Accurate and efficient numerical solutions for elliptic obstacle problems
Directory of Open Access Journals (Sweden)
Philku Lee
2017-02-01
Full Text Available Abstract Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. In order to solve such problems effectively using finite difference (FD methods, the article investigates simple iterative algorithms based on the successive over-relaxation (SOR method. It introduces subgrid FD methods to reduce the accuracy deterioration occurring near the free boundary when the mesh grid does not match with the free boundary. For nonlinear obstacle problems, a method of gradient-weighting is introduced to solve the problem more conveniently and efficiently. The iterative algorithm is analyzed for convergence for both linear and nonlinear obstacle problems. An effective strategy is also suggested to find the optimal relaxation parameter. It has been numerically verified that the resulting obstacle SOR iteration with the optimal parameter converges about one order faster than state-of-the-art methods and the subgrid FD methods reduce numerical errors by one order of magnitude, for most cases. Various numerical examples are given to verify the claim.
Runkel, Robert L.; Chapra, Steven C.
1993-01-01
Several investigators have proposed solute transport models that incorporate the effects of transient storage. Transient storage occurs in small streams when portions of the transported solute become isolated in zones of water that are immobile relative to water in the main channel (e.g., pools, gravel beds). Transient storage is modeled by adding a storage term to the advection-dispersion equation describing conservation of mass for the main channel. In addition, a separate mass balance equation is written for the storage zone. Although numerous applications of the transient storage equations may be found in the literature, little attention has been paid to the numerical aspects of the approach. Of particular interest is the coupled nature of the equations describing mass conservation for the main channel and the storage zone. In the work described herein, an implicit finite difference technique is developed that allows for a decoupling of the governing differential equations. This decoupling method may be applied to other sets of coupled equations such as those describing sediment-water interactions for toxic contaminants. For the case at hand, decoupling leads to a 50% reduction in simulation run time. Computational costs may be further reduced through efficient application of the Thomas algorithm. These techniques may be easily incorporated into existing codes and new applications in which simulation run time is of concern.
An efficient numerical technique for the solution of nonlinear singular boundary value problems
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems
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.
AN EFFICIENT NUMERICAL METHOD FOR THE SOLUTION OF THE L2 OPTIMAL MASS TRANSFER PROBLEM*
Haber, Eldad; Rehman, Tauseef; Tannenbaum, Allen
2010-01-01
In this paper we present a new computationally efficient numerical scheme for the minimizing flow approach for the computation of the optimal L2 mass transport mapping. In contrast to the integration of a time dependent partial differential equation proposed in [S. Angenent, S. Haker, and A. Tannenbaum, SIAM J. Math. Anal., 35 (2003), pp. 61–97], we employ in the present work a direct variational method. The efficacy of the approach is demonstrated on both real and synthetic data. PMID:21278828
On the efficient numerical solution of lattice systems with low-order couplings
Energy Technology Data Exchange (ETDEWEB)
Ammon, A. [OAKLABS GmbH, Hennigsdorf (Germany); Genz, A. [Washington State Univ., Pullman, WA (United States). Dept. of Mathematics; Hartung, T. [King' s College London (United Kingdom). Dept. of Mathematics; Jansen, K.; Volmer, J. [DESY Zeuthen (Germany). NIC; Leoevey, H. [Humboldt Univ. Berlin (Germany). Inst. fuer Mathematik
2015-10-15
We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling.
DEFF Research Database (Denmark)
Vangsgaard, Anna Katrine; Mauricio Iglesias, Miguel; Valverde Perez, Borja
2013-01-01
A pH simulator consisting of an efficient numerical solver of a system of nine nonlinear equations was constructed and implemented in the modeling software MATLAB. The pH simulator was integrated in a granular biofilm model and used to simulate the pH profiles within granules performing the nitri......A pH simulator consisting of an efficient numerical solver of a system of nine nonlinear equations was constructed and implemented in the modeling software MATLAB. The pH simulator was integrated in a granular biofilm model and used to simulate the pH profiles within granules performing...
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 of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...
Numerical Solution for an Epicycloid Crack
Directory of Open Access Journals (Sweden)
Nik Mohd Asri Nik Long
2014-01-01
linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions.
Numerical solution of the bidomain equations.
Linge, S; Sundnes, J; Hanslien, M; Lines, G T; Tveito, A
2009-05-28
Knowledge of cardiac electrophysiology is efficiently formulated in terms of mathematical models. However, most of these models are very complex and thus defeat direct mathematical reasoning founded on classical and analytical considerations. This is particularly so for the celebrated bidomain model that was developed almost 40 years ago for the concurrent analysis of extra- and intracellular electrical activity. Numerical simulations based on this model represent an indispensable tool for studying electrophysiology. However, complex mathematical models, steep gradients in the solutions and complicated geometries lead to extremely challenging computational problems. The greatest achievement in scientific computing over the past 50 years has been to enable the solving of linear systems of algebraic equations that arise from discretizations of partial differential equations in an optimal manner, i.e. such that the central processing unit (CPU) effort increases linearly with the number of computational nodes. Over the past decade, such optimal methods have been introduced in the simulation of electrophysiology. This development, together with the development of affordable parallel computers, has enabled the solution of the bidomain model combined with accurate cellular models, on geometries resembling a human heart. However, in spite of recent progress, the full potential of modern computational methods has yet to be exploited for the solution of the bidomain model. This paper reviews the development of numerical methods for solving the bidomain model. However, the field is huge and we thus restrict our focus to developments that have been made since the year 2000.
Numerical Solution of Differential Algebraic Equations
DEFF Research Database (Denmark)
Thomsen, Per Grove; Bendtsen, Claus
1999-01-01
Lecture notes for a PhD-course on the numerical solution of DAE's. The course was held at IMM in the autumn of 1998 and the early spring of 1999.......Lecture notes for a PhD-course on the numerical solution of DAE's. The course was held at IMM in the autumn of 1998 and the early spring of 1999....
NUMERICAL SOLUTIONS OF SOME PARAMETRIC EFFECTS DUE ...
African Journals Online (AJOL)
Dr A.B.Ahmed
ISSN 1597-6343. Numerical Solutions of Some Parametric Effects Due to Electromagnetic Wave. Scattering by an Infinite Circular Cylinder. NUMERICAL SOLUTIONS OF SOME PARAMETRIC EFFECTS DUE. TO ELECTROMAGNETIC WAVE SCATTERING BY AN INFINITE. CIRCULAR CYLINDER. *1 Suleiman A. B. and 1 ...
Numerical Solution of Turbulence Problems by Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Alicia Cordero
2015-05-01
Full Text Available In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.
Automatic validation of numerical solutions
DEFF Research Database (Denmark)
Stauning, Ole
1997-01-01
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...... is the possiblility to combine the three methods in an extremely flexible way. We examine some applications where this flexibility is very useful. A method for Taylor expanding solutions of ordinary differential equations is presented, and a method for obtaining interval enclosures of the truncation errors incurred......, using this method has been developed. (ADIODES is an abbreviation of `` Automatic Differentiation Interval Ordinary Differential Equation Solver''). ADIODES is used to prove existence and uniqueness of periodic solutions to specific ordinary differential equations occuring in dynamical systems theory...
Carbon Efficient Building Solutions
Directory of Open Access Journals (Sweden)
Pellervo Matilainen
2010-03-01
Full Text Available Traditionally, the Finnish legislation have focused on energy use and especially on energy used for heating space in buildings. However, in many cases this does not lead to the optimal concept in respect to minimizing green house gases. This paper studies how CO2 emission levels are affected by different measures to reduce energy use in buildings. This paper presents two real apartment buildings with different options of energy efficiency and power sources. The calculations clearly show that in the future electricity and domestic hot water use will have high importance in respect to energy efficiency, and therefore also CO2 equivalent (eq emissions. The importance increases when the energy efficiency of the building increases. There are big differences between average Finnish production and individual power plants; CO2 eq emissions might nearly double depending on the energy source and the power plant type. Both a building with an efficient district heating as a power source, and a building with ground heat in addition to nuclear power electricity as a complimentary electricity source performed very similarly to each other in respect to CO2 eq emissions. However, it is dangerous to conclude that it is not important which energy source is chosen. If hypothetically, the use of district heating would dramatically drop, the primary energy factor and CO2 eq emissions from electricity would rise, which in turn would lead to the increase of the ground heat systems emissions. A problem in the yearly calculations is that the fact that it is very important, sometimes even crucial, when energy is needed, is always excluded.
A numerical solution for a telegraph equation
Ashyralyev, Allaberen; Modanli, Mahmut
2014-08-01
In this study, the initial value problem for a telegraph equation in a Hilbert space is considered. The stability estimate for the solution of this problem is given. A first and a second order of approximation difference schemes approximately solving the initial value problem are presented. The stability estimates for the solution of these difference schemes are given. The theoretical statements for the solution of these difference schemes are supported by the results of numerical experiments.
Numerical and approximate solutions for plume rise
Krishnamurthy, Ramesh; Gordon Hall, J.
Numerical and approximate analytical solutions are compared for turbulent plume rise in a crosswind. The numerical solutions were calculated using the plume rise model of Hoult, Fay and Forney (1969, J. Air Pollut. Control Ass.19, 585-590), over a wide range of pertinent parameters. Some wind shear and elevated inversion effects are included. The numerical solutions are seen to agree with the approximate solutions over a fairly wide range of the parameters. For the conditions considered in the study, wind shear effects are seen to be quite small. A limited study was made of the penetration of elevated inversions by plumes. The results indicate the adequacy of a simple criterion proposed by Briggs (1969, AEC Critical Review Series, USAEC Division of Technical Information extension, Oak Ridge, Tennesse).
