of wired communication in WMNs. WEMPP permits transmitting data through wired and stable paths even when the destination is in the same network as the source (Intra-traffic). Tested with four popular routing protocols (Optimized Link State Routing or OLSR as a proactive protocol, Dynamic MANET On-demand or DYMO as a reactive protocol, DYMO with spanning tree ability and HWMP), WEMPP considerably decreases the end-to-end delay, jitter, contentions and interferences on nodes, even when the network size or density varies. WEMPP is also cost-effective and increases the network throughput. Moreover, in contrast to solutions proposed by previous studies, WEMPP is easily implemented by modifying the firmware of the actual Ethernet hardware without altering the routing protocols and/or the functionality of the IP/MAC/Upper layers. In fact, there is no need for modifying the functionalities of other mesh components in order to work with WEMPPs. The results of this study show that WEMPP significantly increases the performance of all routing protocols, thus leading to better video quality on nodes. PMID:25793516

GeoNetwork powered GI-cat: a geoportal hybrid solution

Science.gov (United States)

Baldini, Alessio; Boldrini, Enrico; Santoro, Mattia; Mazzetti, Paolo

2010-05-01

To the aim of setting up a Spatial Data Infrastructures (SDI) the creation of a system for the metadata management and discovery plays a fundamental role. An effective solution is the use of a geoportal (e.g. FAO/ESA geoportal), that has the important benefit of being accessible from a web browser. With this work we present a solution based integrating two of the available frameworks: GeoNetwork and GI-cat. GeoNetwork is an opensource software designed to improve accessibility of a wide variety of data together with the associated ancillary information (metadata), at different scale and from multidisciplinary sources; data are organized and documented in a standard and consistent way. GeoNetwork implements both the Portal and Catalog components of a Spatial Data Infrastructure (SDI) defined in the OGC Reference Architecture. It provides tools for managing and publishing metadata on spatial data and related services. GeoNetwork allows harvesting of various types of web data sources e.g. OGC Web Services (e.g. CSW, WCS, WMS). GI-cat is a distributed catalog based on a service-oriented framework of modular components and can be customized and tailored to support different deployment scenarios. It can federate a multiplicity of catalogs services, as well as inventory and access services in order to discover and access heterogeneous ESS resources. The federated resources are exposed by GI-cat through several standard catalog interfaces (e.g. OGC CSW AP ISO, OpenSearch, etc.) and by the GI-cat extended interface. Specific components implement mediation services for interfacing heterogeneous service providers, each of which exposes a specific standard specification; such components are called Accessors. These mediating components solve providers data modelmultiplicity by mapping them onto the GI-cat internal data model which implements the ISO 19115 Core profile. Accessors also implement the query protocol mapping; first they translate the query requests expressed

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

Science.gov (United States)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

Multiresolution strategies for the numerical solution of optimal control problems

Science.gov (United States)

Jain, Sachin

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a

Numerical analysis

CERN Document Server

Rao, G Shanker

2006-01-01

About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...

Effective Data Backup System Using Storage Area Network Solution ...

African Journals Online (AJOL)

The primary cause of data loss is lack or non- existent of data backup. Storage Area Network Solution (SANS) is internet-based software which will collect clients data and host them in several locations to forestall data loss in case of disaster in one location. The researcher used adobe Dreamweaver (CSC3) embedded with ...

Pareto Optimal Solutions for Network Defense Strategy Selection Simulator in Multi-Objective Reinforcement Learning

Directory of Open Access Journals (Sweden)

Yang Sun

2018-01-01

Full Text Available Using Pareto optimization in Multi-Objective Reinforcement Learning (MORL leads to better learning results for network defense games. This is particularly useful for network security agents, who must often balance several goals when choosing what action to take in defense of a network. If the defender knows his preferred reward distribution, the advantages of Pareto optimization can be retained by using a scalarization algorithm prior to the implementation of the MORL. In this paper, we simulate a network defense scenario by creating a multi-objective zero-sum game and using Pareto optimization and MORL to determine optimal solutions and compare those solutions to different scalarization approaches. We build a Pareto Defense Strategy Selection Simulator (PDSSS system for assisting network administrators on decision-making, specifically, on defense strategy selection, and the experiment results show that the Satisficing Trade-Off Method (STOM scalarization approach performs better than linear scalarization or GUESS method. The results of this paper can aid network security agents attempting to find an optimal defense policy for network security games.

Optimal design of cluster-based ad-hoc networks using probabilistic solution discovery

International Nuclear Information System (INIS)

Cook, Jason L.; Ramirez-Marquez, Jose Emmanuel

2009-01-01

The reliability of ad-hoc networks is gaining popularity in two areas: as a topic of academic interest and as a key performance parameter for defense systems employing this type of network. The ad-hoc network is dynamic and scalable and these descriptions are what attract its users. However, these descriptions are also synonymous for undefined and unpredictable when considering the impacts to the reliability of the system. The configuration of an ad-hoc network changes continuously and this fact implies that no single mathematical expression or graphical depiction can describe the system reliability-wise. Previous research has used mobility and stochastic models to address this challenge successfully. In this paper, the authors leverage the stochastic approach and build upon it a probabilistic solution discovery (PSD) algorithm to optimize the topology for a cluster-based mobile ad-hoc wireless network (MAWN). Specifically, the membership of nodes within the back-bone network or networks will be assigned in such as way as to maximize reliability subject to a constraint on cost. The constraint may also be considered as a non-monetary cost, such as weight, volume, power, or the like. When a cost is assigned to each component, a maximum cost threshold is assigned to the network, and the method is run; the result is an optimized allocation of the radios enabling back-bone network(s) to provide the most reliable network possible without exceeding the allowable cost. The method is intended for use directly as part of the architectural design process of a cluster-based MAWN to efficiently determine an optimal or near-optimal design solution. It is capable of optimizing the topology based upon all-terminal reliability (ATR), all-operating terminal reliability (AoTR), or two-terminal reliability (2TR)

Grad-Shafranov reconstruction: overview and improvement of the numerical solution used in space physics

Energy Technology Data Exchange (ETDEWEB)

Ojeda Gonzalez, A.; Domingues, M.O.; Mendes, O., E-mail: ojeda.gonzalez.a@gmail.com [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil); Kaibara, M.K. [Universidade Federal Fluminense (GMA/IME/UFF), Niteroi, RJ (Brazil); Prestes, A. [Universidade do Vale do Paraiba (IP and D/UNIVAP), Sao Jose dos Campos, SP (Brazil). Lab. de Fisica e Astronomia

2015-10-15

The Grad-Shafranov equation is a Poisson's equation, i.e., a partial differential equation of elliptic type. The problem is depending on the initial condition and can be treated as a Cauchy problem. Although it is ill-posed or ill-conditioned, it can be integrated numerically. In the integration of the GS equation, singularities with large values of the potential arise after a certain number of integration steps away from the original data line, and a filter should be used. The Grad-Shafranov reconstruction (GSR) technique was developed from 1996 to 2000 for recovering two-dimensional structures in the magnetopause in an ideal MHD formulation. Other works have used the GSR techniques to study magnetic flux ropes in the solar wind and in the magnetotail from a single spacecraft dataset; posteriorly, it was extended to treat measurements from multiple satellites. From Vlasov equation, it is possible to arrive at the GS-equation in function of the normalized vector potential. A general solution is obtained using complex variable theory. A specific solution was chosen as benchmark case to solve numerically the GS equation.We propose some changes in the resolution scheme of the GS equation to improve the solution. The result of each method is compared with the solution proposed by Hau and Sonnerup (J. Geophys. Res. 104(A4), 6899-6917 (1999)). The main improvement found in the GS resolution was the need to filter Bx values at each y value. (author)

Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.

Science.gov (United States)

Esmaeeli, Hadi S; Farnam, Yaghoob; Bentz, Dale P; Zavattieri, Pablo D; Weiss, Jason

2017-02-01

This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.

Limit Theorems and Their Relation to Solute Transport in Simulated Fractured Media

Science.gov (United States)

Reeves, D. M.; Benson, D. A.; Meerschaert, M. M.

2003-12-01

Solute particles that travel through fracture networks are subject to wide velocity variations along a restricted set of directions. This may result in super-Fickian dispersion along a few primary scaling directions. The fractional advection-dispersion equation (FADE), a modification of the original advection-dispersion equation in which a fractional derivative replaces the integer-order dispersion term, has the ability to model rapid, non-Gaussian solute transport. The FADE assumes that solute particle motions converge to either α -stable or operator stable densities, which are modeled by spatial fractional derivatives. In multiple dimensions, the multi-fractional dispersion derivative dictates the order and weight of differentiation in all directions, which correspond to the statistics of large particle motions in all directions. This study numerically investigates the presence of super- Fickian solute transport through simulated two-dimensional fracture networks. An ensemble of networks is gen

Application of 1 D Finite Element Method in Combination with Laminar Solution Method for Pipe Network Analysis

Science.gov (United States)

Dudar, O. I.; Dudar, E. S.

2017-11-01

The features of application of the 1D dimensional finite element method (FEM) in combination with the laminar solutions method (LSM) for the calculation of underground ventilating networks are considered. In this case the processes of heat and mass transfer change the properties of a fluid (binary vapour-air mix). Under the action of gravitational forces it leads to such phenomena as natural draft, local circulation, etc. The FEM relations considering the action of gravity, the mass conservation law, the dependence of vapour-air mix properties on the thermodynamic parameters are derived so that it allows one to model the mentioned phenomena. The analogy of the elastic and plastic rod deformation processes to the processes of laminar and turbulent flow in a pipe is described. Owing to this analogy, the guaranteed convergence of the elastic solutions method for the materials of plastic type means the guaranteed convergence of the LSM for any regime of a turbulent flow in a rough pipe. By means of numerical experiments the convergence rate of the FEM - LSM is investigated. This convergence rate appeared much higher than the convergence rate of the Cross - Andriyashev method. Data of other authors on the convergence rate comparison for the finite element method, the Newton method and the method of gradient are provided. These data allow one to conclude that the FEM in combination with the LSM is one of the most effective methods of calculation of hydraulic and ventilating networks. The FEM - LSM has been used for creation of the research application programme package “MineClimate” allowing to calculate the microclimate parameters in the underground ventilating networks.

A probabilistic computational framework for bridge network optimal maintenance scheduling

International Nuclear Information System (INIS)

Bocchini, Paolo; Frangopol, Dan M.

2011-01-01

This paper presents a probabilistic computational framework for the Pareto optimization of the preventive maintenance applications to bridges of a highway transportation network. The bridge characteristics are represented by their uncertain reliability index profiles. The in/out of service states of the bridges are simulated taking into account their correlation structure. Multi-objective Genetic Algorithms have been chosen as numerical tool for the solution of the optimization problem. The design variables of the optimization are the preventive maintenance schedules of all the bridges of the network. The two conflicting objectives are the minimization of the total present maintenance cost and the maximization of the network performance indicator. The final result is the Pareto front of optimal solutions among which the managers should chose, depending on engineering and economical factors. A numerical example illustrates the application of the proposed approach.

Epidemic spreading in weighted networks: an edge-based mean-field solution.

Science.gov (United States)

Yang, Zimo; Zhou, Tao

2012-05-01

Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.

Solution of Fractional Order System of Bagley-Torvik Equation Using Evolutionary Computational Intelligence

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Muhammad Asif Zahoor Raja

2011-01-01

Full Text Available A stochastic technique has been developed for the solution of fractional order system represented by Bagley-Torvik equation. The mathematical model of the equation was developed with the help of feed-forward artificial neural networks. The training of the networks was made with evolutionary computational intelligence based on genetic algorithm hybrid with pattern search technique. Designed scheme was successfully applied to different forms of the equation. Results are compared with standard approximate analytic, stochastic numerical solvers and exact solutions.

Transmission analysis in WDM networks

DEFF Research Database (Denmark)

Rasmussen, Christian Jørgen

1999-01-01

This thesis describes the development of a computer-based simulator for transmission analysis in optical wavelength division multiplexing networks. A great part of the work concerns fundamental optical network simulator issues. Among these issues are identification of the versatility and user...... the different component models are invoked during the simulation of a system. A simple set of rules which makes it possible to simulate any network architectures is laid down. The modelling of the nonlinear fibre and the optical receiver is also treated. The work on the fibre concerns the numerical solution...

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

Science.gov (United States)

Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

Supply network configuration—A benchmarking problem

Science.gov (United States)

Brandenburg, Marcus

2018-03-01

Managing supply networks is a highly relevant task that strongly influences the competitiveness of firms from various industries. Designing supply networks is a strategic process that considerably affects the structure of the whole network. In contrast, supply networks for new products are configured without major adaptations of the existing structure, but the network has to be configured before the new product is actually launched in the marketplace. Due to dynamics and uncertainties, the resulting planning problem is highly complex. However, formal models and solution approaches that support supply network configuration decisions for new products are scant. The paper at hand aims at stimulating related model-based research. To formulate mathematical models and solution procedures, a benchmarking problem is introduced which is derived from a case study of a cosmetics manufacturer. Tasks, objectives, and constraints of the problem are described in great detail and numerical values and ranges of all problem parameters are given. In addition, several directions for future research are suggested.

A numerical solution of a singular boundary value problem arising in boundary layer theory.

Science.gov (United States)

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts

NARCIS (Netherlands)

Rienstra, S.W.; Eversman, W.

2001-01-01

An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass

Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

Science.gov (United States)

Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang

2018-03-01

This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.