Python Classes for Numerical Solution of PDE's
Mushtaq, Asif; Olaussen, Kåre
2015-01-01
We announce some Python classes for numerical solution of partial differential equations, or boundary value problems of ordinary differential equations. These classes are built on routines in \\texttt{numpy} and \\texttt{scipy.sparse.linalg} (or \\texttt{scipy.linalg} for smaller problems).
Numerical Solution of Stochastic Nonlinear Fractional Differential Equations
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 methods for viscoelastic orthotropic materials
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1988-01-01
Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.
Numerical prediction of Pelton turbine efficiency
Jošt, D.; Mežnar, P.; Lipej, A.
2010-08-01
This paper presents a numerical analysis of flow in a 2 jet Pelton turbine with horizontal axis. The analysis was done for the model at several operating points in different operating regimes. The results were compared to the results of a test of the model. Analysis was performed using ANSYS CFX-12.1 computer code. A k-ω SST turbulent model was used. Free surface flow was modelled by two-phase homogeneous model. At first, a steady state analysis of flow in the distributor with two injectors was performed for several needle strokes. This provided us with data on flow energy losses in the distributor and the shape and velocity of jets. The second step was an unsteady analysis of the runner with jets. Torque on the shaft was then calculated from pressure distribution data. Averaged torque values are smaller than measured ones. Consequently, calculated turbine efficiency is also smaller than the measured values, the difference is about 4 %. The shape of the efficiency diagram conforms well to the measurements.
Numerical solution of ordinary differential equations
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...
Numerical Solution of the Beltrami Equation
Porter, R. Michael
2008-01-01
An effective algorithm is presented for solving the Beltrami equation fzbar = mu fz in a planar disk. The algorithm involves no evaluation of singular integrals. The strategy, working in concentric rings, is to construct a piecewise linear mu-conformal mapping and then correct the image using a known algorithm for conformal mappings. Numerical examples are provided and the computational complexity is analyzed.
Efficient Solution Methods for N-component Condensation
van Putten, D.S.
2011-01-01
This thesis describes efficient solution methods developed for N-component condensation processes. These methods are aimed at either the reduction of the numerical effort required for solving the equations describing the condensation process or the simplification of the physical description. The
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver.
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...
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
Numerical solution of the one-dimensional Burgers' equation ...
Indian Academy of Sciences (India)
travelling in a viscous fluid [1]. In literature, many numerical methods have been proposed and implemented for approximating solution of the Burgers' equation. Many authors have used numerical techniques based on finite difference [1–8], finite element [9–13] and boundary element. [14] methods in attempting to solve the ...
Numerical solution of the one-dimensional Burgers' equation ...
Indian Academy of Sciences (India)
Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods ... Research Articles Volume 81 Issue 4 October 2013 pp 547-556 ... This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation.
Power and thermal efficient numerical processing
DEFF Research Database (Denmark)
Liu, Wei; Nannarelli, Alberto
2015-01-01
Numerical processing is at the core of applications in many areas ranging from scientific and engineering calculations to financial computing. These applications are usually executed on large servers or supercomputers to exploit their high speed, high level of parallelism and high bandwidth...
Numerical approximation of random periodic solutions of stochastic differential equations
Feng, Chunrong; Liu, Yu; Zhao, Huaizhong
2017-10-01
In this paper, we discuss the numerical approximation of random periodic solutions of stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of the random periodic solution as the limit of the pull-back flow when the starting time tends to -∞ along the multiple integrals of the period. As the random periodic solution is not explicitly constructible, it is useful to study the numerical approximation. We discretise the SDE using the Euler-Maruyama scheme and modified Milstein scheme. Subsequently, we obtain the existence of the random periodic solution as the limit of the pull-back of the discretised SDE. We prove that the latter is an approximated random periodic solution with an error to the exact one at the rate of √{Δ t} in the mean square sense in Euler-Maruyama method and Δ t in the Milstein method. We also obtain the weak convergence result for the approximation of the periodic measure.
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 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 solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Introduction to the numerical solutions of Markov chains
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 methods for solution of singular integral equations
Boykov, I. V.
2016-01-01
This paper is devoted to overview of the authors works for numerical solution of singular integral equations (SIE), polysingular integral equations and multi-dimensional singular integral equations of the second kind. The authors investigated onsidered iterative - projective methods and parallel methods for solution of singular integral equations, polysingular integral equations and multi-dimensional singular integral equations. The paper is the second part of overview of the authors works de...
Numerical aspects for efficient welding computational mechanics
Directory of Open Access Journals (Sweden)
Aburuga Tarek Kh.S.
2014-01-01
Full Text Available The effect of the residual stresses and strains is one of the most important parameter in the structure integrity assessment. A finite element model is constructed in order to simulate the multi passes mismatched submerged arc welding SAW which used in the welded tensile test specimen. Sequentially coupled thermal mechanical analysis is done by using ABAQUS software for calculating the residual stresses and distortion due to welding. In this work, three main issues were studied in order to reduce the time consuming during welding simulation which is the major problem in the computational welding mechanics (CWM. The first issue is dimensionality of the problem. Both two- and three-dimensional models are constructed for the same analysis type, shell element for two dimension simulation shows good performance comparing with brick element. The conventional method to calculate residual stress is by using implicit scheme that because of the welding and cooling time is relatively high. In this work, the author shows that it could use the explicit scheme with the mass scaling technique, and time consuming during the analysis will be reduced very efficiently. By using this new technique, it will be possible to simulate relatively large three dimensional structures.
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...
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 ...
numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Dr A.B.Ahmed
solving these problems by employing polynomials as trial functions in the ... numerical solution of Volterra integral equations by Galerkin method. Caglar et .... and continuous on [0,1], i α ,. 2,1,0. = i and i β ,. ,1,0. = i are finite real constants. Transforming (10) – (11) to systems of ordinary differential equations, we have. 1 yy. =.
Numerical solutions of fifth order boundary value problems using ...
African Journals Online (AJOL)
Mamadu-Njoseh polynomials are polynomials constructed in the interval [-1,1] with respect to the weight function () = 2 + 1. This paper aims at applying these polynomials, as trial functions satisfying the boundary conditions, in a numerical approach for the solution of fifth order boundary value problems. For this, these ...
Moving Mesh for the Numerical Solution of Partial Differential Equations
Directory of Open Access Journals (Sweden)
OLIVEIRA, F. S.
2013-06-01
Full Text Available In this paper we present moving meshes for the numeric resolution of partial differential equations. We describe some important concepts on this topic and point to existing body of work for the solution of partial differential equations using the methods of finite volumes and finite elements, both with moving meshes.
Smoluchowski aggregation-fragmentation equations: Fast numerical algorithm for steady-state solution
Stadnichuk, Vladimir; Bodrova, Anna; Brilliantov, Nikolai
2015-01-01
We propose an efficient and fast numerical algorithm of finding a \\emph{stationary} solution of large systems of aggregation-fragmentation equations of Smoluchowski type for concentrations of reacting particles. This method is applicable when the stationary concentrations steeply decreases with increasing aggregate size, which is fulfilled for the most important cases. We show that under rather mild restrictions, imposed on the kernel of the Smoluchowski equation, the following numerical proc...
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 solutions of multi-order fractional differential equations by Boubaker polynomials
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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 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.
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)
Zhang, Zhizeng; Zhao, Zhao; Li, Yongtao
2016-06-01
This paper attempts to verify the correctness of the analytical displacement solution in transversely isotropic rock mass, and to determine the scope of its application. The analytical displacement solution of a circular tunnel in transversely isotropic rock mass was derived firstly. The analytical solution was compared with the numerical solution, which was carried out by FLAC3D software. The results show that the expression of the analytical displacement solution is correct, and the allowable engineering range is that the dip angle is less than 15 degrees.
Determination of geopotential coefficients by efficient numerical integration techniques
Hansen, R. A.
An efficient, high accuracy, double integration method which evaluates the iterated form of the surface integral representations of the geopotential coefficients is presented. The efficiency and high accuracy of this method is obtained by the utilization of the Romberg numerical integration scheme. Additional efficiency is obtained by computing the inner integral which is common to many different coefficients only once. This method was tested using a test case earth which represented the basic features of the earth's potential field.
Numerical solution of open string field theory in Schnabl gauge
Arroyo, E. Aldo; Fernandes-Silva, A.; Szitas, R.
2018-01-01
Using traditional Virasoro L 0 level-truncation computations, we evaluate the open bosonic string field theory action up to level (10 , 30). Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value -1 at level L = 6. Extrapolating the level-truncation data for L ≤ 10 to estimate the vacuum energies for L > 10, we predict that the energy reaches a minimum value at L ˜ 12, and then turns back to approach -1 asymptotically as L → ∞. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at L ˜ 26, and then turns back to approach the expected analytical result as L → ∞.
Two different methods for numerical solution of the modified Burgers' equation.
Karakoç, Seydi Battal Gazi; Başhan, Ali; Geyikli, Turabi
2014-01-01
A numerical solution of the modified Burgers' equation (MBE) is obtained by using quartic B-spline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic B-spline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by computing L 2 and L ∞ error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis is also given for the DQM.
Affordable Energy-Efficient New Housing Solutions
Energy Technology Data Exchange (ETDEWEB)
Chandra, Subrato; Widder, Sarah H.; Bartlett, Rosemarie; McIlvaine, Janet; Chasar, David; Beal, David; Sutherland, Karen; Abbott, , K.; Fonorow, Ken; Eklund, Ken; Lubliner, Michael; Salzberg, Emily; Peeks, B.; Hewes, T.; Kosar, D.
2012-05-31
Since 2010, the U.S. Department of Energy’s Building America has sponsored research at PNNL to investigate cost-effective, energy-saving home-building technologies and to demonstrate how high-performance homes can deliver lower utility bills, increased comfort, and improved indoor air quality, while maintaining accessibility for low-income homeowners. PNNL and its contractors have been investigating 1) cost-effective whole-house solutions for Habitat for Humanity International (HFHI) and specific HFH affiliates in hot-humid and marine climates; 2) cost-effective energy-efficiency improvements for heating, ventilation, and air-conditioning (HVAC) systems in new, stick-built and manufactured homes; and 3) energy-efficient domestic hot-water systems.
Numerical solution of the space fractional Fokker-Planck equation
Liu, F.; Anh, V.; Turner, I.
2004-04-01
The traditional second-order Fokker-Planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of Brownian motion. Densities of α-stable type have been used to describe the probability distribution of these motions. The resulting governing equation of these motions is similar to the traditional Fokker-Planck equation except that the order α of the highest derivative is fractional. In this paper, a space fractional Fokker-Planck equation (SFFPE) with instantaneous source is considered. A numerical scheme for solving SFFPE is presented. Using the Riemann-Liouville and Grunwald-Letnikov definitions of fractional derivatives, the SFFPE is transformed into a system of ordinary differential equations (ODE). Then the ODE system is solved by a method of lines. Numerical results for SFFPE with a constant diffusion coefficient are evaluated for comparison with the known analytical solution. The numerical approximation of SFFPE with a time-dependent diffusion coefficient is also used to simulate Levy motion with α-stable densities. We will show that the numerical method of SFFPE is able to more accurately model these heavy-tailed motions.
Numerical Solution of a Model Equation of Price Formation
Chernogorova, T.; Vulkov, L.
2009-10-01
The paper [2] is devoted to the effect of reconciling the classical Black-Sholes theory of option pricing and hedging with various phenomena observed in the markets such as the influence of trading and hedging on the dynamics of an asset. Here we will discuss the numerical solution of initial boundary-value problems to a model equation of the theory. The lack of regularity in the solution as a result from Dirac delta coefficient reduces the accuracy in the numerical computations. First, we apply the finite volume method to discretize the differential problem. Second, we implement a technique of local regularization introduced by A-K. Tornberg and B. Engquist [7] for handling this equation. We derived the numerical regularization process into two steps: the Dirac delta function is regularized and then the regularized differential equation is discretized by difference schemes. Using the discrete maximum principle a priori bounds are obtained for the difference equations that imply stability and convergence of difference schemes for the problem under consideration. Numerical experiments are discussed.
The numerical solution of compressible fluid flow problems
Emmons, Howard W
1944-01-01
Numerical methods have been developed for obtaining the steady, adiabatic flow field of a frictionless, perfect gas about arbitrary two-dimensional bodies. The solutions include the subsonic velocity regions, the supersonic velocity regions, and the transition compression shocks, if required. Furthermore, the rotational motion and entropy changes following shocks are taken into account. Extensive use is made of the relaxation method. In this report the details of the methods of solution are emphasized so as to permit others to solve similar problems. Solutions already obtained are mentioned only by way of illustrating the possibilities of the methods described. The methods can be applied directly to wind tunnel and free air tests of arbitrary airfoil shapes at subsonic, sonic, and supersonic speeds.
Directory of Open Access Journals (Sweden)
John F. Moxnes
2014-06-01
Full Text Available There has been increasing interest in numerical simulations of fragmentation of expanding warheads in 3D. Accordingly there is a pressure on developers of leading commercial codes, such as LS-DYNA, AUTODYN and IMPETUS Afea, to implement the reliable fracture models and the efficient solution techniques. The applicability of the Johnson–Cook strength and fracture model is evaluated by comparing the fracture behaviour of an expanding steel casing of a warhead with experiments. The numerical codes and different numerical solution techniques, such as Eulerian, Lagrangian, Smooth particle hydrodynamics (SPH, and the corpuscular models recently implemented in IMPETUS Afea are compared. For the same solution techniques and material models we find that the codes give similar results. The SPH technique and the corpuscular technique are superior to the Eulerian technique and the Lagrangian technique (with erosion when it is applied to materials that have fluid like behaviour such as the explosive and the tracer. The Eulerian technique gives much larger calculation time and both the Lagrangian and Eulerian techniques seem to give less agreement with our measurements. To more correctly simulate the fracture behaviours of the expanding steel casing, we applied that ductility decreases with strain rate. The phenomena may be explained by the realization of adiabatic shear bands. An implemented node splitting algorithm in IMPETUS Afea seems very promising.
A time splitting algorithm for numerical solution of Richard's equation
Namin, Masoud Montazeri; Boroomand, Mohammad Reza
2012-06-01
SummaryThe Richard's equation mathematically expressing the infiltration problem is a transport type of equation describing two different phenomena namely advection and diffusion being hyperbolic and parabolic type of differential equation, respectively each having their own physical properties thus a single numerical scheme would not essentially be suitable for both. In this paper a numerical algorithm based on time splitting or fractional step method has been proposed and described. This has allowed designing and applying some different numerical schemes more compatible with the mathematical and physical properties of the corresponding phenomenon. In advection part an implicit characteristic based method has been employed to calculate the cell face fluxes and then the new unknowns have been obtained using finite volume method (FVM) explicitly. Two different speed type quantities namely wave celerity and mass velocity have been distinguished in the advection of infiltrated water to the soil, the magnitude of the first being several times larger than the other. The implicit characteristic based method has been designed specifically to cope with the mentioned high wave celerity. An implicit numerical scheme has been employed in which the space derivative term contributed in definition of cell face flux has been discretized in fourth order accurate manner. The extra cells getting involved due to the higher order discretization have been taken in account in a way not to change the tri-diagonal matrix coefficient shape preserving the efficiency of the algorithm. The performance, accuracy and efficiency of the out coming non-iterative numerical algorithm have been successfully examined by some test cases. The relative importance of the advection and diffusion terms in the concerned transport equation and the ration of their contribution in the overall infiltrated flux also have been discussed in detail.
Random ordinary differential equations and their numerical solution
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 ...
Bio-based lubricants for numerical solution of elastohydrodynamic lubrication
Cupu, Dedi Rosa Putra; Sheriff, Jamaluddin Md; Osman, Kahar
2012-06-01
This paper presents a programming code to provide numerical solution of elastohydrodynamic lubrication problem in line contacts which is modeled through an infinite cylinder on a plane to represent the application of roller bearing. In this simulation, vegetable oils will be used as bio-based lubricants. Temperature is assumed to be constant at 40°C. The results show that the EHL pressure for all vegetable oils was increasing from inlet flow until the center, then decrease a bit and rise to the peak pressure. The shapes of EHL film thickness for all tested vegetable oils are almost flat at contact region.
Numerical solution to nonlinear Tricomi equation using WENO schemes
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Adrian Sescu
2010-09-01
Full Text Available Nonlinear Tricomi equation is a hybrid (hyperbolic-elliptic second order partial differential equation, modelling the sonic boom focusing. In this paper, the Tricomi equation is transformed into a hyperbolic system of first order equations, in conservation law form. On the upper boundary, a new mixed boundary condition for the acoustic pressure is used to avoid the inclusion of the Dirac function in the numerical solution. Weighted Essentially Non-Oscillatory (WENO schemes are used for the spatial discretization, and the time marching is carried out using the second order accurate Runge-Kutta total-variation diminishing (TVD scheme.
Numerical solution of dynamic equilibrium models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
2013-01-01
of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel......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...
Novel Approaches To Numerical Solutions Of Quantum Field Theories
Petrov, D
2005-01-01
Two new approaches to numerically solving Quantum Field Theories are presented. The Source Galerkin technique is a direct approach to determining the generating functional of a theory by solving the Schwinger-Dyson equations. The properties of the Source Galerkin technique are tested by using it to determine the phase structure of the Ultralocal &phis;4 theory. A framework for applying this approach to solving O( N) Nonlinear Sigma model is constructed. The Sinc Function approximation is a highly efficient method of numerically evaluating Feynman diagrams. In the present dissertation the Sinc Function approximation is applied to fermionic fields. The Sinc expanded versions of fermion and photon propagators are derived. The accuracy of this approximation is tested by a direct comparison of the Sinc expanded propagators with exact propagators and by performing several sample calculations of one loop QED diagrams. An analysis of computational properties of the Sinc Function approach is presented.
A numerical solution for the diffusion equation in hydrogeologic systems
Ishii, A.L.; Healy, R.W.; Striegl, R.G.
1989-01-01
The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)
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.
Accelerating numerical solution of stochastic differential equations with CUDA
Januszewski, M.; Kostur, M.
2010-01-01
hundreds of threads simultaneously makes it possible to speed up the computation by over two orders of magnitude, compared to a typical modern CPU. Solution method: The stochastic Runge-Kutta method of the second order is applied to integrate the equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system. Unusual features: The numerical solution of the stochastic differential equations in question is performed on a GPU using the CUDA environment. Running time: < 1 minute
Directory of Open Access Journals (Sweden)
Thoudam Roshan
2016-10-01
Full Text Available Numerical solutions of the coupled Klein-Gordon-Schrödinger equations is obtained by using differential quadrature methods based on polynomials and quintic B-spline functions for space discretization and Runge-Kutta fourth order for time discretization. Stability of the schemes are studied using matrix stability analysis. The accuracy and efficiency of the methods are shown by conducting some numerical experiments on test problems. The motion of single soliton and interaction of two solitons are simulated by the proposed methods.