Numerical solution of fully developed heat transfer problem with constant wall temperature and application to isosceles triangle and parabolic ducts

International Nuclear Information System (INIS)

Karabulut, Halit; Ipci, Duygu; Cinar, Can

2016-01-01

Highlights: • A numerical method has been developed for fully developed flows with constant wall temperature. • The governing equations were transformed to boundary fitted coordinates. • The Nusselt number of parabolic duct has been investigated. • Validation of the numerical method has been made by comparing published data. - Abstract: In motor-vehicles the use of more compact radiators have several advantages such as; improving the aerodynamic form of cars, reducing the weight and volume of the cars, reducing the material consumption and environmental pollutions, and enabling faster increase of the engine coolant temperature after starting to run and thereby improving the thermal efficiency. For the design of efficient and compact radiators, the robust determination of the heat transfer coefficient becomes imperative. In this study the external heat transfer coefficient of the radiator has been investigated for hydrodynamically and thermally fully developed flows in channels with constant wall temperature. In such situation the numerical treatment of the problem results in a trivial solution. To find a non-trivial solution the problem is treated either as an eigenvalue problem or as a thermally developing flow problem. In this study a numerical solution procedure has been developed and the heat transfer coefficients of the fully developed flow in triangular and parabolic air channels were investigated. The governing equations were transformed to boundary fitted coordinates and numerically solved. The non-trivial solution was obtained by means of guessing the temperature of any grid point within the solution domain. The correction of the guessed temperature was performed via smoothing the temperature profile on a line passing through the mentioned grid point. Results were compared with literature data and found to be consistent.

Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation

International Nuclear Information System (INIS)

Vasileva, D.P.

1993-01-01

Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u t = Δ u σ+1 + u β are found in the case β = σ + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case β>σ + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs

Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

International Nuclear Information System (INIS)

Yildirim, A.; Gökdoğan, A.; Merdan, M.; Lakshminarayanan, V.

2012-01-01

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge—Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms. (fundamental areas of phenomenology(including applications))

The numerical solution of thawing process in phase change slab using variable space grid technique

Directory of Open Access Journals (Sweden)

Serttikul, C.

2007-09-01

Full Text Available This paper focuses on the numerical analysis of melting process in phase change material which considers the moving boundary as the main parameter. In this study, pure ice slab and saturated porous packed bed are considered as the phase change material. The formulation of partial differential equations is performed consisting heat conduction equations in each phase and moving boundary equation (Stefan equation. The variable space grid method is then applied to these equations. The transient heat conduction equations and the Stefan condition are solved by using the finite difference method. A one-dimensional melting model is then validated against the available analytical solution. The effect of constant temperature heat source on melting rate and location of melting front at various times is studied in detail.It is found that the nonlinearity of melting rate occurs for a short time. The successful comparison with numerical solution and analytical solution should give confidence in the proposed mathematical treatment, and encourage the acceptance of this method as useful tool for exploring practical problems such as forming materials process, ice melting process, food preservation process and tissue preservation process.

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

Numerical solution of quadratic matrix equations for free vibration analysis of structures

Science.gov (United States)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

Coordinated Platoon Routing in a Metropolitan Network

Energy Technology Data Exchange (ETDEWEB)

Larson, Jeffrey; Munson, Todd; Sokolov, Vadim

2016-10-10

Platooning vehicles—connected and automated vehicles traveling with small intervehicle distances—use less fuel because of reduced aerodynamic drag. Given a network de- fined by vertex and edge sets and a set of vehicles with origin/destination nodes/times, we model and solve the combinatorial optimization problem of coordinated routing of vehicles in a manner that routes them to their destination on time while using the least amount of fuel. Common approaches decompose the platoon coordination and vehicle routing into separate problems. Our model addresses both problems simultaneously to obtain the best solution. We use modern modeling techniques and constraints implied from analyzing the platoon routing problem to address larger numbers of vehicles and larger networks than previously considered. While the numerical method used is unable to certify optimality for candidate solutions to all networks and parameters considered, we obtain excellent solutions in approximately one minute for much larger networks and vehicle sets than previously considered in the literature.

Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification

Energy Technology Data Exchange (ETDEWEB)

Blottner, F.G.; Lopez, A.R.

1998-10-01

This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

Science.gov (United States)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

Numerical modelling of coupled fluid, heat, and solute transport in deformable fractured rock

International Nuclear Information System (INIS)

Chan, T.; Reid, J.A.K.

1987-01-01

This paper reports on a three-dimensional (3D) finite-element code, MOTIF (model of transport in fractured/porous media), developed to model the coupled processes of groundwater flow, heat transport, brine transport, and one-species radionuclide transport in geological media. Three types of elements are available: a 3D continuum element, a planar fracture element that can be oriented in any arbitrary direction in 3D space or pipe flow in 3D space, and a line element for simulating fracture flow in 2D space or pipe flow in 3D space. As a quality-assurance measure, the MOTIF code was verified by comparison of its results with analytical solutions and other published numerical solutions

Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies

Science.gov (United States)

Fuller, Franklyn B.

1961-01-01

The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.

The development of high performance numerical simulation code for transient groundwater flow and reactive solute transport problems based on local discontinuous Galerkin method

International Nuclear Information System (INIS)

Suzuki, Shunichi; Motoshima, Takayuki; Naemura, Yumi; Kubo, Shin; Kanie, Shunji

2009-01-01

The authors develop a numerical code based on Local Discontinuous Galerkin Method for transient groundwater flow and reactive solute transport problems in order to make it possible to do three dimensional performance assessment on radioactive waste repositories at the earliest stage possible. Local discontinuous Galerkin Method is one of mixed finite element methods which are more accurate ones than standard finite element methods. In this paper, the developed numerical code is applied to several problems which are provided analytical solutions in order to examine its accuracy and flexibility. The results of the simulations show the new code gives highly accurate numeric solutions. (author)

Numerical Upscaling of Solute Transport in Fractured Porous Media Based on Flow Aligned Blocks

Science.gov (United States)

Leube, P.; Nowak, W.; Sanchez-Vila, X.

2013-12-01

High-contrast or fractured-porous media (FPM) pose one of the largest unresolved challenges for simulating large hydrogeological systems. The high contrast in advective transport between fast conduits and low-permeability rock matrix, including complex mass transfer processes, leads to the typical complex characteristics of early bulk arrivals and long tailings. Adequate direct representation of FPM requires enormous numerical resolutions. For large scales, e.g. the catchment scale, and when allowing for uncertainty in the fracture network architecture or in matrix properties, computational costs quickly reach an intractable level. In such cases, multi-scale simulation techniques have become useful tools. They allow decreasing the complexity of models by aggregating and transferring their parameters to coarser scales and so drastically reduce the computational costs. However, these advantages come at a loss of detail and accuracy. In this work, we develop and test a new multi-scale or upscaled modeling approach based on block upscaling. The novelty is that individual blocks are defined by and aligned with the local flow coordinates. We choose a multi-rate mass transfer (MRMT) model to represent the remaining sub-block non-Fickian behavior within these blocks on the coarse scale. To make the scale transition simple and to save computational costs, we capture sub-block features by temporal moments (TM) of block-wise particle arrival times to be matched with the MRMT model. By predicting spatial mass distributions of injected tracers in a synthetic test scenario, our coarse-scale solution matches reasonably well with the corresponding fine-scale reference solution. For predicting higher TM-orders (such as arrival time and effective dispersion), the prediction accuracy steadily decreases. This is compensated to some extent by the MRMT model. If the MRMT model becomes too complex, it loses its effect. We also found that prediction accuracy is sensitive to the choice of

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

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

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

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Optimality conditions for the numerical solution of optimization problems with PDE constraints :

Energy Technology Data Exchange (ETDEWEB)

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

Develop a solution for protecting and securing enterprise networks from malicious attacks

Science.gov (United States)

Kamuru, Harshitha; Nijim, Mais

2014-05-01

In the world of computer and network security, there are myriad ways to launch an attack, which, from the perspective of a network, can usually be defined as "traffic that has huge malicious intent." Firewall acts as one of the measure in order to secure the device from incoming unauthorized data. There are infinite number of computer attacks that no firewall can prevent, such as those executed locally on the machine by a malicious user. From the network's perspective, there are numerous types of attack. All the attacks that degrade the effectiveness of data can be grouped into two types: brute force and precision. The Firewall that belongs to Juniper has the capability to protect against both types of attack. Denial of Service (DoS) attacks are one of the most well-known network security threats under brute force attacks, which is largely due to the high-profile way in which they can affect networks. Over the years, some of the largest, most respected Internet sites have been effectively taken offline by Denial of Service (DOS) attacks. A DoS attack typically has a singular focus, namely, to cause the services running on a particular host or network to become unavailable. Some DoS attacks exploit vulnerabilities in an operating system and cause it to crash, such as the infamous Win nuke attack. Others submerge a network or device with traffic so that there are no more resources to handle legitimate traffic. Precision attacks typically involve multiple phases and often involves a bit more thought than brute force attacks, all the way from reconnaissance to machine ownership. Before a precision attack is launched, information about the victim needs to be gathered. This information gathering typically takes the form of various types of scans to determine available hosts, networks, and ports. The hosts available on a network can be determined by ping sweeps. The available ports on a machine can be located by port scans. Screens cover a wide variety of attack traffic

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

Science.gov (United States)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

A GPU-based solution for fast calculation of the betweenness centrality in large weighted networks

Directory of Open Access Journals (Sweden)

Rui Fan

2017-12-01

Full Text Available Betweenness, a widely employed centrality measure in network science, is a decent proxy for investigating network loads and rankings. However, its extremely high computational cost greatly hinders its applicability in large networks. Although several parallel algorithms have been presented to reduce its calculation cost for unweighted networks, a fast solution for weighted networks, which are commonly encountered in many realistic applications, is still lacking. In this study, we develop an efficient parallel GPU-based approach to boost the calculation of the betweenness centrality (BC for large weighted networks. We parallelize the traditional Dijkstra algorithm by selecting more than one frontier vertex each time and then inspecting the frontier vertices simultaneously. By combining the parallel SSSP algorithm with the parallel BC framework, our GPU-based betweenness algorithm achieves much better performance than its CPU counterparts. Moreover, to further improve performance, we integrate the work-efficient strategy, and to address the load-imbalance problem, we introduce a warp-centric technique, which assigns many threads rather than one to a single frontier vertex. Experiments on both realistic and synthetic networks demonstrate the efficiency of our solution, which achieves 2.9× to 8.44× speedups over the parallel CPU implementation. Our algorithm is open-source and free to the community; it is publicly available through https://dx.doi.org/10.6084/m9.figshare.4542405. Considering the pervasive deployment and declining price of GPUs in personal computers and servers, our solution will offer unprecedented opportunities for exploring betweenness-related problems and will motivate follow-up efforts in network science.

Strategies for optical transport network recovery under epidemic network failures

DEFF Research Database (Denmark)

Ruepp, Sarah Renée; Fagertun, Anna Manolova; Kosteas, Vasileios

2015-01-01

The current trend in deploying automatic control plane solutions for increased flexibility in the optical transport layer leads to numerous advantages for both the operators and the customers, but also pose challenges related to the stability of the network and its ability to operate in a robust...... manner under different failure scenarios. This work evaluates two rerouting strategies and proposes four policies for failure handling in a connection-oriented optical transport network, under generalized multiprotocol label switching control plane. The performance of the strategies and the policies......, and that there exist a clear trade-off between policy performance and network resource consumption, which must be addressed by network operators for improved robustness of their transport infrastructures. Applying proactive methods for avoiding areas where epidemic failures spread results in 50% less connections...

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

Directory of Open Access Journals (Sweden)

Panou G.

2017-02-01

Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

Wearable and Implantable Wireless Sensor Network Solutions for Healthcare Monitoring

Science.gov (United States)

Darwish, Ashraf; Hassanien, Aboul Ella

2011-01-01

Wireless sensor network (WSN) technologies are considered one of the key research areas in computer science and the healthcare application industries for improving the quality of life. The purpose of this paper is to provide a snapshot of current developments and future direction of research on wearable and implantable body area network systems for continuous monitoring of patients. This paper explains the important role of body sensor networks in medicine to minimize the need for caregivers and help the chronically ill and elderly people live an independent life, besides providing people with quality care. The paper provides several examples of state of the art technology together with the design considerations like unobtrusiveness, scalability, energy efficiency, security and also provides a comprehensive analysis of the various benefits and drawbacks of these systems. Although offering significant benefits, the field of wearable and implantable body sensor networks still faces major challenges and open research problems which are investigated and covered, along with some proposed solutions, in this paper. PMID:22163914

Wearable and implantable wireless sensor network solutions for healthcare monitoring.

Science.gov (United States)

Darwish, Ashraf; Hassanien, Aboul Ella

2011-01-01

Wireless sensor network (WSN) technologies are considered one of the key research areas in computer science and the healthcare application industries for improving the quality of life. The purpose of this paper is to provide a snapshot of current developments and future direction of research on wearable and implantable body area network systems for continuous monitoring of patients. This paper explains the important role of body sensor networks in medicine to minimize the need for caregivers and help the chronically ill and elderly people live an independent life, besides providing people with quality care. The paper provides several examples of state of the art technology together with the design considerations like unobtrusiveness, scalability, energy efficiency, security and also provides a comprehensive analysis of the various benefits and drawbacks of these systems. Although offering significant benefits, the field of wearable and implantable body sensor networks still faces major challenges and open research problems which are investigated and covered, along with some proposed solutions, in this paper.

Numerical solution of kinetics equation for point defects accumulation in metals under irradiation

International Nuclear Information System (INIS)

Aldzhambekova, G.T.; Iskakov, B.M.

1999-01-01

In the report the mathematical model, describing processes of generation and accumulation of defects in solids under irradiation is considered. The equations of this model take into account the velocity of Frenkel pairs generation, the mutual recombination of vacancies and the interstitials, as well as velocity of defects absorption by discharge channeling of vacancies and interstitials. By Runge-Kutta method the numerical solution of the model was carried out

Numerical Solutions of Mechanical Turbulent Filtration Equation Used in Mechatronics and Micro Mechanic

OpenAIRE

Hassan Fathabadi

2013-01-01

In this study, several novel numerical solutions are presented to solve the turbulent filtration equation and its special case called “Non-Newtonian mechanical filtration equation”. The turbulent filtration equation in porous media is a very important equation which has many applications to solve the problems appearing especially in mechatronics, micro mechanic and fluid mechanic. Many applied mechanical problems can be solved using this equation. For example, non-Newtonian mechanical filtrat...