Numerical Comparison of Solutions of Kinetic Model Equations
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A. A. Frolova
2015-01-01
Full Text Available The collision integral approximation by different model equations has created a whole new trend in the theory of rarefied gas. One widely used model is the Shakhov model (S-model obtained by expansion of inverse collisions integral in a series of Hermite polynomials up to the third order. Using the same expansion with another value of free parameters leads to a linearized ellipsoidal statistical model (ESL.Both model equations (S and ESL have the same properties, as they give the correct relaxation of non-equilibrium stress tensor components and heat flux vector, the correct Prandtl number at the transition to the hydrodynamic regime and do not guarantee the positivity of the distribution function.The article presents numerical comparison of solutions of Shakhov equation, ESL- model and full Boltzmann equation in the four Riemann problems for molecules of hard spheres.We have considered the expansion of two gas flows, contact discontinuity, the problem of the gas counter-flows and the problem of the shock wave structure. For the numerical solution of the kinetic equations the method of discrete ordinates is used.The comparison shows that solution has a weak sensitivity to the form of collision operator in the problem of expansions of two gas flows and results obtained by the model and the kinetic Boltzmann equations coincide.In the problem of the contact discontinuity the solution of model equations differs from full kinetic solutions at the point of the initial discontinuity. The non-equilibrium stress tensor has the maximum errors, the error of the heat flux is much smaller, and the ESL - model gives the exact value of the extremum of heat flux.In the problems of gas counter-flows and shock wave structure the model equations give significant distortion profiles of heat flux and non-equilibrium stress tensor components in front of the shock waves. This behavior is due to fact that in the models under consideration there is no dependency of the
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....
Numerical conversion efficiency of thermally isolated Seebeck nanoantennas
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Edgar Briones
2016-11-01
Full Text Available In this letter, we evaluate the conversion efficiency of thermally isolated Seebeck nanoantennas by numerical simulations and discuss their uses and scope for energy harvesting applications. This analysis includes the simple case of titanium-nickel dipoles suspended in air above the substrate by a 200 nm silicon dioxide membrane to isolate the heat dissipation. Results show that substantially thermal gradients are induced along the devices leading to a harvesting efficiency around 10-4 %, 400 % higher than the previously reported Seebeck nanoantennas. In the light of these results, different optimizing strategies should be considered in order to make the Seebeck nanoantennas useful for harvesting applications.
Deorbit efficiency assessment through numerical simulation of electromagnetic tether devices
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Alexandru IONEL
2016-03-01
Full Text Available This paper examines the deorbit efficiency of an electromagnetic tether deorbit device when used to deorbit an upper stage at end of mission from low Earth orbit. This is done via a numerical simulation in Matlab R2013a, using ode45, taking into account perturbations on the upper stage’s trajectory. The perturbations taken into account are the atmospheric drag, the 3rd body (Sun and Moon, and Earth’s gravitational potential expanded into spherical harmonics.
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 practice. Rather, we use light-emitting diodes to illuminate the scene to be reconstructed. Such point light sources are very convenient to use, yet they yield a more complex photometric stereo model which is arduous to solve. We first derive in a physically sound manner this model, and show how...... approach is not established. The second one directly recovers the depth, by formulating photometric stereo as a system of nonlinear partial differential equations (PDEs), which are linearized using image ratios. Although the sequential approach is avoided, initialization matters a lot and convergence...
Numerical solution of Lord-Shulman thermopiezoelectricity dynamical problem
Stelmashchuk, Vitaliy; Shynkarenko, Heorhiy
2018-01-01
Using Lord-Shulman hypothesis we formulate the initial boundary value problem and its corresponding variational problem of a generalized linear thermopiezoelectricity in terms of the displacement, electrical potential, temperature increment and heat flux, which describes the dynamic behavior of the coupled mechanic, electric and heat waves in pyroelectric materials. We construct the corresponding energy balance equation and determine input data regularity for the variational problem, which guarantees the existence, uniqueness and stability of its solution in the problem energy norm. Based on these results, we propose a numerical scheme for solving this problem, which includes spatial finite element semi-discretization and one-step recurrent time integration procedures and generalizes the similar one for classic thermopiezoelectricity problem. We give the sufficient conditions on the values of the scheme parameters which guarantee properties of conservatism and unconditional stability of the scheme. The rest of the article is devoted to the analysis of performed numerical experiments with 1D model problem and their results are then compared with the ones obtained by the other researchers.
Bahşı, Ayşe Kurt; Yalçınbaş, Salih
2016-01-01
In this study, the Fibonacci collocation method based on the Fibonacci polynomials are presented to solve for the fractional diffusion equations with variable coefficients. The fractional derivatives are described in the Caputo sense. This method is derived by expanding the approximate solution with Fibonacci polynomials. Using this method of the fractional derivative this equation can be reduced to a set of linear algebraic equations. Also, an error estimation algorithm which is based on the residual functions is presented for this method. The approximate solutions are improved by using this error estimation algorithm. If the exact solution of the problem is not known, the absolute error function of the problems can be approximately computed by using the Fibonacci polynomial solution. By using this error estimation function, we can find improved solutions which are more efficient than direct numerical solutions. Numerical examples, figures, tables are comparisons have been presented to show efficiency and usable of proposed method.
Numerical study of particle capture efficiency in fibrous filter
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Fan Jianhua
2017-01-01
Full Text Available Numerical simulations are performed for transport and deposition of particles over a fixed obstacle in a fluid flow. The effect of particle size and Stokes number on the particle capture efficiency is investigated using two methods. The first one is one-way coupling combining Lattice Boltzmann (LB method with Lagrangian point-like approach. The second one is two-way coupling based on the coupling between Lattice Boltzmann method and discrete element (DE method, which consider the particle influence on the fluid. Then the single fiber collection efficiency characterized by Stokes number (St are simulated by LB-DE methods. Results show that two-way coupling method is more appropriate in our case for particles larger than 8 μm. A good agreement has also been observed between our simulation results and existing correlations for single fiber collection efficiency. The numerical simulations presented in this work are useful to understand the particle transport and deposition and to predict the capture efficiency.
A Mechatronic Solution for Efficiency Optimisation
DEFF Research Database (Denmark)
Conrad, Finn; Hansen, M.R.; Andersen, T.O.
2004-01-01
This paper presents and discusses concepts concerning regeneration of potential energy in hydraulic forklift trucks. A conventional forklift system has been investigated for energy efficiency and compared to an investigated for energy efficiency and compared to an investigated for energy efficiency...
An efficient numerical method for solving nonlinear foam drainage equation
Parand, Kourosh; Delkhosh, Mehdi
2018-02-01
In this paper, the nonlinear foam drainage equation, which is a famous nonlinear partial differential equation, is solved by using a hybrid numerical method based on the quasilinearization method and the bivariate generalized fractional order of the Chebyshev functions (B-GFCF) collocation method. First, using the quasilinearization method, the equation is converted into a sequence of linear partial differential equations (LPD), and then these LPDs are solved using the B-GFCF collocation method. A very good approximation of solutions is obtained, and comparisons show that the obtained results are more accurate than the results of other researchers.
Directory of Open Access Journals (Sweden)
A. H. Bhrawy
2014-01-01
Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.
Carmona, A.; Pérez-Segarra, C. D.; Lehmkuhl, O.; Oliva, A.
2012-11-01
The aim of this work is to provide numerical solutions for the fluid flow and the heat transfer generated in closed systems containing viscoplastic-type non-Newtonian fluids. A lid driven cavity (LDC) and a differentially heated cavity (DHC) are used as test cases. These numerical solutions can be an appropriate tool for verifying CFD codes which have been developed or adapted to deal with this kind of non-Newtonian fluids. In order to achieve this objective, an in-house CFD code has been implemented and correctly verified by the method of manufactured solutions and by some numerical solutions too. Furthermore, a high-performance CFD code (Termo Fluids S.L.) has been adapted and properly verified, by the corresponding numerical solutions, to deal with this kind of non-Newtonian fluids. The viscoplastic behaviour of certain non-Newtonian fluids will be generated from a viscous stress which has been defined by a potential-type rheological law. The pseudoplastic and dilatant behaviours will be studied. On this matter, the influence of different physical aspects on the numerical simulations will be analysed, e.g. different exponent values in the potential-type rheological law and different values of the non-dimensional numbers. Moreover, the influence of different numerical aspects on the numerical simulations will also be analysed, e.g. unstructured meshes, conservative numerical schemes and more efficient and parallel algorithms and solvers.
Numerical modelling of the binary alloys solidification with solutal undercooling
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T. Skrzypczak
2008-03-01
Full Text Available In thc papcr descrip~ion of mathcmn~icaI and numerical modcl of binay alloy sot idification is prcscntcd. Mctal alloy consisting of maincomponent and solulc is introduced. Moving, sharp solidification rmnt is assumcd. Conaitulional undcrcooling phcnomcnon is tnkcn intoconsidcralion. As a solidifica~ionf ront advances, solutc is rcdistributcd at thc intcrfacc. Commonly, solutc is rejccted into Itlc liquid. whcrcit accumuIatcs into solittc boundary laycr. Depending on thc tcmpcrature gradient, such tiquid may be undcrcoolcd hclow its mclting point,cvcn though it is hot~crth an liquid at thc Front. This phcnomcnon is orten callcd constitutional or soIr~talu ndcrcool ing, to cmphasizc that itariscs from variations in solutal distribution or I iquid. An important conscqucncc of this accurnulntion of saIutc is that it can cause thc frontto brcak down into cclls or dendri~csT. his occurs bccausc thcrc is a liquid ahcad of thc front with lowcr solutc contcnt, and hcncc a highcrme1 ting tcmpcraturcs than liquid at thc front. In rhc papcr locarion and shapc of wndcrcoolcd rcgion dcpcnding on solidification pararnctcrsis discussed. Nurncrical mcthod basing on Fini tc Elelncnt Mctbod (FEM allowi~lgp rcdiction of breakdown of inoving planar front duringsolidification or binary alloy is proposed.