Hydrologic behavior of fracture networks

International Nuclear Information System (INIS)

Long, J.C.S.; Endo, H.K.; Karasaki, K.; Pyrak, L.; MacLean, P.; Witherspoon, P.A.

1985-01-01

This paper reviews recent research on the nature of flow and transport in discontinuous fracture networks. The hydrologic behavior of these networks has been examined using two- and three-dimensional numerical models. The numerical models represent random realizations of fracture networks based on statistical field measurements of fracture geometry and equivalent hydraulic aperture. The authors have compared the flux and mechanical transported behavior of these networks to the behavior of equivalent continua. In this way they were able to determine whether a given fracture network could be modeled as an equivalent porous media in both flux and advective transport studies. They have examined departures from porous media behavior both as a function of interconnectivity and heterogeneity. Parameter studies have revealed behavior patterns such as: given a fracture frequency that can be measured in the field, porous media like behavior and the magnitude of permeability are both enhanced if the fractures are longer and the standard deviation of fracture permeabilities is smaller. The behavior of well tests in fractured networks has been modeled and compared to a new analytical well test solution which accounts for the early time dominance of the fractures intersecting the well. Finally, a three-dimensional fracture flow model has been constructed which assumes fractures are randomly located discs. This model has been constructed which assumes fractures are randomly located discs. This model uses a semi-analytical solution for flow such that it is relatively easy to use the model as a tool for stochastic analysis. 13 references, 12 figures

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

International Nuclear Information System (INIS)

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

1991-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1991-02-01

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

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

Science.gov (United States)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Application of synthetic diffusion method in the numerical solution of the equations of neutron transport in slab geometry

International Nuclear Information System (INIS)

Valdes Parra, J.J.

1986-01-01

One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)

Numerical Leak Detection in a Pipeline Network of Complex Structure with Unsteady Flow

Science.gov (United States)

Aida-zade, K. R.; Ashrafova, E. R.

2017-12-01

An inverse problem for a pipeline network of complex loopback structure is solved numerically. The problem is to determine the locations and amounts of leaks from unsteady flow characteristics measured at some pipeline points. The features of the problem include impulse functions involved in a system of hyperbolic differential equations, the absence of classical initial conditions, and boundary conditions specified as nonseparated relations between the states at the endpoints of adjacent pipeline segments. The problem is reduced to a parametric optimal control problem without initial conditions, but with nonseparated boundary conditions. The latter problem is solved by applying first-order optimization methods. Results of numerical experiments are presented.

Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...

Numerical doubly-periodic solution of the (2+1)-dimensional Boussinesq equation with initial conditions by the variational iteration method

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

In this Letter, a scheme is developed to study numerical doubly-periodic solutions of the (2+1)-dimensional Boussinesq equation with initial condition by the variational iteration method. As a result, the approximate and exact doubly-periodic solutions are obtained. For different modulus m, comparison between the approximate solution and the exact solution is made graphically, revealing that the variational iteration method is a powerful and effective tool to non-linear problems

Salpeter equation in position space: Numerical solution for arbitrary confining potentials

International Nuclear Information System (INIS)

Nickisch, L.J.; Durand, L.; Durand, B.

1984-01-01

We present and test two new methods for the numerical solution of the relativistic wave equation [(-del 2 +m 1 2 )/sup 1/2/+(-del 2 +m 2 2 )/sup 1/2/+V(r)-M]psi( r ) = 0, which appears in the theory of relativistic quark-antiquark bound states. Our methods work directly in position space, and hence have the desirable features that we can vary the potential V(r) locally in fitting the qq-bar mass spectrum, and can easily build in the expected behavior of V for r→0,infinity. Our first method converts the nonlocal square-root operators to mildly singular integral operators involving hyperbolic Bessel functions. The resulting integral equation can be solved numerically by matrix techniques. Our second method approximates the square-root operators directly by finite matrices. Both methods converge rapidly with increasing matrix size (the square-root matrix method more rapidly) and can be used in fast-fitting routines. We present some tests for oscillator and Coulomb interactions, and for the realistic Coulomb-plus-linear potential used in qq-bar phenomenology

Numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities

International Nuclear Information System (INIS)

Milioli, F.E.

1985-01-01

In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Science.gov (United States)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

Science.gov (United States)

Mohebbi, Akbar

2018-02-01

In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

Numerical fluid solutions for nonlocal electron transport in hot plasmas: Equivalent diffusion versus nonlocal source

International Nuclear Information System (INIS)

Colombant, Denis; Manheimer, Wallace

2010-01-01

Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion solution, namely treating the transport as only a diffusion process. We introduce here a new approach called the nonlocal source solution and show it is numerically viable for laser produced plasmas. It turns out that the equivalent diffusion solution generally underestimates preheat. Furthermore, the advance of the temperature front, and especially the preheat, can be held up by artificial 'thermal barriers'. The nonlocal source method of solution, on the other hand more accurately describes preheat and can stably calculate the solution for the temperature even if the heat flux is up the gradient.

Network Simulation solution of free convective flow from a vertical cone with combined effect of non- uniform surface heat flux and heat generation or absorption

Science.gov (United States)

Immanuel, Y.; Pullepu, Bapuji; Sambath, P.

2018-04-01

A two dimensional mathematical model is formulated for the transitive laminar free convective, incompressible viscous fluid flow over vertical cone with variable surface heat flux combined with the effects of heat generation and absorption is considered . using a powerful computational method based on thermoelectric analogy called Network Simulation Method (NSM0, the solutions of governing nondimensionl coupled, unsteady and nonlinear partial differential conservation equations of the flow that are obtained. The numerical technique is always stable and convergent which establish high efficiency and accuracy by employing network simulator computer code Pspice. The effects of velocity and temperature profiles have been analyzed for various factors, namely Prandtl number Pr, heat flux power law exponent n and heat generation/absorption parameter Δ are analyzed graphically.

Convergence and periodic solutions for the input impedance of a standard ladder network

International Nuclear Information System (INIS)

Ucak, C; Acar, C

2007-01-01

The input impedance of an infinite ladder network is computed by using the recursive relation and by assuming that the input impedance does not change when a new block is added to the network. However, this assumption is not true in general and standard textbooks do not always treat these networks correctly. This paper develops a general solution to obtain the input impedance of a standard ladder network of impedances and admittances for any number of blocks. Then, this result is used to provide the convergence condition for the infinite ladder network. The conditions which lead to periodic input impedance are exploited. It is shown that there are infinite numbers of periodic points and no paradoxical behaviour exists in the standard ladder network

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

Science.gov (United States)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

Science.gov (United States)

Bian, Wei; Ma, Litao; Qin, Sitian; Xue, Xiaoping

2018-05-01

In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included. Copyright © 2018 Elsevier Ltd. All rights reserved.

Security in software-defined wireless sensor networks: threats, challenges and potential solutions

CSIR Research Space (South Africa)

Pritchard, SW

2017-07-01

Full Text Available have focused on low resource cryptography methods to secure the network [27] - [29], [33]. Cryptography methods are separated into symmetric cryptography and asymmetric cryptography. While symmetric cryptography solutions are preferred due to low... implementation cost and efficiency [5], they present many problems when managing large networks and attempts to improve this cryptography for WSNs [11] have resulted in the cost of resources. Symmetric cryptography is also difficult to implement in software...

Analytical solution and numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe

Science.gov (United States)

Cai, Haibing; Xu, Liuxun; Yang, Yugui; Li, Longqi

2018-05-01

Artificial liquid nitrogen freezing technology is widely used in urban underground engineering due to its technical advantages, such as simple freezing system, high freezing speed, low freezing temperature, high strength of frozen soil, and absence of pollution. However, technical difficulties such as undefined range of liquid nitrogen freezing and thickness of frozen wall gradually emerge during the application process. Thus, the analytical solution of the freezing-temperature field of a single pipe is established considering the freezing temperature of soil and the constant temperature of freezing pipe wall. This solution is then applied in a liquid nitrogen freezing project. Calculation results show that the radius of freezing front of liquid nitrogen is proportional to the square root of freezing time. The radius of the freezing front also decreases with decreased the freezing temperature, and the temperature gradient of soil decreases with increased distance from the freezing pipe. The radius of cooling zone in the unfrozen area is approximately four times the radius of the freezing front. Meanwhile, the numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe is conducted using the Abaqus finite-element program. Results show that the numerical simulation of soil temperature distribution law well agrees with the analytical solution, further verifies the reliability of the established analytical solution of the liquid nitrogen freezing-temperature field of a single pipe.

Human-computer interfaces applied to numerical solution of the Plateau problem

Science.gov (United States)

Elias Fabris, Antonio; Soares Bandeira, Ivana; Ramos Batista, Valério

2015-09-01

In this work we present a code in Matlab to solve the Problem of Plateau numerically, and the code will include human-computer interface. The Problem of Plateau has applications in areas of knowledge like, for instance, Computer Graphics. The solution method will be the same one of the Surface Evolver, but the difference will be a complete graphical interface with the user. This will enable us to implement other kinds of interface like ocular mouse, voice, touch, etc. To date, Evolver does not include any graphical interface, which restricts its use by the scientific community. Specially, its use is practically impossible for most of the Physically Challenged People.

Automated smoother for the numerical decoupling of dynamics models.

Science.gov (United States)

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

2007-08-21

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

Business Collaboration in Food Networks: Incremental Solution Development

Directory of Open Access Journals (Sweden)

Harald Sundmaeker

2014-10-01

Full Text Available The paper will present an approach for an incremental solution development that is based on the usage of the currently developed Internet based FIspace business collaboration platform. Key element is the clear segmentation of infrastructures that are either internal or external to the collaborating business entity in the food network. On the one hand, the approach enables to differentiate between specific centralised as well as decentralised ways for data storage and hosting of IT based functionalities. The selection of specific dataexchange protocols and data models is facilitated. On the other hand, the supported solution design and subsequent development is focusing on reusable “software Apps” that can be used on their own and are incorporating a clear added value for the business actors. It will be outlined on how to push the development and introduction of Apps that do not require basic changes of the existing infrastructure. The paper will present an example that is based on the development of a set of Apps for the exchange of product quality related information in food networks, specifically addressing fresh fruits and vegetables. It combines workflow support for data exchange from farm to retail as well as to provide quality feedback information to facilitate the business process improvement. Finally, the latest status of theFIspace platform development will be outlined. Key features and potential ways for real users and software developers in using the FIspace platform that is initiated by science and industry will be outlined.

An Explicit Finite Difference scheme for numerical solution of fractional neutron point kinetic equation

International Nuclear Information System (INIS)

Saha Ray, S.; Patra, A.

2012-01-01

Highlights: ► In this paper fractional neutron point kinetic equation has been analyzed. ► The numerical solution for fractional neutron point kinetic equation is obtained. ► Explicit Finite Difference Method has been applied. ► Supercritical reactivity, critical reactivity and subcritical reactivity analyzed. ► Comparison between fractional and classical neutron density is presented. - Abstract: In the present article, a numerical procedure to efficiently calculate the solution for fractional point kinetics equation in nuclear reactor dynamics is investigated. The Explicit Finite Difference Method is applied to solve the fractional neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (). Fractional Neutron Point Kinetic Model has been analyzed for the dynamic behavior of the neutron motion in which the relaxation time associated with a variation in the neutron flux involves a fractional order acting as exponent of the relaxation time, to obtain the best operation of a nuclear reactor dynamics. Results for neutron dynamic behavior for subcritical reactivity, supercritical reactivity and critical reactivity and also for different values of fractional order have been presented and compared with the classical neutron point kinetic (NPK) equation as well as the results obtained by the learned researchers .

Numerical and analytical solutions for problems relevant for quantum computers

International Nuclear Information System (INIS)

Spoerl, Andreas

2008-01-01

Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)

Neural Network for Sparse Reconstruction

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Qingfa Li

2014-01-01

Full Text Available We construct a neural network based on smoothing approximation techniques and projected gradient method to solve a kind of sparse reconstruction problems. Neural network can be implemented by circuits and can be seen as an important method for solving optimization problems, especially large scale problems. Smoothing approximation is an efficient technique for solving nonsmooth optimization problems. We combine these two techniques to overcome the difficulties of the choices of the step size in discrete algorithms and the item in the set-valued map of differential inclusion. In theory, the proposed network can converge to the optimal solution set of the given problem. Furthermore, some numerical experiments show the effectiveness of the proposed network in this paper.

Experimental and Numerical Investigation of Preferential Flow in Fractured Network with Clogging Process

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Xiaobing Chen

2014-01-01

Full Text Available In this study, physical experiments and numerical simulations are combined to provide a detailed understanding of flow dynamics in fracture network. Hydraulic parameters such as pressure head, velocity field, Reynolds number on certain monitoring cross points, and total flux rate are examined under various clogging conditions. Applying the COMSOL Multiphysics code to solve the Navier-Stokes equation instead of Reynolds equation and using the measured data to validate the model, the fluid flow in the horizontal 2D cross-sections of the fracture network was simulated. Results show that local clogging leads to a significant reshaping of the flow velocity field and a reduction of the transport capacity of the entire system. The flow rate distribution is highly influenced by the fractures connected to the dominant flow channels, although local disturbances in velocity field are unlikely to spread over the whole network. Also, modeling results indicate that water flow in a fracture network, compared with that in a single fracture, is likely to transit into turbulence earlier under the same hydraulic gradient due to the influence of fracture intersections.

Periodic solution for state-dependent impulsive shunting inhibitory CNNs with time-varying delays.

Science.gov (United States)

Şaylı, Mustafa; Yılmaz, Enes

2015-08-01

In this paper, we consider existence and global exponential stability of periodic solution for state-dependent impulsive shunting inhibitory cellular neural networks with time-varying delays. By means of B-equivalence method, we reduce these state-dependent impulsive neural networks system to an equivalent fix time impulsive neural networks system. Further, by using Mawhin's continuation theorem of coincide degree theory and employing a suitable Lyapunov function some new sufficient conditions for existence and global exponential stability of periodic solution are obtained. Previous results are improved and extended. Finally, we give an illustrative example with numerical simulations to demonstrate the effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Wearable and Implantable Wireless Sensor Network Solutions for Healthcare Monitoring

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Ashraf Darwish

2011-05-01

Full Text Available Wireless sensor network (WSN technologies are considered one of the key research areas in computer science and the healthcare application industries for improving the quality of life. The purpose of this paper is to provide a snapshot of current developments and future direction of research on wearable and implantable body area network systems for continuous monitoring of patients. This paper explains the important role of body sensor networks in medicine to minimize the need for caregivers and help the chronically ill and elderly people live an independent life, besides providing people with quality care. The paper provides several examples of state of the art technology together with the design considerations like unobtrusiveness, scalability, energy efficiency, security and also provides a comprehensive analysis of the various benefits and drawbacks of these systems. Although offering significant benefits, the field of wearable and implantable body sensor networks still faces major challenges and open research problems which are investigated and covered, along with some proposed solutions, in this paper.

Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification

Science.gov (United States)

Rehman, Khalil Ur; Malik, M. Y.; Khan, Abid Ali; Zehra, Iffat; Zahri, Mostafa; Tahir, M.

2017-12-01

We have found that only a few attempts are available in the literature relatively to the tangent hyperbolic fluid flow induced by stretching cylindrical surfaces. In particular, temperature and concentration stratification effects have not been investigated until now with respect to the tangent hyperbolic fluid model. Therefore, we have considered the tangent hyperbolic fluid flow induced by an acutely inclined cylindrical surface in the presence of both temperature and concentration stratification effects. To be more specific, the fluid flow is attained with the no slip condition, which implies that the bulk motion of the fluid particles is the same as the stretching velocity of a cylindrical surface. Additionally, the flow field situation is manifested with heat generation, mixed convection and chemical reaction effects. The flow partial differential equations give a complete description of the present problem. Therefore, to trace out the solution, a set of suitable transformations is introduced to convert these equations into ordinary differential equations. In addition, a self-coded computational algorithm is executed to inspect the numerical solution of these reduced equations. The effect logs of the involved parameters are provided graphically. Furthermore, the variations of the physical quantities are examined and given with the aid of tables. It is observed that the fluid temperature is a decreasing function of the thermal stratification parameter and a similar trend is noticed for the concentration via the solutal stratification parameter.

An efficient approach to the numerical solution of rate-independent problems with nonconvex energies

Czech Academy of Sciences Publication Activity Database

Bartels, S.; Kružík, Martin

2011-01-01

Roč. 9, č. 3 (2011), s. 1275-1300 ISSN 1540-3459 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : numerical solution * nonconvexity Subject RIV: BA - General Mathematics Impact factor: 2.009, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/kruzik-0364707.pdf

New results of almost periodic solutions for cellular neural networks with mixed delays

International Nuclear Information System (INIS)

Zhao Weirui; Zhang Huanshui

2009-01-01

In this paper, for cellular neural networks with mixed delays, we prove some new results on the existence of almost periodic solutions by contraction principle. The global exponential stability of almost periodic solutions is discussed further, and conditions for exponential convergence are given. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases.

A network of experimental forests and ranges: Providing soil solutions for a changing world

Science.gov (United States)

Mary Beth. Adams

2010-01-01

The network of experimental forests and ranges of the USDA Forest Service represents significant opportunities to provide soil solutions to critical issues of a changing world. This network of 81 experimental forests and ranges encompasses broad geographic, biological, climatic and physical scales, and includes long-term data sets, and long-term experimental...

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

Science.gov (United States)

Keslerová, Radka; Trdlička, David

2015-09-01

This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

Science.gov (United States)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

Science.gov (United States)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Numerical solution of the helmholtz equation for the superellipsoid via the galerkin method

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Hy Dinh

2013-01-01

Full Text Available The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation for a smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: $x=cos(xsin(y^{n},y=sin(xsin(y^{n},z=cos(y$ where $n$ varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green's theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala , Warnapala and Morgan .

Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models

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Gajda Paweł

2016-01-01

Full Text Available Monte Carlo methodology provides reference statistical solution of neutron transport criticality problems of nuclear systems. Estimated reaction rates can be applied as an input to Bateman equations that govern isotopic evolution of reactor materials. Because statistical solution of Boltzmann equation is computationally expensive, it is in practice applied to time steps of limited length. In this paper we show that simple staircase step model leads to underprediction of numerical fuel burnup (Fissions per Initial Metal Atom – FIMA. Theoretical considerations indicates that this error is inversely proportional to the length of the time step and origins from the variation of heating per source neutron. The bias can be diminished by application of predictor-corrector step model. A set of burnup simulations with various step length and coupling schemes has been performed. SERPENT code version 1.17 has been applied to the model of a typical fuel assembly from Pressurized Water Reactor. In reference case FIMA reaches 6.24% that is equivalent to about 60 GWD/tHM of industrial burnup. The discrepancies up to 1% have been observed depending on time step model and theoretical predictions are consistent with numerical results. Conclusions presented in this paper are important for research and development concerning nuclear fuel cycle also in the context of Gen4 systems.

Numerical solutions of the N-body problem

International Nuclear Information System (INIS)

Marciniak, A.

1985-01-01

Devoted to the study of numerical methods for solving the general N-body problem and related problems, this volume starts with an overview of the conventional numerical methods for solving the initial value problem. The major part of the book contains original work and features a presentation of special numerical methods conserving the constants of motion in the general N-body problem and methods conserving the Jacobi constant in the problem of motion of N bodies in a rotating frame, as well as an analysis of the applications of both (conventional and special) kinds of methods for solving these problems. For all the methods considered, the author presents algorithms which are easily programmable in any computer language. Moreover, the author compares various methods and presents adequate numerical results. The appendix contains PL/I procedures for all the special methods conserving the constants of motion. 91 refs.; 35 figs.; 41 tabs

Domain wall networks on solitons

International Nuclear Information System (INIS)

Sutcliffe, Paul

2003-01-01

Domain wall networks on the surface of a soliton are studied in a simple theory. It consists of two complex scalar fields, in 3+1 dimensions, with a global U(1)xZ n symmetry, where n>2. Solutions are computed numerically in which one of the fields forms a Q ball and the other field forms a network of domain walls localized on the surface of the Q ball. Examples are presented in which the domain walls lie along the edges of a spherical polyhedron, forming junctions at its vertices. It is explained why only a small restricted class of polyhedra can arise as domain wall networks

Topological inversion for solution of geodesy-constrained geophysical problems

Science.gov (United States)

Saltogianni, Vasso; Stiros, Stathis

2015-04-01

Geodetic data, mostly GPS observations, permit to measure displacements of selected points around activated faults and volcanoes, and on the basis of geophysical models, to model the underlying physical processes. This requires inversion of redundant systems of highly non-linear equations with >3 unknowns; a situation analogous to the adjustment of geodetic networks. However, in geophysical problems inversion cannot be based on conventional least-squares techniques, and is based on numerical inversion techniques (a priori fixing of some variables, optimization in steps with values of two variables each time to be regarded fixed, random search in the vicinity of approximate solutions). Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solutions with poor error control (usually sampling-based approaches). To overcome these problems, a numerical-topological, grid-search based technique in the RN space is proposed (N the number of unknown variables). This technique is in fact a generalization and refinement of techniques used in lighthouse positioning and in some cases of low-accuracy 2-D positioning using Wi-Fi etc. The basic concept is to assume discrete possible ranges of each variable, and from these ranges to define a grid G in the RN space, with some of the gridpoints to approximate the true solutions of the system. Each point of hyper-grid G is then tested whether it satisfies the observations, given their uncertainty level, and successful grid points define a sub-space of G containing the true solutions. The optimal (minimal) space containing one or more solutions is obtained using a trial-and-error approach, and a single optimization factor. From this essentially deterministic identification of the set of gridpoints satisfying the system of equations, at a following step, a stochastic optimal solution is computed corresponding to the center of gravity of this set of gridpoints. This solution corresponds to a

Numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1982-01-01

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

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

Science.gov (United States)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Numerical solution of the Schrodinger equation for stationary bound states using nodel theorem

International Nuclear Information System (INIS)

Chen Zhijiang; Kong Fanmei; Din Yibin

1987-01-01

An iterative procedure for getting the numerical solution of Schrodinger equation on stationary bound states is introduced. The theoretical foundtion, the practical steps and the method are presented. An example is added at the end. Comparing with other methods, the present one requires less storage, less running time but posesses higher accuracy. It can be run on the personal computer or microcomputer with 256 K memory and 16 bit word length such as IBM/PC, MC68000/83/20, PDP11/23 etc

Highway Passenger Transport Based Express Parcel Service Network Design: Model and Algorithm

Directory of Open Access Journals (Sweden)

Yuan Jiang

2017-01-01

Full Text Available Highway passenger transport based express parcel service (HPTB-EPS is an emerging business that uses unutilised room of coach trunk to ship parcels between major cities. While it is reaping more and more express market, the managers are facing difficult decisions to design the service network. This paper investigates the HPTB-EPS network design problem and analyses the time-space characteristics of such network. A mixed-integer programming model is formulated integrating the service decision, frequency, and network flow distribution. To solve the model, a decomposition-based heuristic algorithm is designed by decomposing the problem as three steps: construction of service network, service path selection, and distribution of network flow. Numerical experiment using real data from our partner company demonstrates the effectiveness of our model and algorithm. We found that our solution could reduce the total cost by up to 16.3% compared to the carrier’s solution. The sensitivity analysis demonstrates the robustness and flexibility of the solutions of the model.

On the numerical solution of the neutron fractional diffusion equation

International Nuclear Information System (INIS)

Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto

2014-01-01

Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative

Continuum Modeling of Biological Network Formation

KAUST Repository

Albi, Giacomo

2017-04-10

We present an overview of recent analytical and numerical results for the elliptic–parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transportation networks. The model describes the pressure field using a Darcy type equation and the dynamics of the conductance network under pressure force effects. Randomness in the material structure is represented by a linear diffusion term and conductance relaxation by an algebraic decay term. We first introduce micro- and mesoscopic models and show how they are connected to the macroscopic PDE system. Then, we provide an overview of analytical results for the PDE model, focusing mainly on the existence of weak and mild solutions and analysis of the steady states. The analytical part is complemented by extensive numerical simulations. We propose a discretization based on finite elements and study the qualitative properties of network structures for various parameter values.

Applications of Operator-Splitting Methods to the Direct Numerical Simulation of Particulate and Free-Surface Flows and to the Numerical Solution of the Two-Dimensional Elliptic Monge--Ampère Equation

OpenAIRE

Glowinski, R.; Dean, E.J.; Guidoboni, G.; Juárez, L.H.; Pan, T.-W.

2008-01-01

The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge--Ampère equation. The results of numerical ...

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Science.gov (United States)

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.

Mean-field learning for satisfactory solutions

KAUST Repository

Tembine, Hamidou

2013-12-01

One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.

The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1995-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs

Simulation of two-phase flow in horizontal fracture networks with numerical manifold method

Science.gov (United States)

Ma, G. W.; Wang, H. D.; Fan, L. F.; Wang, B.

2017-10-01

The paper presents simulation of two-phase flow in discrete fracture networks with numerical manifold method (NMM). Each phase of fluids is considered to be confined within the assumed discrete interfaces in the present method. The homogeneous model is modified to approach the mixed fluids. A new mathematical cover formation for fracture intersection is proposed to satisfy the mass conservation. NMM simulations of two-phase flow in a single fracture, intersection, and fracture network are illustrated graphically and validated by the analytical method or the finite element method. Results show that the motion status of discrete interface significantly depends on the ratio of mobility of two fluids rather than the value of the mobility. The variation of fluid velocity in each fracture segment and the driven fluid content are also influenced by the ratio of mobility. The advantages of NMM in the simulation of two-phase flow in a fracture network are demonstrated in the present study, which can be further developed for practical engineering applications.

Training Recurrent Networks

DEFF Research Database (Denmark)

Pedersen, Morten With

1997-01-01

Training recurrent networks is generally believed to be a difficult task. Excessive training times and lack of convergence to an acceptable solution are frequently reported. In this paper we seek to explain the reason for this from a numerical point of view and show how to avoid problems when...... training. In particular we investigate ill-conditioning, the need for and effect of regularization and illustrate the superiority of second-order methods for training...

Localization and Communication for UWB-based Wireless Sensor Networks

NARCIS (Netherlands)

Wang, Y.

2011-01-01

The great demand for location-aware wireless sensor networks (WSNs) motivates the research in this thesis. The unique characteristics of WSNs impose numerous challenges on localization and communication. In this thesis, we handle some key challenges and provide affordable solutions. Impulse radio

Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ

DEFF Research Database (Denmark)

Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A

2012-01-01

This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of der...... in solution of partial differential equations (PDEs).......This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...

Dual-mode ultraflow access networks: a hybrid solution for the access bottleneck

Science.gov (United States)

Kazovsky, Leonid G.; Shen, Thomas Shunrong; Dhaini, Ahmad R.; Yin, Shuang; De Leenheer, Marc; Detwiler, Benjamin A.

2013-12-01

Optical Flow Switching (OFS) is a promising solution for large Internet data transfers. In this paper, we introduce UltraFlow Access, a novel optical access network architecture that offers dual-mode service to its end-users: IP and OFS. With UltraFlow Access, we design and implement a new dual-mode control plane and a new dual-mode network stack to ensure efficient connection setup and reliable and optimal data transmission. We study the impact of the UltraFlow system's design on the network throughput. Our experimental results show that with an optimized system design, near optimal (around 10 Gb/s) OFS data throughput can be attained when the line rate is 10Gb/s.