Numerical solution of the Fokker-Planck equation
Energy Technology Data Exchange (ETDEWEB)
Shoucri, M. [Institut de Recherche Hydro-Quebec (IREQ), Varennes Quebec (Canada); Peysson, Y. [Association Euratom-CEA Cadarache, CEA/DSM/DRFC, 13 - Saint-Paul-lez-Durance (France); Shkarofsky, I. [MPB Technologies Inc., Quebec (Canada)
2006-06-15
A code to solve the Fokker-Planck kinetic equation for electrons and ions is presented. The electrons are treated with a relativistic collision operator. The importance of the numerical approach associated with an exact relativistic treatment for the solution of the electrons dynamic is emphasized in order to study accurately all the physics associated with the electron distribution function, as for instance the physics associated with the hot tail, the fast electron transport and the shape of the distribution function. Accurate relativistic treatment of the hot tail helps make the study of these problems less phenomenological and more physical. The pertinent equations for two different ions species, a majority ion and a minority ion population, are included in the code. The ions are treated with non-relativistic equations. The code also includes the appropriate quasi-linear operator for lower hybrid current drive, electron cyclotron heating and current drive, ion cyclotron heating for each of the ion species. This allows accurate study of synergy effects between the different sources for plasma heating and current drive. The exchange terms between the different species are included. The code includes also the option of a variable grid size for electrons and ions. (authors)
Efficient numerical simulation of heat storage in subsurface georeservoirs
Boockmeyer, A.; Bauer, S.
2015-12-01
The transition of the German energy market towards renewable energy sources, e.g. wind or solar power, requires energy storage technologies to compensate for their fluctuating production. Large amounts of energy could be stored in georeservoirs such as porous formations in the subsurface. One possibility here is to store heat with high temperatures of up to 90°C through borehole heat exchangers (BHEs) since more than 80 % of the total energy consumption in German households are used for heating and hot water supply. Within the ANGUS+ project potential environmental impacts of such heat storages are assessed and quantified. Numerical simulations are performed to predict storage capacities, storage cycle times, and induced effects. For simulation of these highly dynamic storage sites, detailed high-resolution models are required. We set up a model that accounts for all components of the BHE and verified it using experimental data. The model ensures accurate simulation results but also leads to large numerical meshes and thus high simulation times. In this work, we therefore present a numerical model for each type of BHE (single U, double U and coaxial) that reduces the number of elements and the simulation time significantly for use in larger scale simulations. The numerical model includes all BHE components and represents the temporal and spatial temperature distribution with an accuracy of less than 2% deviation from the fully discretized model. By changing the BHE geometry and using equivalent parameters, the simulation time is reduced by a factor of ~10 for single U-tube BHEs, ~20 for double U-tube BHEs and ~150 for coaxial BHEs. Results of a sensitivity study that quantify the effects of different design and storage formation parameters on temperature distribution and storage efficiency for heat storage using multiple BHEs are then shown. It is found that storage efficiency strongly depends on the number of BHEs composing the storage site, their distance and
Numerical solution of linear Klein-Gordon equation using FDAM scheme
Kasron, Noraini; Suharto, Erni Suryani; Deraman, Ros Fadilah; Othman, Khairil Iskandar; Nasir, Mohd Agos Salim
2017-05-01
Many scientific areas appear in a hyperbolic partial differential equation like the Klien-Gordon equation. The analytical solutions of the Klein-Gordon equation have been approximated by the suggested numerical approaches. However, the arithmetic mean (AM) method has not been studied on the Klein-Gordon equation. In this study, a new proposed scheme has utilized central finite difference formula in time and space (CTCS) incorporated with AM formula averaging of functional values for approximating the solutions of the Klein-Gordon equation. Three-point AM is considered to a linear inhomogeneous Klein-Gordon equation. The theoretical aspects of the numerical scheme for the Klein-Gordon equation are also considered. The stability analysis is analyzed by using von Neumann stability analysis and Miller Norm Lemma. Graphical results verify the necessary conditions of Miller Norm Lemma. Good results obtained relate to the theoretical aspects of the numerical scheme. The numerical experiments are examined to verify the theoretical analysis. Comparative study shows the new CTCS scheme incorporated with three-point AM method produced better accuracy and shown its reliable and efficient over the standard CTCS scheme.
Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes
Chesler, Paul M.; Yaffe, Laurence G.
2014-07-01
A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.
Milne, a routine for the numerical solution of Milne's problem
Rawat, Ajay; Mohankumar, N.
2010-11-01
The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.
An Efficient Compact Finite Difference Method for the Solution of the Gross-Pitaevskii Equation
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Rongpei Zhang
2015-01-01
matrices. The CFDM-AIF method is implemented to investigate the ground and first excited state solutions of the Gross-Pitaevskii equation in two-dimensional (2D and three-dimensional (3D Bose-Einstein condensates (BECs. Numerical results are presented to demonstrate the validity, accuracy, and efficiency of the CFDM-AIF method.
Numerical solution of quadratic matrix equations for free vibration analysis of structures
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.
On the numerical solution of the one-dimensional convection-diffusion equation
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Dehghan Mehdi
2005-01-01
Full Text Available The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.
New Numerical Solution of von Karman Equation of Lengthwise Rolling
Rudolf Pernis; Tibor Kvackaj
2015-01-01
The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a) by polygonal curve and (b) by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rol...
Numerical solution of the stochastic parabolic equation with the dependent operator coefficient
Energy Technology Data Exchange (ETDEWEB)
Ashyralyev, Allaberen [Department of Elementary Mathematics Education, Fatih University, 34500, Istanbul (Turkey); Department of Mathematics, ITTU, Ashgabat (Turkmenistan); Okur, Ulker [Institute for Stochastics and Applications, Department of Mathematics, University of Stuttgart, 70569, Stuttgart (Germany)
2015-09-18
In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.
Solution for Improve the Efficiency of Solar Photovoltaic Installation
Petru Chioncel; Cristian Paul Chioncel; Nicoleta Gillich
2013-01-01
This paper present a solution for improving efficiency of solar photovoltaic installation, realized with fixed solar photovoltaic modules, placed in solar parks or individual installations. The proposed solution to increase the radiation on the solar photovoltaic panels is to use some thin plates covered with a reflective blanket, mounted in front of the solar photovoltaic modules, with the possibility of their adjustment.
Directory of Open Access Journals (Sweden)
S. Saha Ray
2014-01-01
Full Text Available A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the reliability and efficiency of the method.
Robust and efficient solution procedures for association models
DEFF Research Database (Denmark)
Michelsen, Michael Locht
2006-01-01
Equations of state that incorporate the Wertheim association expression are more difficult to apply than conventional pressure explicit equations, because the association term is implicit and requires solution for an internal set of composition variables. In this work, we analyze the convergence...... behavior of different solution methods and demonstrate how a simple and efficient, yet globally convergent, procedure for the solution of the equation of state can be formulated....
Numerical Solution of Magnetostatic Field of Maglev System
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Jaroslav Sobotka
2008-01-01
Full Text Available The paper deals with the design of the levitation and guidance system of the levitation train Transrapid 08 by means of QuickField 5.0 – a 2D program formagnetic electromagnetic fields solutions.
An efficient numerical scheme for the simulation of parallel-plate active magnetic regenerators
DEFF Research Database (Denmark)
Torregrosa-Jaime, Bárbara; Corberán, José M.; Payá, Jorge
2015-01-01
A one-dimensional model of a parallel-plate active magnetic regenerator (AMR) is presented in this work. The model is based on an efficient numerical scheme which has been developed after analysing the heat transfer mechanisms in the regenerator bed. The new finite difference scheme optimally...... combines explicit and implicit techniques in order to solve the one-dimensional conjugate heat transfer problem in an accurate and fast manner while ensuring energy conservation. The present model has been thoroughly validated against passive regenerator cases with an analytical solution. Compared...
Numerical solution of boundary layer MHD flow with viscous dissipation.
Mishra, S R; Jena, S
2014-01-01
The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.
Efficient Solutions for Time-Consuming Jobs in the Library
Bailey, Kieren
2011-01-01
Two of the most time-consuming jobs in the library are taking inventory and keeping track of in-house uses of library material. Librarians have long been searching for more efficient solution for these two activities. New technology can be the answer to creating efficiency for libraries. In fact, if one is a SirsiDynix library, there is an easy…
Numerically efficient estimation of relaxation effects in magnetic particle imaging.