The Numerical Solution of the Navier-Stokes Equations for Laminar, Incompressible Flow past a Parabolic Cylinder

NARCIS (Netherlands)

Botta, E.F.F.; Dijkstra, D.; Veldman, A.E.P.

1972-01-01

The numerical method of solution for the semi-infinite flat plate has been extended to the case of the parabolic cylinder. Results are presented for the skin friction, the friction drag, the pressure and the pressure drag. The drag coefficients have been checked by means of an application of the

Fluid and solute transport in a network of channels

International Nuclear Information System (INIS)

Moreno, L.; Neretnieks, I.

1991-09-01

A three-dimensional channel network model is presented. The fluid flow and solute transport are assumed to take place through a network of connected channels. The channels are generated assuming that the conductances are lognormally distributed. The flow is calculated resolving the pressure distribution and the sole transport is calculated by using a particle tracking technique. The model includes diffusion into the rock matrix and sorption within the matrix in addition to advection along the channel network. Different approaches are used to describe the channel volume and its relation to the conductivity. To quantify the diffusion into the rock matrix the size of the flow wetted surface (contact surface between the channel and the rock) is needed in addition to the diffusion properties and the sorption capacity of the rock. Two different geometries were simulated: regional parallel flow and convergent flow toward a tunnel. In the generation of the channel network, it is found that its connectivity is reduced when the standard deviation in conductances is increased. For large standard deviations, the water conducting channels are found to be few. Standard deviations for the distribution of the effluent channel flowrates were calculated. Comparisons were made with experimental data from drifts and tunnels as well as boreholes as a means to validate the model. (au) (31 refs.)

Generalized master equations for non-Poisson dynamics on networks.

Science.gov (United States)

Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

2012-10-01

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

Analytic models for the evolution of semilocal string networks

International Nuclear Information System (INIS)

Nunes, A. S.; Martins, C. J. A. P.; Avgoustidis, A.; Urrestilla, J.

2011-01-01

We revisit previously developed analytic models for defect evolution and adapt them appropriately for the study of semilocal string networks. We thus confirm the expectation (based on numerical simulations) that linear scaling evolution is the attractor solution for a broad range of model parameters. We discuss in detail the evolution of individual semilocal segments, focusing on the phenomenology of segment growth, and also provide a preliminary comparison with existing numerical simulations.

Solution methods for compartment models of transport through the environment using numerical inversion of Laplace transforms

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

Compartment models for the transport of radionuclides in the biosphere are conventionally solved using a numerical time-stepping procedure. This report examines an alternative method based on the numerical inversion of Laplace transforms, which is potentially more efficient and accurate for some classes of problem. The central problem considered is the most efficient and robust technique for solving the Laplace-transformed rate equations. The conclusion is that Gaussian elimination is the most efficient and robust solution method. A general compartment model has been implemented on a personal computer and used to solve a realistic case including radionuclide decay chains. (author)

Some properties of band matrix and its application to the numerical solution one-dimensional Bratu's problem

Directory of Open Access Journals (Sweden)

Reza Jalilian

2014-07-01

Full Text Available ‎A Class of new methods based on a septic non-polynomial spline‎‎function for the numerical solution one-dimensional Bratu's problem‎are presented‎. ‎The local truncation errors and the methods of order‎‎2th‎, ‎4th‎, ‎6th‎, ‎8th‎, ‎10th‎, ‎and 12th‎, ‎are obtained‎. ‎The inverse of‎some band matrixes are obtained which are required in provingthe‎ convergence analysis of the presented method‎. ‎Associatedboundary‎ formulas are developed‎. ‎Convergence analysis of thesemethods is‎ discussed‎. ‎Numerical results are given to illustrate theefficiency‎ of methods‎.

INTERCONNECTING NETWORKS WITH DIFFERENT LEVELS OF SECURITY – A PRESENT NATO PROBLEM

Directory of Open Access Journals (Sweden)

LIVIU TATOMIR

2016-07-01

Full Text Available A situation often met in the Romanian Armed Forces in recent years is the need for interconnecting two networks (domains with different levels of classification. Considering that the Romanian armed troops are involved in numerous missions with NATO partners, solutions, already implemented across the organization, are considered to be applied in domestic systems, also. This paper presents the solutions adopted by NATO in order to solve the problem of cross -domains interconnections. We present the maturity level reached by these solutions and the possibility of implementing these solutions in the Romanian Armed Forces, with or without specific adaptation to our own rules and regulations. The goal is to use a NATO already proved solution to our national classified networks.

Numerical modelling of solute transport at Forsmark with MIKE SHE. Site descriptive modelling SDM-Site Forsmark

Energy Technology Data Exchange (ETDEWEB)

Gustafsson, Lars-Goeran; Sassner, Mona (DHI Sverige AB, Stockholm (Sweden)); Bosson, Emma (Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden))

2008-12-15

The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site investigations at two different locations in Sweden, referred to as the Forsmark and Laxemar areas, with the objective of siting a final repository for high-level radioactive waste. Data from the site investigations are used in a variety of modelling activities. This report presents model development and results of numerical transport modelling based on the numerical flow modelling of surface water and near-surface groundwater at the Forsmark site. The numerical modelling was performed using the modelling tool MIKE SHE and is based on the site data and conceptual model of the Forsmark areas. This report presents solute transport applications based on both particle tracking simulations and advection-dispersion calculations. The MIKE SHE model is the basis for the transport modelling presented in this report. Simulation cases relevant for the transport from a deep geological repository have been studied, but also the pattern of near surface recharge and discharge areas. When the main part of the modelling work presented in this report was carried out, the flow modelling of the Forsmark site was not finalised. Thus, the focus of this work is to describe the sensitivity to different transport parameters, and not to point out specific areas as discharge areas from a future repository (this is to be done later, within the framework of the safety assessment). In the last chapter, however, results based on simulations with the re-calibrated MIKE SHE flow model are presented. The results from the MIKE SHE water movement calculations were used by cycling the calculated transient flow field for a selected one-year period as many times as needed to achieve the desired simulation period. The solute source was located either in the bedrock or on top of the model. In total, 15 different transport simulation cases were studied. Five of the simulations were particle tracking simulations, whereas the rest

A novel recurrent neural network with finite-time convergence for linear programming.

Science.gov (United States)

Liu, Qingshan; Cao, Jinde; Chen, Guanrong

2010-11-01

In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

Homogenized blocked arcs for multicriteria optimization of radiotherapy: Analytical and numerical solutions

International Nuclear Information System (INIS)

Fenwick, John D.; Pardo-Montero, Juan

2010-01-01

Purpose: Homogenized blocked arcs are intuitively appealing as basis functions for multicriteria optimization of rotational radiotherapy. Such arcs avoid an organ-at-risk (OAR), spread dose out well over the rest-of-body (ROB), and deliver homogeneous doses to a planning target volume (PTV) using intensity modulated fluence profiles, obtainable either from closed-form solutions or iterative numerical calculations. Here, the analytic and iterative arcs are compared. Methods: Dose-distributions have been calculated for nondivergent beams, both including and excluding scatter, beam penumbra, and attenuation effects, which are left out of the derivation of the analytic arcs. The most straightforward analytic arc is created by truncating the well-known Brahme, Roos, and Lax (BRL) solution, cutting its uniform dose region down from an annulus to a smaller nonconcave region lying beyond the OAR. However, the truncation leaves behind high dose hot-spots immediately on either side of the OAR, generated by very high BRL fluence levels just beyond the OAR. These hot-spots can be eliminated using alternative analytical solutions ''C'' and ''L,'' which, respectively, deliver constant and linearly rising fluences in the gap region between the OAR and PTV (before truncation). Results: Measured in terms of PTV dose homogeneity, ROB dose-spread, and OAR avoidance, C solutions generate better arc dose-distributions than L when scatter, penumbra, and attenuation are left out of the dose modeling. Including these factors, L becomes the best analytical solution. However, the iterative approach generates better dose-distributions than any of the analytical solutions because it can account and compensate for penumbra and scatter effects. Using the analytical solutions as starting points for the iterative methodology, dose-distributions almost as good as those obtained using the conventional iterative approach can be calculated very rapidly. Conclusions: The iterative methodology is

Analytical solution and numerical study on water hammer in a pipeline closed with an elastically attached valve

Science.gov (United States)

Henclik, Sławomir

2018-03-01

The influence of dynamic fluid-structure interaction (FSI) onto the course of water hammer (WH) can be significant in non-rigid pipeline systems. The essence of this effect is the dynamic transfer of liquid energy to the pipeline structure and back, which is important for elastic structures and can be negligible for rigid ones. In the paper a special model of such behavior is analyzed. A straight pipeline with a steady flow, fixed to the floor with several rigid supports is assumed. The transient is generated by a quickly closed valve installed at the end of the pipeline. FSI effects are assumed to be present mainly at the valve which is fixed with a spring dash-pot attachment. Analysis of WH runs, especially transient pressure changes, for various stiffness and damping parameters of the spring dash-pot valve attachment is presented in the paper. The solutions are found analytically and numerically. Numerical results have been computed with the use of an own computer program developed on the basis of the four equation model of WH-FSI and the specific boundary conditions formulated at the valve. Analytical solutions have been found with the separation of variables method for slightly simplified assumptions. Damping at the dash-pot is taken into account within the numerical study. The influence of valve attachment parameters onto the WH courses was discovered and it was found the transient amplitudes can be reduced. Such a system, elastically attached shut-off valve in a pipeline or other, equivalent design can be a real solution applicable in practice.

Numerical simulations of coupled problems in engineering

CERN Document Server

2014-01-01

This book presents and discusses mathematical models, numerical methods and computational techniques used for solving coupled problems in science and engineering. It takes a step forward in the formulation and solution of real-life problems with a multidisciplinary vision, accounting for all of the complex couplings involved in the physical description. Simulation of multifaceted physics problems is a common task in applied research and industry. Often a suitable solver is built by connecting together several single-aspect solvers into a network. In this book, research in various fields was selected for consideration: adaptive methodology for multi-physics solvers, multi-physics phenomena and coupled-field solutions, leading to computationally intensive structural analysis. The strategies which are used to keep these problems computationally affordable are of special interest, and make this an essential book.

Stability of Almost Periodic Solution for a General Class of Discontinuous Neural Networks with Mixed Time-Varying Delays

Directory of Open Access Journals (Sweden)

Yingwei Li

2013-01-01

Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.

The numerical solution of linear multi-term fractional differential equations: systems of equations

Science.gov (United States)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Existence and stability of periodic solution in impulsive Hopfield neural networks with finite distributed delays

International Nuclear Information System (INIS)

Yang Xiaofan; Liao Xiaofeng; Evans, David J.; Tang Yuanyan

2005-01-01

In this Letter, we introduce a class of Hopfield neural networks with periodic impulses and finite distributed delays. We then derive a sufficient condition for the existence and global exponential stability of a unique periodic solution of the networks, which assumes neither the differentiability nor the monotonicity of the activation functions. Our condition extends and generalizes a known condition for the global exponential periodicity of continuous Hopfield neural networks with finite distributed delays

Numerical analysis

CERN Document Server

Brezinski, C

2012-01-01

Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

Science.gov (United States)

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally

Link importance incorporated failure probability measuring solution for multicast light-trees in elastic optical networks

Science.gov (United States)

Li, Xin; Zhang, Lu; Tang, Ying; Huang, Shanguo

2018-03-01

The light-tree-based optical multicasting (LT-OM) scheme provides a spectrum- and energy-efficient method to accommodate emerging multicast services. Some studies focus on the survivability technologies for LTs against a fixed number of link failures, such as single-link failure. However, a few studies involve failure probability constraints when building LTs. It is worth noting that each link of an LT plays different important roles under failure scenarios. When calculating the failure probability of an LT, the importance of its every link should be considered. We design a link importance incorporated failure probability measuring solution (LIFPMS) for multicast LTs under independent failure model and shared risk link group failure model. Based on the LIFPMS, we put forward the minimum failure probability (MFP) problem for the LT-OM scheme. Heuristic approaches are developed to address the MFP problem in elastic optical networks. Numerical results show that the LIFPMS provides an accurate metric for calculating the failure probability of multicast LTs and enhances the reliability of the LT-OM scheme while accommodating multicast services.

Stable architectures for deep neural networks

Science.gov (United States)

Haber, Eldad; Ruthotto, Lars

2018-01-01

Deep neural networks have become invaluable tools for supervised machine learning, e.g. classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in data, deep architectures are known to be challenging to design and train such that they generalize well to new data. Critical issues with deep architectures are numerical instabilities in derivative-based learning algorithms commonly called exploding or vanishing gradients. In this paper, we propose new forward propagation techniques inspired by systems of ordinary differential equations (ODE) that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks. The backbone of our approach is our interpretation of deep learning as a parameter estimation problem of nonlinear dynamical systems. Given this formulation, we analyze stability and well-posedness of deep learning and use this new understanding to develop new network architectures. We relate the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and present several strategies for stabilizing deep learning for very deep networks. While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

Directory of Open Access Journals (Sweden)

Fukang Yin

2013-01-01

Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems

International Nuclear Information System (INIS)

Anastassi, Z. A.; Simos, T. E.

2010-01-01

We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.

Two numerical methods for the solution of two-dimensional eddy current problems

International Nuclear Information System (INIS)

Biddlecombe, C.S.

1978-07-01

A general method for the solution of eddy current problems in two dimensions - one component of current density and two of magnetic field, is reported. After examining analytical methods two numerical methods are presented. Both solve the two dimensional, low frequency limit of Maxwell's equations for transient eddy currents in conducting material, which may be permeable, in the presence of other non-conducting permeable material. Both solutions are expressed in terms of the magnetic vector potential. The first is an integral equation method, using zero order elements in the discretisation of the unknown source regions. The other is a differential equation method, using a first order finite element mesh, and the Galerkin weighted residual procedure. The resulting equations are solved as initial-value problems. Results from programs based on each method are presented showing the power and limitations of the methods and the range of problems solvable. The methods are compared and recommendations are made for choosing between them. Suggestions are made for improving both methods, involving boundary integral techniques. (author)

The numerical solution of the Navier-Stokes equations for laminar incompressible flow past a paraboloid of revolution

NARCIS (Netherlands)

Veldman, A.E.P.

1973-01-01

A numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

International Nuclear Information System (INIS)

Jo, Jong Chull; Shin, Won Ky

1997-01-01

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available

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

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

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

Numerical solution to a multi-dimensional linear inverse heat conduction problem by a splitting-based conjugate gradient method

International Nuclear Information System (INIS)

Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem

2008-01-01

In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by aids of an adjoint problem and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.

Numerical modelling of solute transport at Forsmark with MIKE SHE. Site descriptive modelling SDM-Site Forsmark

International Nuclear Information System (INIS)

Gustafsson, Lars-Goeran; Sassner, Mona; Bosson, Emma

2008-12-01

The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site investigations at two different locations in Sweden, referred to as the Forsmark and Laxemar areas, with the objective of siting a final repository for high-level radioactive waste. Data from the site investigations are used in a variety of modelling activities. This report presents model development and results of numerical transport modelling based on the numerical flow modelling of surface water and near-surface groundwater at the Forsmark site. The numerical modelling was performed using the modelling tool MIKE SHE and is based on the site data and conceptual model of the Forsmark areas. This report presents solute transport applications based on both particle tracking simulations and advection-dispersion calculations. The MIKE SHE model is the basis for the transport modelling presented in this report. Simulation cases relevant for the transport from a deep geological repository have been studied, but also the pattern of near surface recharge and discharge areas. When the main part of the modelling work presented in this report was carried out, the flow modelling of the Forsmark site was not finalised. Thus, the focus of this work is to describe the sensitivity to different transport parameters, and not to point out specific areas as discharge areas from a future repository (this is to be done later, within the framework of the safety assessment). In the last chapter, however, results based on simulations with the re-calibrated MIKE SHE flow model are presented. The results from the MIKE SHE water movement calculations were used by cycling the calculated transient flow field for a selected one-year period as many times as needed to achieve the desired simulation period. The solute source was located either in the bedrock or on top of the model. In total, 15 different transport simulation cases were studied. Five of the simulations were particle tracking simulations, whereas the rest

Numerical relativity

CERN Document Server

Shibata, Masaru

2016-01-01

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

Numerical analysis

CERN Document Server

Khabaza, I M

1960-01-01

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

A link prediction method for heterogeneous networks based on BP neural network

Science.gov (United States)

Li, Ji-chao; Zhao, Dan-ling; Ge, Bing-Feng; Yang, Ke-Wei; Chen, Ying-Wu

2018-04-01

Most real-world systems, composed of different types of objects connected via many interconnections, can be abstracted as various complex heterogeneous networks. Link prediction for heterogeneous networks is of great significance for mining missing links and reconfiguring networks according to observed information, with considerable applications in, for example, friend and location recommendations and disease-gene candidate detection. In this paper, we put forward a novel integrated framework, called MPBP (Meta-Path feature-based BP neural network model), to predict multiple types of links for heterogeneous networks. More specifically, the concept of meta-path is introduced, followed by the extraction of meta-path features for heterogeneous networks. Next, based on the extracted meta-path features, a supervised link prediction model is built with a three-layer BP neural network. Then, the solution algorithm of the proposed link prediction model is put forward to obtain predicted results by iteratively training the network. Last, numerical experiments on the dataset of examples of a gene-disease network and a combat network are conducted to verify the effectiveness and feasibility of the proposed MPBP. It shows that the MPBP with very good performance is superior to the baseline methods.

WaterNet: The NASA water cycle solutions network - Danubian regional applications

International Nuclear Information System (INIS)

Matthews, Dave; Brilly, Mitja; Kobold, Mira; Zagar, Mark; Houser, Paul

2008-01-01

WaterNet is a new international network of researchers, stakeholders, and end-users of remote sensing tools that will benefit the water resources management community. This paper provides an overview and it discusses the concept of solutions networks focusing on the WaterNet. It invites Danubian research and applications teams to join our WaterNet network. The NASA Water cycle Solutions Network's goal is to improve and optimize the sustained ability of water cycle researchers, stakeholders, organizations and networks to interact, identify, harness, and extend NASA research results to augment decision support tools and meet national needs. Our team will develop WaterNet by engaging relevant NASA water cycle research resources and community-of-practice organizations, to develop what we term an 'actionable database' that can be used to communicate and connect NASA Water cycle research Results (NWRs) towards the improvement of water-related Decision Support Tools (DSTs). Recognizing that the European Commission and European Space Agency have also developed many related Water Research products (EWRs), we seek to learn about these and network with the EU teams to include their information in the WaterNet actionable data base and Community of Practice. WaterNet will then develop strategies to connect researchers and decision-makers via innovative communication strategies, improved user access to NASA and EU - Danubian resources, improved water cycle research community appreciation for user requirements, improved policymaker, management and stakeholder knowledge of research and application products, and improved identification of pathways for progress. Finally, WaterNet will develop relevant benchmarking and metrics, to understand the network's characteristics, to optimize its performance, and to establish sustainability. This paper provides examples of several NASA products based on remote sensing and land data assimilation systems that integrate remotely sensed and in

Solution of weakly compressible isothermal flow in landfill gas collection networks

Science.gov (United States)

Nec, Y.; Huculak, G.

2017-12-01

Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy-Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein.

Numerical study of partitions effect on multiplicity of solutions in an infinite channel periodically heated from below

International Nuclear Information System (INIS)

Abourida, B.; Hasnaoui, M.

2005-01-01

Laminar natural convection in an infinite horizontal channel heated periodically from below and provided with thin adiabatic partitions on its lower wall, is investigated numerically. The effect of these partitions on the multiplicity of solutions and heat transfer characteristics in the computational domain is studied. The parameters of the study are the Rayleigh number (10 2 Ra 4.9 x 10 6 ) and the height of the partitions (0 B = h'/H' 1/2). The results obtained in the case of air (Pr = 0.72) as working fluid show that depending on the governing parameters, the existence of multiple solutions is possible. Important differences in terms of heat transfer are observed between two different solutions

An Algorithm for the Mixed Transportation Network Design Problem.

Science.gov (United States)

Liu, Xinyu; Chen, Qun

2016-01-01

This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.

An Algorithm for the Mixed Transportation Network Design Problem.

Directory of Open Access Journals (Sweden)

Xinyu Liu

Full Text Available This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA, for solving a mixed transportation network design problem (MNDP, which is generally expressed as a mathematical programming with equilibrium constraint (MPEC. The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium (UE problem. The idea of the proposed solution algorithm (DDIA is to reduce the dimensions of the problem. A group of variables (discrete/continuous is fixed to optimize another group of variables (continuous/discrete alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems and DNDPs (discrete network design problems repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions. Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.

Incentive-Based Voltage Regulation in Distribution Networks

Energy Technology Data Exchange (ETDEWEB)

Dall-Anese, Emiliano [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Baker, Kyri A [National Renewable Energy Laboratory (NREL), Golden, CO (United States); Zhou, Xinyang [University of Colorado; Chen, Lijun [University of Colorado

2017-07-03

This paper considers distribution networks fea- turing distributed energy resources, and designs incentive-based mechanisms that allow the network operator and end-customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Two different network-customer coordination mechanisms that require different amounts of information shared between the network operator and end-customers are developed to identify a solution of a well-defined social-welfare maximization prob- lem. Notably, the signals broadcast by the network operator assume the connotation of prices/incentives that induce the end- customers to adjust the generated/consumed powers in order to avoid the violation of the voltage constraints. Stability of the proposed schemes is analytically established and numerically corroborated.

New convergence behavior of solutions to Cohen-Grossberg neural networks with delays and time-varying coefficients

International Nuclear Information System (INIS)

Liu Bingwen

2008-01-01

In this Letter the convergence behavior of Cohen-Grossberg neural networks with delays and time-varying coefficients are considered. Some sufficient conditions are established to ensure that the solutions of the networks converge locally exponentially to zero point, which are new and complement of previously known results

Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations

Czech Academy of Sciences Publication Activity Database

Papež, Jan; Liesen, J.; Strakoš, Z.

2014-01-01

Roč. 449, 15 May (2014), s. 89-114 ISSN 0024-3795 R&D Projects: GA AV ČR IAA100300802; GA ČR GA201/09/0917 Grant - others:GA MŠk(CZ) LL1202; GA UK(CZ) 695612 Institutional support: RVO:67985807 Keywords : numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebra ic error * spatial distribution of the error Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

An Energy-Efficient Cluster-Based Vehicle Detection on Road Network Using Intention Numeration Method

Directory of Open Access Journals (Sweden)

Deepa Devasenapathy

2015-01-01

Full Text Available The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.

An energy-efficient cluster-based vehicle detection on road network using intention numeration method.

Science.gov (United States)

Devasenapathy, Deepa; Kannan, Kathiravan

2015-01-01

The traffic in the road network is progressively increasing at a greater extent. Good knowledge of network traffic can minimize congestions using information pertaining to road network obtained with the aid of communal callers, pavement detectors, and so on. Using these methods, low featured information is generated with respect to the user in the road network. Although the existing schemes obtain urban traffic information, they fail to calculate the energy drain rate of nodes and to locate equilibrium between the overhead and quality of the routing protocol that renders a great challenge. Thus, an energy-efficient cluster-based vehicle detection in road network using the intention numeration method (CVDRN-IN) is developed. Initially, sensor nodes that detect a vehicle are grouped into separate clusters. Further, we approximate the strength of the node drain rate for a cluster using polynomial regression function. In addition, the total node energy is estimated by taking the integral over the area. Finally, enhanced data aggregation is performed to reduce the amount of data transmission using digital signature tree. The experimental performance is evaluated with Dodgers loop sensor data set from UCI repository and the performance evaluation outperforms existing work on energy consumption, clustering efficiency, and node drain rate.

Optimization with PDE constraints ESF networking program 'OPTPDE'

CERN Document Server

2014-01-01

This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).

A new fuzzy mathematical model for green supply chain network design

Directory of Open Access Journals (Sweden)

Mohsen Sadegh Amalnick

2017-01-01

Full Text Available The environmental changes caused by industrial activities have spurred a significant interest in designing supply chain networks by considering environmental issues such as CO2 emission. The pivotal role of taking uncertainty and risk into account in closed-loop supply chain networks has induced numerous researchers and practitioners to develop appropriate decision making tools to cope with these issues in such networks. To design a supply chain regarding environmental impacts under uncertainty of the input data and to cope with the operational risks, this paper proposes a multi objective possibilistic optimization model. The proposed model minimizes traditional costs such as cost of products shipment, purchasing machines and so on, as well as minimizing the environmental impact, and as a results strikes a balance between the two objective functions. Furthermore, in order to solve the proposed multi objective fuzzy mathematical programming model, an interactive fuzzy solution approach is applied. Numerical experiments are used to prove the applicability and feasibility of the developed possibilistic programming model and the usefulness of the applied hybrid solution approach.

Global existence of periodic solutions of BAM neural networks with variable coefficients

International Nuclear Information System (INIS)

Guo Shangjiang; Huang Lihong; Dai Binxiang; Zhang Zhongzhi

2003-01-01

In this Letter, we study BAM (bidirectional associative memory) networks with variable coefficients. By some spectral theorems and a continuation theorem based on coincidence degree, we not only obtain some new sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified for the globally Lipschitz and the spectral radius being less than 1. Therefore, our results should be useful in the design and applications of periodic oscillatory neural circuits for neural networks with delays

Implementation and Performance Evaluation of Distributed Cloud Storage Solutions using Random Linear Network Coding

DEFF Research Database (Denmark)

Fitzek, Frank; Toth, Tamas; Szabados, Áron

2014-01-01

This paper advocates the use of random linear network coding for storage in distributed clouds in order to reduce storage and traffic costs in dynamic settings, i.e. when adding and removing numerous storage devices/clouds on-the-fly and when the number of reachable clouds is limited. We introduce...... various network coding approaches that trade-off reliability, storage and traffic costs, and system complexity relying on probabilistic recoding for cloud regeneration. We compare these approaches with other approaches based on data replication and Reed-Solomon codes. A simulator has been developed...... to carry out a thorough performance evaluation of the various approaches when relying on different system settings, e.g., finite fields, and network/storage conditions, e.g., storage space used per cloud, limited network use, and limited recoding capabilities. In contrast to standard coding approaches, our...

Global convergence of periodic solution of neural networks with discontinuous activation functions

International Nuclear Information System (INIS)

Huang Lihong; Guo Zhenyuan

2009-01-01

In this paper, without assuming boundedness and monotonicity of the activation functions, we establish some sufficient conditions ensuring the existence and global asymptotic stability of periodic solution of neural networks with discontinuous activation functions by using the Yoshizawa-like theorem and constructing proper Lyapunov function. The obtained results improve and extend previous works.

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1994-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

Energy Technology Data Exchange (ETDEWEB)

Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)

1994-12-31

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

International Nuclear Information System (INIS)

Khotylev, V.A.; Hoogenboom, J.E.