Rückert, Martin A; Vogel, Patrick; Jakob, Peter M; Behr, Volker C
2013-12-01
Current simulations of the signal in magnetic particle imaging (MPI) are either based on the Langevin function or on directly measuring the system function. The former completely ignores the influence of finite relaxation times of magnetic particles, and the latter requires time-consuming reference scans with an existing MPI scanner. Therefore, the resulting system function only applies for a given tracer type and the properties of the applied scanning trajectory. It requires separate reference scans for different trajectories and does not allow simulating theoretical magnetic particle suspensions. The most accessible and accurate way for including relaxation effects in the signal simulation would be using the Langevin equation. However, this is a very time-consuming approach because it calculates the stochastic dynamics of the individual particles and averages over large particle ensembles. In the current article, a numerically efficient way for approximating the averaged Langevin equation is proposed, which is much faster than the approach based on the Langevin equation because it is directly calculating the averaged time evolution of the magnetization. The proposed simulation yields promising results. Except for the case of small orthogonal offset fields, a high agreement with the full but significantly slower simulation could be shown.
Directory of Open Access Journals (Sweden)
Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
A numerical solution of the Burgers' equation using septic B-splines
Energy Technology Data Exchange (ETDEWEB)
Ramadan, Mohamed A. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)] e-mail: mramadan@mailer.eun.eg; El-Danaf, Talaat S. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt); Abd Alaal, Faisal E.I. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)
2005-11-01
In this paper, numerical solutions of the nonlinear Burgers' equation are obtained by a method based on collocation of septic B-splines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Numerical solutions of the modified Burgers' equation are also obtained by making a simple change of the suggested numerical scheme for the Burgers' equation. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
A numerical solution of the Burgers' equation using septic B-sp lines
Energy Technology Data Exchange (ETDEWEB)
Ramadan, Mohamed A. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)] e-mail: mramadan@mailer.eun.eg; El-Danaf, Talaat S. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt); Abd Alaal, Faisal E.I. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Koom (Egypt)
2005-11-01
In this paper, numerical solutions of the nonlinear Burgers' equation are obtained by a method based on collocation of septic B-sp lines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Numerical solutions of the modified Burgers' equation are also obtained by making a simple change of the suggested numerical scheme for the Burgers' equation. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.
Numerical solutions of Einstein field equations with radial dark matter
Klimenko, Stanislav; Nikitin, Igor; Nikitina, Lialia
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant velocities of circular motion, i.e. flat rotation curves. At smaller distances, the field switches to Newtonian regime, then to Schwarzschild regime. Deviations from Schwarzschild regime start below the gravitational radius. The dark matter prevents the creation of event horizon, instead, a spherical region possessing extremely large redshift is created. The structure of space-time for the obtained solutions is investigated and the implications for the models of the galaxies are discussed.
Numerical Solution of Hamilton-Jacobi Equations in High Dimension
2012-11-23
high dimension FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA-Universita di Roma P. Aldo Moro, 2 00185 ROMA AH930...solution of Hamilton-Jacobi equations in high dimension AFOSR contract n. FA9550-10-1-0029 Maurizio Falcone Dipartimento di Matematica SAPIENZA
Efficient calculation of degenerate atomic rates by numerical quadrature on GPUs
Aslanyan, V.; Aslanyan, A. G.; Tallents, G. J.
2017-10-01
The rates of atomic processes in cold, dense plasma are governed strongly by effects of quantum degeneracy. The electrons follow Fermi-Dirac statistics and their high density limits the number of quantum states available for occupation after a collision. These factors preclude a direct solution to the usual rate coefficient integrals. We summarize the formulation of this problem and present a simple, but efficient method of evaluating collisional rate coefficients via direct numerical integration. Numerical quadrature has an intrinsically high level of parallelism, ideally suited for graphics processor units. GPUs are particularly suited to this problem because of the large number of integrals which must be carried out simultaneously for a given atomic model. A CUDA code to calculate the rates of significant atomic processes as part of a collisional-radiative model is presented and discussed. This approach may be readily extended to other applications where rapid and repeated evaluation of many integrals is required.
Efficient traveltime solutions of the acoustic TI eikonal equation
Waheed, Umair bin
2015-02-01
Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial for every grid point. Analytical solutions of the quartic polynomial yield numerically unstable formulations. Thus, it requires a numerical root finding algorithm, adding significantly to the computational load. Using perturbation theory we approximate, in a first order discretized form, the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution, in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter, such as that for the complicated Marmousi model. The formulation allows for large cost reduction compared to using the direct TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm, without any addition to the computational cost.
WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method
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
Efficient numerical integration of neutrino oscillations in matter
Casas, Fernando; D'Olivo, Juan Carlos
2016-01-01
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.
New explicit methods for the numerical solution of diffusion problems
Evans, David J.
In this survey paper, Part 1 is concerned with new explicit methods for the finite difference solution of a parabolic partial differential equation in 1 space dimension. The new methods use stable asymmetric approximations to the partial differential equation which when coupled in groups of 2 adjacent points on the grid result in implicit equations which can be easily converted to explicit form which in turn offer many advantages. By judicious use of alternating this strategy on the grid points of the domain results in an algorithm which possesses unconditional stability. Part II briefly surveys existing methods and then an explicit finite difference approximation procedure which is unconditionally stable for the solution of the two-dimensional nonhomogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment.
Numerical solutions of the complete Navier-Stokes equations
Hassan, H. A.
1993-01-01
The objective of this study is to compare the use of assumed pdf (probability density function) approaches for modeling supersonic turbulent reacting flowfields with the more elaborate approach where the pdf evolution equation is solved. Assumed pdf approaches for averaging the chemical source terms require modest increases in CPU time typically of the order of 20 percent above treating the source terms as 'laminar.' However, it is difficult to assume a form for these pdf's a priori that correctly mimics the behavior of the actual pdf governing the flow. Solving the evolution equation for the pdf is a theoretically sound approach, but because of the large dimensionality of this function, its solution requires a Monte Carlo method which is computationally expensive and slow to coverage. Preliminary results show both pdf approaches to yield similar solutions for the mean flow variables.
New Numerical Solution of von Karman Equation of Lengthwise Rolling
Directory of Open Access Journals (Sweden)
Rudolf Pernis
2015-01-01
Full Text Available The calculation of average material contact pressure to rolls base on mathematical theory of rolling process given by Karman equation was solved by many authors. The solutions reported by authors are used simplifications for solution of Karman equation. The simplifications are based on two cases for approximation of the circular arch: (a by polygonal curve and (b by parabola. The contribution of the present paper for solution of two-dimensional differential equation of rolling is based on description of the circular arch by equation of a circle. The new term relative stress as nondimensional variable was defined. The result from derived mathematical models can be calculated following variables: normal contact stress distribution, front and back tensions, angle of neutral point, coefficient of the arm of rolling force, rolling force, and rolling torque during rolling process. Laboratory cold rolled experiment of CuZn30 brass material was performed. Work hardening during brass processing was calculated. Comparison of theoretical values of normal contact stress with values of normal contact stress obtained from cold rolling experiment was performed. The calculations were not concluded with roll flattening.
Solution of simple numerical problems using spreadsheet programs
Riggi, F.
1986-11-01
Spreadsheet programs are now extensively used for the analysis of business problems. A spreadsheet program reproduces the structure of a large page with columns and rows. The intersection of a column and a row defines a cell, each cell being identified by a column letter and a row number, starting at the upper left. The screen is a window over this matrix, whose dimensions depend on the machine's resources. Unlike that which occurs with paper spreadsheets, the elements (cells) of such a matrix structure can hold not only labels or numerical values but also mathematical formulae relating them to other matrix elements.
Numerical solutions of Williamson fluid with pressure dependent viscosity
Directory of Open Access Journals (Sweden)
Iffat Zehra
2015-01-01
Full Text Available In the present paper, we have examined the flow of Williamson fluid in an inclined channel with pressure dependent viscosity. The governing equations of motion for Williamson fluid model under the effects of pressure dependent viscosity and pressure dependent porosity are modeled and then solved numerically by the shooting method with Runge Kutta Fehlberg for two types of geometries i.e., (i Poiseuille flow and (ii Couette flow. Four different cases for pressure dependent viscosity and pressure dependent porosity are assumed and the physical features of pertinent parameters are discussed through graphs.
Numerical solution of two dimensional time fractional-order biological population model
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Prakash Amit
2016-01-01
Full Text Available In this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM. Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional order α.
Semi-numerical solution for a fractal telegraphic dual-porosity fluid flow model
Herrera-Hernández, E C; Luis, D P; Hernández, D; Camacho-Velázquez, R G
2016-01-01
In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose numerical treatment outcomes in a tri-diagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor sem...
The numerical solution of the vorticity transport equation
Dennis, S C R
1973-01-01
A method of approximating the two-dimensional vorticity transport equation in which the matrix associated with the difference equations is diagonally dominant and the truncation error is the same as that of the fully central-difference approximation, is discussed. An example from boundary layer theory is given by calculating the viscous stagnation point flow at the nose of a cylinder. Some new solutions of the Navier-Stokes equations are obtained for symmetrical flow past a flat plate of finite length. (16 refs).
Solution for Improve the Efficiency of Solar Photovoltaic Installation
Directory of Open Access Journals (Sweden)
Petru Chioncel
2013-01-01
Full Text Available This paper present a solution for improving efficiency of solar photovoltaic installation, realized with fixed solar photovoltaic modules, placed in solar parks or individual installations. The proposed solution to increase the radiation on the solar photovoltaic panels is to use some thin plates covered with a reflective blanket, mounted in front of the solar photovoltaic modules, with the possibility of their adjustment.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
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...
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
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.
Directory of Open Access Journals (Sweden)
A. H. Bhrawy
2012-01-01
Full Text Available A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. A quadrature Galerkin method is introduced for the numerical solution of these problems with variable coefficients. A new shifted Jacobi collocation method based on basis functions satisfying the initial conditions is presented for solving nonlinear initial value problems. Through several numerical examples, we evaluate the accuracy and performance of the proposed algorithms. The algorithms are easy to implement and yield very accurate results.
Texture functions in image analysis: A computationally efficient solution
Cox, S. C.; Rose, J. F.
1983-01-01
A computationally efficient means for calculating texture measurements from digital images by use of the co-occurrence technique is presented. The calculation of the statistical descriptors of image texture and a solution that circumvents the need for calculating and storing a co-occurrence matrix are discussed. The results show that existing efficient algorithms for calculating sums, sums of squares, and cross products can be used to compute complex co-occurrence relationships directly from the digital image input.
Final Scientific Report - Wireless and Sensing Solutions Advancing Industrial Efficiency
Energy Technology Data Exchange (ETDEWEB)
Budampati, Rama; McBrady, Adam; Nusseibeh, Fouad
2009-09-28
The project team's goal for the Wireless and Sensing Solution Advancing Industrial Efficiency award (DE-FC36-04GO14002) was to develop, demonstrate, and test a number of leading edge technologies that could enable the emergence of wireless sensor and sampling systems for the industrial market space. This effort combined initiatives in advanced sensor development, configurable sampling and deployment platforms, and robust wireless communications to address critical obstacles in enabling enhanced industrial efficiency.
Milani, Massimo; Montorsi, Luca; Stefani, Matteo; Saponelli, Roberto; Lizzano, Maurizio
2017-12-01
The paper focuses on the analysis of an industrial ceramic kiln in order to improve the energy efficiency and thus the fuel consumption and the corresponding carbon dioxide emissions. A lumped and distributed parameter model of the entire system is constructed to simulate the performance of the kiln under actual operating conditions. The model is able to predict accurately the temperature distribution along the different modules of the kiln and the operation of the many natural gas burners employed to provide the required thermal power. Furthermore, the temperature of the tiles is also simulated so that the quality of the final product can be addressed by the modelling. Numerical results are validated against experimental measurements carried out on a real ceramic kiln during regular production operations. The developed numerical model demonstrates to be an efficient tool for the investigation of different design solutions for the kiln's components. In addition, a number of control strategies for the system working conditions can be simulated and compared in order to define the best trade off in terms of fuel consumption and product quality. In particular, the paper analyzes the effect of a new burner type characterized by internal heat recovery capability aimed at improving the energy efficiency of the ceramic kiln. The fuel saving and the relating reduction of carbon dioxide emissions resulted in the order of 10% when compared to the standard burner. Copyright © 2017 Elsevier Ltd. All rights reserved.
A Computationally-Efficient Numerical Model to Characterize the Noise Behavior of Metal-Framed Walls
Directory of Open Access Journals (Sweden)
Arun Arjunan
2015-08-01
Full Text Available Architects, designers, and engineers are making great efforts to design acoustically-efficient metal-framed walls, minimizing acoustic bridging. Therefore, efficient simulation models to predict the acoustic insulation complying with ISO 10140 are needed at a design stage. In order to achieve this, a numerical model consisting of two fluid-filled reverberation chambers, partitioned using a metal-framed wall, is to be simulated at one-third-octaves. This produces a large simulation model consisting of several millions of nodes and elements. Therefore, efficient meshing procedures are necessary to obtain better solution times and to effectively utilise computational resources. Such models should also demonstrate effective Fluid-Structure Interaction (FSI along with acoustic-fluid coupling to simulate a realistic scenario. In this contribution, the development of a finite element frequency-dependent mesh model that can characterize the sound insulation of metal-framed walls is presented. Preliminary results on the application of the proposed model to study the geometric contribution of stud frames on the overall acoustic performance of metal-framed walls are also presented. It is considered that the presented numerical model can be used to effectively visualize the noise behaviour of advanced materials and multi-material structures.
Numerical solutions to the cosmological 3-fluid problem
Azreg-Aïnou, Mustapha
2013-12-01
We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration (TPA) is much larger than the set discussed in the literature. The gradual inclusion of ordinary and dark matters results in an everywhere, but near the origin, smoother and right shifted (along the time axis) acceleration curve. For the 3-fluid problem, the energy density need not exhibit a plateau during the acceleration period. Much excess in the dark matter and/or ordinary matter energy densities would lead the universe to undergo an eternal deceleration expansion. For the 3-fluid problem with a single exponential potential we conclude that the Big Bang Nucleosynthesis constraint is not fulfilled if the universe is to undergo a TPA. The 3-fluid model remains a good approximation for the description of large scale structures.
Symmetry preserving compact schemes for numerical solution of PDEs
Ozbenli, Ersin; Vedula, Prakash
2017-11-01
In this study, a new approach for construction of invariant, high order accurate compact finite difference schemes that preserve Lie symmetry groups of underlying partial differential equations (PDEs) is presented. It is well known that compact numerical schemes based on Pade approximants achieve high order accuracy with a relatively small number of stencil points and are found to have good spectral-like resolution. Considering applicable Lie symmetry groups (such as translation, scaling, rotation, and projection groups) of underlying PDEs, invariant compact schemes are developed based on the use of equivariant moving frames and extended group transformations. This work represents an extension of the authors recent work on construction of invariant, high-order, non-compact, finite difference schemes based on the method of modified equations. Performance of the proposed symmetry preserving compact schemes is evaluated via consideration of some canonical PDEs like linear advection-diffusion equation, inviscid Burgers' equation, and viscous Burgers' equation. Effects on accuracy due to choice of subgroups used in construction of these schemes will be discussed. Generalization of the proposed framework to multidimensional problems and non-orthogonal grids will also be presented.
Directory of Open Access Journals (Sweden)
Emran Tohidi
2016-01-01
Full Text Available This article contributes a matrix approach by using Taylor approximation to obtain the numerical solution of one-dimensional time-dependent parabolic partial differential equations (PDEs subject to nonlocal boundary integral conditions. We first impose the initial and boundary conditions to the main problems and then reach to the associated integro-PDEs. By using operational matrices and also the completeness of the monomials basis, the obtained integro-PDEs will be reduced to the generalized Sylvester equations. For solving these algebraic systems, we apply a famous technique in Krylov subspace iterative methods. A numerical example is considered to show the efficiency of the proposed idea.
Pareto Efficient Solutions of Attack-Defence Trees
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2015-01-01
maximising probability. In order to tackle this challenge, we devise automated techniques that optimise all parameters at once. Moreover, in the case of conflicting parameters our techniques compute the set of all optimal solutions, defined in terms of Pareto efficiency. The developments are carried out...
An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation AXB+CXHD=F
Directory of Open Access Journals (Sweden)
Ning Li
2013-01-01
Full Text Available We propose an iterative algorithm for solving the reflexive solution of the quaternion matrix equation AXB+CXHD=F. When the matrix equation is consistent over reflexive matrix X, a reflexive solution can be obtained within finite iteration steps in the absence of roundoff errors. By the proposed iterative algorithm, the least Frobenius norm reflexive solution of the matrix equation can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate reflexive solution to a given reflexive matrix X0 can be derived by finding the least Frobenius norm reflexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
National Research Council Canada - National Science Library
Thiago Antonini Alves; Ricardo Alan Verdú Ramos; Cassio Roberto Macedo Maia
2015-01-01
In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT...
Efficient solution and analysis of large-scale goal programmes
Energy Technology Data Exchange (ETDEWEB)
Jones, D.; Tamiz, M.
1994-12-31
Goal Programming (GP) models are formed by the extension of Linear Programming (LP) to include multiple, possibly conflicting, objectives. The past two decades have seen a wealth of GP applications along with theoretical papers describing methods for the analysis and solution of GPs. With the application area of GP covering and extending that of LP, GP models the size of recent large-scale LP models have arisen. Such models may contain large numbers of objectives as well as constraints and variables. These models require the adaption of LP analysis techniques to account for their size and further specialized GP-speed-ups to lower solution time. This paper investigates efficient methods of pareto-efficiency analysis and restoration, normalization, redundancy checking, preference function modelling, and interactive method application, appropriate for large-scale GPs as well as suggesting a refined simplex procedure more appropriate for solution of GPs.
Efficiency of Osmotic Dehydration of Apples in Polyols Solutions
Directory of Open Access Journals (Sweden)
Joanna Cichowska
2018-02-01
Full Text Available The present study aimed to evaluate the influence of selected compounds from the polyol group, as well as other saccharides, on the osmotic dehydration process of apples. The following alternative solutions were examined: erythritol, xylitol, maltitol, inulin and oligofructose. Efficiency of the osmotic dehydration process was evaluated based on the kinetics of the process, and through comparison of the results obtained during the application of a sucrose solution. This innovative research utilizes alternative solutions in osmotic pretreatment, which until now, have not been commonly used in fruit processing by researchers worldwide. Results indicate that erythritol and xylitol show stronger or similar efficiency to sucrose; however, the use of inulin, as well as oligofructose, was not satisfactory due to the insufficient, small osmotic driving forces of the process, and the low values of mass transfer parameters.
Numerical methods for the solution of ordinary differential equations
Azeem, M
1999-01-01
The ode 113 code solves non-stiff differential equations and is a fully variable step, variable order, PECE implementation in terms of modified divided differences of Adams-Bashforth-Moulton family of formulas of order 1-12. The main objectives of this project were to modify PECE mode of ode 113 into PEC mode, study the variable step size and variable order strategy of both the modes and finally, develop the switching strategy between both PECE and PEC modes to minimize the cost of solving the ordinary differential equations. Using some test problems (including stiff, mild stiff and non-stiff), it was found that the PEC mode was more efficient for non-stiff problems at crude and intermediate tolerances and the PECE mode for all problems at the stringent tolerance. An automatic switching strategy was developed using the results observed from the step size and order plots of all the test problems for both the modes and gave the optimum results.