1996-01-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

Energy Technology Data Exchange (ETDEWEB)

Khotylev, V.A.; Hoogenboom, J.E. [Delft Univ. of Technology, Interfaculty Reactor Inst., Delft (Netherlands)

1996-07-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

Conductivity enhancement of silver nanowire networks via simple electrolyte solution treatment and solvent washing

Science.gov (United States)

Gu, Jiahui; Wang, Xuelin; Chen, Hongtao; Yang, Shihua; Feng, Huanhuan; Ma, Xing; Ji, Hongjun; Wei, Jun; Li, Mingyu

2018-06-01

As a promising replacement material for indium tin oxide in flexible electronics, silver nanowires (AgNWs) usually need complicated post-treatment to reduce the high contact resistance across the intersections when used as transparent conductive films. In this work, a widely applicable nano-joining method for improving the overall conductivity of AgNW networks with different kinds of electrolyte solutions is presented. By treatment with an electrolyte solution with appropriate ionic strengths, the insulating surfactant layer (polyvinylpyrrolidone, PVP) on the AgNWs could be desorbed, and the AgNW network could be densified. The sheet resistance of the AgNW film on a glass slide is reduced by 60.9% (from 67.5 to 26.4 Ohm sq‑1) with a transmittance of 92.5%. High-resolution transmission electron microscopy analysis indicates that atomic diffusion occurs at the intersection of two AgNWs. Thus, metallurgical bonding on the nanometer scale is achieved across the junctions of the AgNWs, leading to a significant enhancement in the conductivity of the AgNW network.

Solution of weakly compressible isothermal flow in landfill gas collection networks

Energy Technology Data Exchange (ETDEWEB)

Nec, Y [Thompson Rivers University, Kamloops, British Columbia (Canada); Huculak, G, E-mail: cranberryana@gmail.com, E-mail: greg@gnhconsulting.ca [GNH Consulting, Delta, British Columbia (Canada)

2017-12-15

Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy–Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein. (paper)

Solution of weakly compressible isothermal flow in landfill gas collection networks

International Nuclear Information System (INIS)

Nec, Y; Huculak, G

2017-01-01

Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy–Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein. (paper)

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1998-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1997-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

Cerebellum-inspired neural network solution of the inverse kinematics problem.

Science.gov (United States)

Asadi-Eydivand, Mitra; Ebadzadeh, Mohammad Mehdi; Solati-Hashjin, Mehran; Darlot, Christian; Abu Osman, Noor Azuan

2015-12-01

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

A Practical Solution for Time Synchronization in Wireless Sensor Networks

Directory of Open Access Journals (Sweden)

COCA, E.

2012-11-01

Full Text Available Time synchronization in wireless sensor node networks is a hot topic. Many papers present various software algorithms and hardware solutions to keep accurate time information on mobile nodes. In terms of real life applications wireless sensor nodes are preferred in many domains, starting with simple room monitoring and finishing with pipeline surveillance projects. Positioning applications are far more restrictive on timekeeping accuracy, as for the velocity of nodes calculations precise time or time difference values are needed. The accuracy of time information on nodes has to be always correlated with the application requirements. In this paper, we present some considerations regarding time synchronization linked with specific needs for individual practical applications. A practical low energy method of time keeping at node level is proposed and tested. The performances of the proposed solution in terms of short and long term stability and energy requirements are analyzed and compared with existing solutions. Simulation and experimental results, some advantages and disadvantages of the method are presented at the end of the paper.

Green mobile networks a networking perspective

CERN Document Server

Ansari, Nirwan

2016-01-01

Combines the hot topics of energy efficiency and next generation mobile networking, examining techniques and solutions. Green communications is a very hot topic. Ever increasing mobile network bandwidth rates significantly impacts on operating costs due to aggregate network energy consumption. As such, design on 4G networks and beyond has increasingly started to focus on 'energy efficiency' or so-called 'green' networks. Many techniques and solutions have been proposed to enhance the energy efficiency of mobile networks, yet no book has provided an in-depth analysis of the energy consumption issues in mobile networks nor offers detailed theories, tools and solutions for solving the energy efficiency problems.

Periodicity and stability for variable-time impulsive neural networks.

Science.gov (United States)

Li, Hongfei; Li, Chuandong; Huang, Tingwen

2017-10-01

The paper considers a general neural networks model with variable-time impulses. It is shown that each solution of the system intersects with every discontinuous surface exactly once via several new well-proposed assumptions. Moreover, based on the comparison principle, this paper shows that neural networks with variable-time impulse can be reduced to the corresponding neural network with fixed-time impulses under well-selected conditions. Meanwhile, the fixed-time impulsive systems can be regarded as the comparison system of the variable-time impulsive neural networks. Furthermore, a series of sufficient criteria are derived to ensure the existence and global exponential stability of periodic solution of variable-time impulsive neural networks, and to illustrate the same stability properties between variable-time impulsive neural networks and the fixed-time ones. The new criteria are established by applying Schaefer's fixed point theorem combined with the use of inequality technique. Finally, a numerical example is presented to show the effectiveness of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

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

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

in developing of this work are presented. In Appendix B a general list of computer program is given, in Appendix C analytical solutions for two simple problems are presented and finally in appendix D some concepts and definitions about numerical stability are given. It can also be mentioned that computer code has no limitation with to number of regions and number of energy groups. Furnishing cross sections, the computer program gives the following results. 1) Angular flux when a problem with independent source without fissions are considered, 2) number of secondary neutrons for collition or 3) effective multiplication factor (Author)

Numerical solution of a flow inside a labyrinth seal

Directory of Open Access Journals (Sweden)

Šimák Jan

2012-04-01

Full Text Available The aim of this study is a behaviour of a flow inside a labyrinth seal on a rotating shaft. The labyrinth seal is a type of a non-contact seal where a leakage of a fluid is prevented by a rather complicated path, which the fluid has to overcome. In the presented case the sealed medium is the air and the seal is made by a system of 20 teeth on a rotating shaft situated against a smooth static surface. Centrifugal forces present due to the rotation of the shaft create vortices in each chamber and thus dissipate the axial velocity of the escaping air.The structure of the flow field inside the seal is studied through the use of numerical methods. Three-dimensional solution of the Navier-Stokes equations for turbulent flow is very time consuming. In order to reduce the computational time we can simplify our problem and solve it as an axisymmetric problem in a two-dimensional meridian plane. For this case we use a transformation of the Navier-Stokes equations and of the standard k-omega turbulence model into a cylindrical coordinate system. A finite volume method is used for the solution of the resulting problem. A one-side modification of the Riemann problem for boundary conditions is used at the inlet and at the outlet of the axisymmetric channel. The total pressure and total density (temperature are to be used preferably at the inlet whereas the static pressure is used at the outlet for the compatibility. This idea yields physically relevant boundary conditions. The important characteristics such as a mass flow rate and a power loss, depending on a pressure ratio (1.1 - 4 and an angular velocity (1000 - 15000 rpm are evaluated.

Numerical analysis of the chimera states in the multilayered network model

Science.gov (United States)

Goremyko, Mikhail V.; Maksimenko, Vladimir A.; Makarov, Vladimir V.; Ghosh, Dibakar; Bera, Bidesh K.; Dana, Syamal K.; Hramov, Alexander E.

2017-03-01

We numerically study the interaction between the ensembles of the Hindmarsh-Rose (HR) neuron systems, arranged in the multilayer network model. We have shown that the fully identical layers, demonstrated individually different chimera due to the initial mismatch, come to the identical chimera state with the increase of inter-layer coupling. Within the multilayer model we also consider the case, when the one layer demonstrates chimera state, while another layer exhibits coherent or incoherent dynamics. It has been shown that the interactions chimera-coherent state and chimera-incoherent state leads to the both excitation of chimera as from the ensemble of fully coherent or incoherent oscillators, and suppression of initially stable chimera state

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

Science.gov (United States)

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

2017-01-01

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

Numerical calculations on heterogeneity of groundwater flow

International Nuclear Information System (INIS)

Follin, S.

1992-01-01

The upscaling of model parameters is a key issue in many research fields concerned with parameter heterogeneity. The upscaling process allows for fewer model blocks and relaxes the numerical problems caused by high contrasts in the hydraulic conductivity. The trade-offs are dependent on the object but the general drawback is an increasing uncertainty about the representativeness. The present study deals with numerical calculations of heterogeneity of groundwater flow and solute transport in hypothetical blocks of fractured hard rock in a '3m scale' and addresses both conceptual and practical problems in numerical simulation. Evidence that the hydraulic conductivity (K) of the rock mass between major fracture zones is highly heterogeneous in a 3m scale is provided by a large number of field investigations. The present uses the documented heterogeneity and investigates flow and transport in a two-dimensional stochastic continuum characterized by a variance in Y = In(K) of σ y 2 = 16, corresponding to about 12 log 10 cycles in K. The study considers anisotropy, channelling, non-Fickian and Fickian transport, and conditional simulation. The major conclusions are: * heterogeneity gives rise to anisotropy in the upscaling process, * the choice of support scale is crucial for the modelling of solute transport. As a consequence of the obtained results, a two-dimensional stochastic discontinuum model is presented, which provides a tool for linking stochastic continuum models to discrete fracture network models. (au) (14 figs., 136 refs.)

New numerical methods for open-loop and feedback solutions to dynamic optimization problems

Science.gov (United States)

Ghosh, Pradipto

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development

Discrete convolution-operators and radioactive disintegration. [Numerical solution

Energy Technology Data Exchange (ETDEWEB)

Kalla, S L; VALENTINUZZI, M E [UNIVERSIDAD NACIONAL DE TUCUMAN (ARGENTINA). FACULTAD DE CIENCIAS EXACTAS Y TECNOLOGIA

1975-08-01

The basic concepts of discrete convolution and discrete convolution-operators are briefly described. Then, using the discrete convolution - operators, the differential equations associated with the process of radioactive disintegration are numerically solved. The importance of the method is emphasized to solve numerically, differential and integral equations.

Incentive-Based Voltage Regulation in Distribution Networks: Preprint

Energy Technology Data Exchange (ETDEWEB)

Zhou, Xinyang; Chen, Lijun; Dall' Anese, Emiliano; Baker, Kyri

2017-03-03

This paper considers distribution networks fea- turing distributed energy resources, and designs incentive-based mechanisms that allow the network operator and end-customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Two different network-customer coordination mechanisms that require different amounts of information shared between the network operator and end-customers are developed to identify a solution of a well-defined social-welfare maximization prob- lem. Notably, the signals broadcast by the network operator assume the connotation of prices/incentives that induce the end- customers to adjust the generated/consumed powers in order to avoid the violation of the voltage constraints. Stability of the proposed schemes is analytically established and numerically corroborated.

Direct numerical simulation of cellular-scale blood flow in microvascular networks

Science.gov (United States)

Balogh, Peter; Bagchi, Prosenjit

2017-11-01

A direct numerical simulation method is developed to study cellular-scale blood flow in physiologically realistic microvascular networks that are constructed in silico following published in vivo images and data, and are comprised of bifurcating, merging, and winding vessels. The model resolves large deformation of individual red blood cells (RBC) flowing in such complex networks. The vascular walls and deformable interfaces of the RBCs are modeled using the immersed-boundary methods. Time-averaged hemodynamic quantities obtained from the simulations agree quite well with published in vivo data. Our simulations reveal that in several vessels the flow rates and pressure drops could be negatively correlated. The flow resistance and hematocrit are also found to be negatively correlated in some vessels. These observations suggest a deviation from the classical Poiseuille's law in such vessels. The cells are observed to frequently jam at vascular bifurcations resulting in reductions in hematocrit and flow rate in the daughter and mother vessels. We find that RBC jamming results in several orders of magnitude increase in hemodynamic resistance, and thus provides an additional mechanism of increased in vivo blood viscosity as compared to that determined in vitro. Funded by NSF CBET 1604308.

Numerical simulation of shower cooling tower based on artificial neural network

International Nuclear Information System (INIS)

Qi Xiaoni; Liu Zhenyan; Li Dandan

2008-01-01

This study was prompted by the need to design towers for applications in which, due to salt deposition on the packing and subsequent blockage, the use of tower packing is not practical. The cooling tower analyzed in this study is void of fill, named shower cooling tower (SCT). However, the present study focuses mostly on experimental investigation of the SCT, and no systematic numerical method is available. In this paper, we first developed a one dimensional model and analyzed the heat and mass transfer processes of the SCT; then we used the concept of artificial neural network (ANN) to propose a computer design tool that can help the designer evaluate the outlet water temperature from a given set of experimentally obtained data. For comparison purposes and accurate evaluation of the predictions, part of the experimental data was used to train the neural network and the remainder to test the model. The results predicted by the ANN model were compared with those of the standard model and the experimental data. The ANN model predicted the outlet water temperature with a MAE (mean absolute error) of 1.31%, whereas the standard one dimensional model showed a MAE of 9.42%

Wireless three-hop networks with stealing II : exact solutions through boundary value problems

NARCIS (Netherlands)

Guillemin, F.; Knessl, C.; Leeuwaarden, van J.S.H.

2013-01-01

We study the stationary distribution of a random walk in the quarter plane arising in the study of three-hop wireless networks with stealing. Our motivation is to find exact tail asymptotics (beyond logarithmic estimates) for the marginal distributions, which requires an exact solution for the

A neural network based implementation of an MPC algorithm applied in the control systems of electromechanical plants

Science.gov (United States)

Marusak, Piotr M.; Kuntanapreeda, Suwat

2018-01-01

The paper considers application of a neural network based implementation of a model predictive control (MPC) control algorithm to electromechanical plants. Properties of such control plants implicate that a relatively short sampling time should be used. However, in such a case, finding the control value numerically may be too time-consuming. Therefore, the current paper tests the solution based on transforming the MPC optimization problem into a set of differential equations whose solution is the same as that of the original optimization problem. This set of differential equations can be interpreted as a dynamic neural network. In such an approach, the constraints can be introduced into the optimization problem with relative ease. Moreover, the solution of the optimization problem can be obtained faster than when the standard numerical quadratic programming routine is used. However, a very careful tuning of the algorithm is needed to achieve this. A DC motor and an electrohydraulic actuator are taken as illustrative examples. The feasibility and effectiveness of the proposed approach are demonstrated through numerical simulations.

Born approximation to a perturbative numerical method for the solution of the Schroedinger equation

International Nuclear Information System (INIS)

Adam, Gh.

1978-01-01

A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)

Unifying Pore Network Modeling, Continuous Time Random Walk (CTRW) Theory and Experiment to Describe Impact of Spatial Heterogeneities on Solute Dispersion at Multiple Length-scales

Science.gov (United States)

Bijeljic, B.; Blunt, M. J.; Rhodes, M. E.

2009-04-01

This talk will describe and highlight the advantages offered by a novel methodology that unifies pore network modeling, CTRW theory and experiment in description of solute dispersion in porous media. Solute transport in a porous medium is characterized by the interplay of advection and diffusion (described by Peclet number, Pe) that cause dispersion of solute particles. Dispersion is traditionally described by dispersion coefficients, D, that are commonly calculated from the spatial moments of the plume. Using a pore-scale network model based on particle tracking, the rich Peclet-number dependence of dispersion coefficient is predicted from first principles and is shown to compare well with experimental data for restricted diffusion, transition, power-law and mechanical dispersion regimes in the asymptotic limit. In the asymptotic limit D is constant and can be used in an averaged advection-dispersion equation. However, it is highly important to recognize that, until the velocity field is fully sampled, the particle transport is non-Gaussian and D possesses temporal or spatial variation. Furthermore, temporal probability density functions (PDF) of tracer particles are studied in pore networks and an excellent agreement for the spectrum of transition times for particles from pore to pore is obtained between network model results and CTRW theory. Based on the truncated power-law interpretation of PDF-s, the physical origin of the power-law scaling of dispersion coefficient vs. Peclet number has been explained for unconsolidated porous media, sands and a number of sandstones, arriving at the same conclusion from numerical network modelling, analytic CTRW theory and experiment. The length traveled by solute plumes before Gaussian behaviour is reached increases with an increase in heterogeneity and/or Pe. This opens up the question on the nature of dispersion in natural systems where the heterogeneities at the larger scales will significantly increase the range of

A simulated annealing approach for redesigning a warehouse network problem

Science.gov (United States)

Khairuddin, Rozieana; Marlizawati Zainuddin, Zaitul; Jiun, Gan Jia

2017-09-01

Now a day, several companies consider downsizing their distribution networks in ways that involve consolidation or phase-out of some of their current warehousing facilities due to the increasing competition, mounting cost pressure and taking advantage on the economies of scale. Consequently, the changes on economic situation after a certain period of time require an adjustment on the network model in order to get the optimal cost under the current economic conditions. This paper aimed to develop a mixed-integer linear programming model for a two-echelon warehouse network redesign problem with capacitated plant and uncapacitated warehouses. The main contribution of this study is considering capacity constraint for existing warehouses. A Simulated Annealing algorithm is proposed to tackle with the proposed model. The numerical solution showed the model and method of solution proposed was practical.

Spread of epidemic disease on networks

Science.gov (United States)

Newman, M. E.

2002-07-01

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

Methods of numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1983-01-01

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

A One-Layer Recurrent Neural Network for Constrained Complex-Variable Convex Optimization.

Science.gov (United States)

Qin, Sitian; Feng, Jiqiang; Song, Jiahui; Wen, Xingnan; Xu, Chen

2018-03-01

In this paper, based on calculus and penalty method, a one-layer recurrent neural network is proposed for solving constrained complex-variable convex optimization. It is proved that for any initial point from a given domain, the state of the proposed neural network reaches the feasible region in finite time and converges to an optimal solution of the constrained complex-variable convex optimization finally. In contrast to existing neural networks for complex-variable convex optimization, the proposed neural network has a lower model complexity and better convergence. Some numerical examples and application are presented to substantiate the effectiveness of the proposed neural network.

Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media

KAUST Repository

Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed

2012-01-01

In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like

An automated approach for solution based mesh adaptation to enhance numerical accuracy for a given number of grid cells

NARCIS (Netherlands)

Lucas, P.; Van Zuijlen, A.H.; Bijl, H.

2009-01-01

Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This

Optical Access Networks

Science.gov (United States)

Zheng, Jun; Ansari, Nirwan

2005-06-01

Call for Papers: Optical Access Networks With the wide deployment of fiber-optic technology over the past two decades, we have witnessed a tremendous growth of bandwidth capacity in the backbone networks of today's telecommunications infrastructure. However, access networks, which cover the "last-mile" areas and serve numerous residential and small business users, have not been scaled up commensurately. The local subscriber lines for telephone and cable television are still using twisted pairs and coaxial cables. Most residential connections to the Internet are still through dial-up modems operating at a low speed on twisted pairs. As the demand for access bandwidth increases with emerging high-bandwidth applications, such as distance learning, high-definition television (HDTV), and video on demand (VoD), the last-mile access networks have become a bandwidth bottleneck in today's telecommunications infrastructure. To ease this bottleneck, it is imperative to provide sufficient bandwidth capacity in the access networks to open the bottleneck and thus present more opportunities for the provisioning of multiservices. Optical access solutions promise huge bandwidth to service providers and low-cost high-bandwidth services to end users and are therefore widely considered the technology of choice for next-generation access networks. To realize the vision of optical access networks, however, many key issues still need to be addressed, such as network architectures, signaling protocols, and implementation standards. The major challenges lie in the fact that an optical solution must be not only robust, scalable, and flexible, but also implemented at a low cost comparable to that of existing access solutions in order to increase the economic viability of many potential high-bandwidth applications. In recent years, optical access networks have been receiving tremendous attention from both academia and industry. A large number of research activities have been carried out or

Survey of a numerical procedure for the solution of hyperbolic systems of three dimensional fluid flow

International Nuclear Information System (INIS)

Graf, U.

1986-01-01

A combination of several numerical methods is used to construct a procedure for effective calculation of complex three-dimensional fluid flow problems. The split coefficient matrix (SCM) method is used so that the differenced equations of the hyperbolic system do not disturb correct signal propagation. The semi-discretisation of the equations of the SCM method is done with the asymmetric, separated region, weighted residual (ASWR) method to give accurate solutions on a relatively coarse mesh. For the resulting system of ordinary differential equations, a general-purpose ordinary differential equation solver is used in conjunction with a method of fractional steps for an economic solution of the large system of linear equations. (orig.) [de

A numerical model for the determination of periodic solutions of pipes subjected to non-conservative loads

International Nuclear Information System (INIS)

Velloso, P.A.; Galeao, A.C.

1989-05-01

This paper deals with nonlinear vibrations of pipes subjected to non-conservative loads. Periodic solutions of these problems are determined using a variational approach based on Hamilton's Principle combined with a Fourier series expansion to describe the displacement field time dependence. A finite element model which utilizes Hemite's cubic interpolation for both axial and transversal displacement amplitudes is used. This model is applied to the problem of a pipe subjected to a tangential and a normal follower force. The numerical results obtained with this model are compared with the corespondent solutions determined using a total lagrangian description for the Principle of Virtual Work, coupled with Newmark's step-by-step integration procedure. It is shown that for small to moderate displacement amplitudes the one-term Fourier series approximation compares fairly well with the predicted solution. For large displacements as least a two-term approximation should be utilized [pt

Protocol design and analysis for cooperative wireless networks

CERN Document Server

Song, Wei; Jin, A-Long

2017-01-01

This book focuses on the design and analysis of protocols for cooperative wireless networks, especially at the medium access control (MAC) layer and for crosslayer design between the MAC layer and the physical layer. It highlights two main points that are often neglected in other books: energy-efficiency and spatial random distribution of wireless devices. Effective methods in stochastic geometry for the design and analysis of wireless networks are also explored. After providing a comprehensive review of existing studies in the literature, the authors point out the challenges that are worth further investigation. Then, they introduce several novel solutions for cooperative wireless network protocols that reduce energy consumption and address spatial random distribution of wireless nodes. For each solution, the book offers a clear system model and problem formulation, details of the proposed cooperative schemes, comprehensive performance analysis, and extensive numerical and simulation results that validate th...

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

Science.gov (United States)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Optical Networks Solutions planning - performances - management

DEFF Research Database (Denmark)

Fenger, Christian

2002-01-01

It has been a decisive goal in the compilation of this thesis to make us capable of realizing the future national and regional telecommunication networks in an efficient and resource optimal way. By future telecommunication network is assumed an all optical network where the information in transit...... are kept optical and not converted into the optical domain. The focus is on the scientific results achieved throughout the Ph.D. period. Five subjects – all increasing the understanding of optical networks – are studied. Static wavelength routed optical networks are studied. Management on terms...... of lightpath allocation and design is considered. By using statistical models (simultaneous analysis of many networks) the correspondence between parameters determining the network topology and the performance of the optical network is found. These dependencies are important knowledge in the process...

Community-Based Social Networks: Generation of Power Law Degree Distribution and IP Solutions to the KPP

Science.gov (United States)

Wu, Wentao

2012-01-01

The objective of this thesis is two-fold: (1) to investigate the degree distribution property of community-based social networks (CSNs) and (2) to provide solutions to a pertinent problem, the Key Player Problem. In the first part of this thesis, we consider a growing community-based network in which the ability of nodes competing for links to new…

Numerical Solution of a Fractional Order Model of HIV Infection of CD4+T Cells Using Müntz-Legendre Polynomials

Directory of Open Access Journals (Sweden)

Mojtaba Rasouli Gandomani

2016-06-01

Full Text Available In this paper, the model of HIV infection of CD4+ T cells is considered as a system of fractional differential equations. Then, a numerical method by using collocation method based on the Müntz-Legendre polynomials to approximate solution of the model is presented. The application of the proposed numerical method causes fractional differential equations system to convert into the algebraic equations system. The new system can be solved by one of the existing methods. Finally, we compare the result of this numerical method with the result of the methods have already been presented in the literature.

Connection Management and Recovery Strategies under Epidemic Network Failures in Optical Transport Networks

DEFF Research Database (Denmark)

Fagertun, Anna Manolova; Ruepp, Sarah Renée

2014-01-01

The current trend in deploying automatic control plane solutions for increased flexibility in the optical transport layer leads to numerous advantages for both the operators and the customers, but also pose challenges related to the stability of the network and its ability to operate in a robust...... manner under attacks. This work proposes four policies for failure handling in a connection-oriented optical transport network, under Generalized MultiProtocol Label Switching control plane, and evaluates their performance under multiple correlated large-scale failures. We employ the Susceptible...... of their transport infrastructures. Applying proactive methods for avoiding areas where epidemic failures spread results in 50% less connections requiring recovery, which translates in improved quality of service to customers....

River networks and ecological corridors: Reactive transport on fractals, migration fronts, hydrochory

Science.gov (United States)

Bertuzzo, E.; Maritan, A.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.

2007-04-01

Moving from a recent quantitative model of the US colonization in the 19th century that relies on analytical and numerical results of reactive-diffusive transport on fractal river networks, this paper considers its generalization to include an embedded flow direction which biases transport. We explore the properties of biased reaction-dispersal models, in which the reaction rates are described by a logistic equation. The relevance of the work is related to the prediction of the role of hydrologic controls on invasion processes (of species, populations, propagules, or infective agents, depending on the specifics of reaction and transport) occurring in river basins. Exact solutions are obtained along with general numerical solutions, which are applied to fractal constructs like Peano basins and real rivers. We also explore similarities and departures from different one-dimensional invasion models where a bias is added to both the diffusion and the telegraph equations, considering their respective ecological insight. We find that the geometrical constraints imposed by the fractal networks imply strong corrections on the speed of traveling fronts that can be enhanced or smoothed by the bias. Applications to real river networks show that the chief morphological parameters affecting the front speed are those characterizing the node-to-node distances measured along the network structure. The spatial density and number of reactive sites thus prove to be a vital hydrologic control on invasions. We argue that our solutions, currently tied to the validity of the logistic growth, might be relevant to the general study of species' spreading along ecological corridors defined by the river network structure.

Numerical Algorithm for Delta of Asian Option

Directory of Open Access Journals (Sweden)

Boxiang Zhang

2015-01-01

Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.

Numerical Modeling of Conjugate Heat Transfer in Fluid Network

Science.gov (United States)

Majumdar, Alok

2004-01-01

Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.

Development and testing of a compartmentalized reaction network model for redox zones in contaminated aquifers

Science.gov (United States)

Abrams , Robert H.; Loague, Keith; Kent, Douglas B.

1998-01-01

The work reported here is the first part of a larger effort focused on efficient numerical simulation of redox zone development in contaminated aquifers. The sequential use of various electron acceptors, which is governed by the energy yield of each reaction, gives rise to redox zones. The large difference in energy yields between the various redox reactions leads to systems of equations that are extremely ill-conditioned. These equations are very difficult to solve, especially in the context of coupled fluid flow, solute transport, and geochemical simulations. We have developed a general, rational method to solve such systems where we focus on the dominant reactions, compartmentalizing them in a manner that is analogous to the redox zones that are often observed in the field. The compartmentalized approach allows us to easily solve a complex geochemical system as a function of time and energy yield, laying the foundation for our ongoing work in which we couple the reaction network, for the development of redox zones, to a model of subsurface fluid flow and solute transport. Our method (1) solves the numerical system without evoking a redox parameter, (2) improves the numerical stability of redox systems by choosing which compartment and thus which reaction network to use based upon the concentration ratios of key constituents, (3) simulates the development of redox zones as a function of time without the use of inhibition factors or switching functions, and (4) can reduce the number of transport equations that need to be solved in space and time. We show through the use of various model performance evaluation statistics that the appropriate compartment choice under different geochemical conditions leads to numerical solutions without significant error. The compartmentalized approach described here facilitates the next phase of this effort where we couple the redox zone reaction network to models of fluid flow and solute transport.

Attractors in complex networks

Science.gov (United States)

Rodrigues, Alexandre A. P.

2017-10-01

In the framework of the generalized Lotka-Volterra model, solutions representing multispecies sequential competition can be predictable with high probability. In this paper, we show that it occurs because the corresponding "heteroclinic channel" forms part of an attractor. We prove that, generically, in an attracting heteroclinic network involving a finite number of hyperbolic and non-resonant saddle-equilibria whose linearization has only real eigenvalues, the connections corresponding to the most positive expanding eigenvalues form part of an attractor (observable in numerical simulations).