Numerical solution of the Fokker--Planck equations for a multi-species plasma
Energy Technology Data Exchange (ETDEWEB)
Killeen, J.; Mirin, A.A.
1977-03-11
Two numerical models used for studying collisional multispecies plasmas are described. The mathematical model is the Boltzmann kinetic equation with Fokker-Planck collision terms. A one-dimensional code and a two-dimensional code, used for the solution of the time-dependent Fokker-Planck equations for ion and electron distribution functions in velocity space, are described. The required equations and boundary conditions are derived and numerical techniques for their solution are given.
Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind
Directory of Open Access Journals (Sweden)
Abdon Atangana
2013-01-01
Full Text Available This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.
Directory of Open Access Journals (Sweden)
Susmita Paul
2016-03-01
Full Text Available This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using the Runge–Kutta–Fehlberg method (RKF. A comparison between Runge–Kutta–Fehlberg method (RKF and the Laplace Adomian Decomposition method (LADM is carried out and exact solution is found out to verify the applicability, efficiency and accuracy of the method. The obtained approximate solution shows that the Runge–Kutta–Fehlberg method (RKF is a more powerful numerical technique for solving a system of nonlinear differential equations.
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.
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.
Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil
Kozel K.; Kryštůfek P.
2013-01-01
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.
A numerical solution for a class of time fractional diffusion equations with delay
Directory of Open Access Journals (Sweden)
Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
Directory of Open Access Journals (Sweden)
Grégory Antoni
2017-01-01
Full Text Available The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.
Yıgıt, Gülsemay; Bayram, Mustafa
2017-01-01
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient matrix which is necessary to get numerical results. Following this, different class of perturbation problems are considered as test problems. Then, all results are shown in tables and also comparison between numerical and exact solution shows the accuracy a...
Efficient Numerical Calculation of Evaporating Sprays in Combustion Chamber Flows
Schmehl, R.; Klose, G.; Maier, G.; Wittig, S.
1998-01-01
Representing two different conceptual approaches, either Eulerian continuum models or Lagrangian particle models are commonly applied for the numerical description of dispersed two phase flows. Taking advantage of the positive features inherent to each model, a combination approach is presented in
Efficient Numerical Methods for Stochastic Differential Equations in Computational Finance
Happola, Juho
2017-09-19
Stochastic Differential Equations (SDE) offer a rich framework to model the probabilistic evolution of the state of a system. Numerical approximation methods are typically needed in evaluating relevant Quantities of Interest arising from such models. In this dissertation, we present novel effective methods for evaluating Quantities of Interest relevant to computational finance when the state of the system is described by an SDE.
Numerical solution of first order initial value problem using quartic spline method
Ala'yed, Osama; Ying, Teh Yuan; Saaban, Azizan
2015-12-01
Any first order initial value problem can be integrated numerically by discretizing the interval of integration into a number of subintervals, either with equally distributed grid points or non-equally distributed grid points. Hence, as the integration advances, the numerical solutions at the grid points are calculated and being known. However, the numerical solutions between the grid points remain unknown. This will form difficulty to individuals who wish to study a particular solution which may not fall on the grid points. Therefore, some sorts of interpolation techniques are needed to deal with such difficulty. Spline interpolation technique remains as a well known approach to approximate the numerical solution of a first order initial value problem, not only at the grid points but also everywhere between the grid points. In this short article, a new quartic spline method has been derived to obtain the numerical solution for first order initial value problem. The key idea of the derivation is to treat the third derivative of the quartic spline function to be a linear polynomial, and obtain the quartic spline function with undetermined coefficients after three integrations. The new quartic spline function is ready to be used when all unknown coefficients are found. We also described an algorithm for the new quartic spline method when used to obtain the numerical solution of any first order initial value problem. Two test problems have been used for numerical experimentations purposes. Numerical results seem to indicate that the new quartic spline method is reliable in solving first order initial value problem. We have compared the numerical results generated by the new quartic spline method with those obtained from an existing spline method. Both methods are found to have comparable accuracy.
Nadeem, Sohail; Masood, Sadaf; Mehmood, Rashid; Sadiq, Muhammad Adil
2015-01-01
The present analysis deals with flow and heat transfer aspects of a micropolar nanofluid between two horizontal parallel plates in a rotating system. The governing partial differential equations for momentum, energy, micro rotation and nano-particles concentration are presented. Similarity transformations are utilized to convert the system of partial differential equations into system of ordinary differential equations. The reduced equations are solved analytically with the help of optimal homotopy analysis method (OHAM). Analytical solutions for velocity, temperature, micro-rotation and concentration profiles are expressed graphically against various emerging physical parameters. Physical quantities of interest such as skin friction co-efficient, local heat and local mass fluxes are also computed both analytically and numerically through mid-point integration scheme. It is found that both the solutions are in excellent agreement. Local skin friction coefficient is found to be higher for the case of strong concentration i.e. n=0, as compared to the case of weak concentration n=0.50. Influence of strong and weak concentration on Nusselt and Sherwood number appear to be similar in a quantitative sense.
Assessment of Efficiency and Performance in Tsunami Numerical Modeling with GPU
Yalciner, Bora; Zaytsev, Andrey
2017-04-01
Non-linear shallow water equations (NSWE) are used to solve the propagation and coastal amplification of long waves and tsunamis. Leap Frog scheme of finite difference technique is one of the satisfactory numerical methods which is widely used in these problems. Tsunami numerical models are necessary for not only academic but also operational purposes which need faster and accurate solutions. Recent developments in information technology provide considerably faster numerical solutions in this respect and are becoming one of the crucial requirements. Tsunami numerical code NAMI DANCE uses finite difference numerical method to solve linear and non-linear forms of shallow water equations for long wave problems, specifically for tsunamis. In this study, the new code is structured for Graphical Processing Unit (GPU) using CUDA API. The new code is applied to different (analytical, experimental and field) benchmark problems of tsunamis for tests. One of those applications is 2011 Great East Japan tsunami which was instrumentally recorded on various types of gauges including tide and wave gauges and offshore GPS buoys cabled Ocean Bottom Pressure (OBP) gauges and DART buoys. The accuracy of the results are compared with the measurements and fairly well agreements are obtained. The efficiency and performance of the code is also compared with the version using multi-core Central Processing Unit (CPU). Dependence of simulation speed with GPU on linear or non-linear solutions is also investigated. One of the results is that the simulation speed is increased up to 75 times comparing to the process time in the computer using single 4/8 thread multi-core CPU. The results are presented with comparisons and discussions. Furthermore how multi-dimensional finite difference problems fits towards GPU architecture is also discussed. The research leading to this study has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No
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 Quantum Cosmological Model Simulating Boson and Fermion Creation
Directory of Open Access Journals (Sweden)
Christianto V.
2009-04-01
Full Text Available A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented. This solution is based on a Wheeler-De Witt equation obtained by Krechet, Fil’chenkov, and Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.
Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method
Directory of Open Access Journals (Sweden)
Limei Yan
2013-01-01
Full Text Available A relatively new iterative Laplace transform method, which combines two methods; the iterative method and the Laplace transform method, is applied to obtain the numerical solutions of fractional Fokker-Planck equations. The method gives numerical solutions in the form of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and straightforward when applied to space-time fractional Fokker-Planck equations. The method provides a promising tool for solving space-time fractional partial differential equations.
Mohammed, Y.; Forgotson, J.
2006-12-01
Dehydration of shales is a key feature in mediating shale related problems such as wellbore stability, swelling, landslides and soil stability problems. Chemical osmotic behaviors of shale have been studied as a means of dehydration of shale when exposed to pore fluid chemical potential gradients. New laboratory studies using Pierre Shale and clayey sediments are presented examining osmotic membrane efficiency, solute diffusion, swelling pressure, permeability, and mineralogical and textural changes with time as functions of temperature, effective pressure, and pore fluid chemistry. Experiments were run with up to 2 molal calcium, sodium, and potassium nitrate salt solutions, to 200 degrees Celsius and 34.5 MPa effective pressure, and were several months in duration. Competing effects increase or decrease membrane efficiency with time and are highly dependent on dominant cation in solution. Membrane efficiency progressively increases with consolidation and swelling, while it decreases with chemical diffusion and continued illitization of smectite. These effects are captured in a mathematical model for membrane efficiency and by numerical solution of coupled solute and water reaction-transport equations modeling experimental results.
Cisneros, L. A.; Ize, J.; Minzoni, A. A.
2009-07-01
We develop a modulation theory based on a suitably averaged Lagrangian for steady solutions of the Sine-Gordon equation in a two dimensional lattice. These lump solutions are nonzero in circular or polygonal regions and zero elsewhere. The modulation theory gives approximate solutions away from small perturbations of the exact anti-continuum solutions for both radial and polygonal solutions. We show how the Peierls-Nabarro potential determines the shape of the boundary between excited sites and the zero solution. These solutions are compared with the corresponding numerical solutions and significant agreement is found. Moreover, we show that solutions with a large radius (more than sixteen lattice sites) can be explained using a continuous trial function for the averaged Lagrangian, while smaller polygonal solutions can be constructed using a trial function, which takes into account the angular variation of the boundary imposed by the lattice. Finally, the ideas of equivariant bifurcation theory are used to obtain a full numerical description of the solution branches as functions of the coupling parameter between neighboring sites. The results of this work can be used to study steady solutions for other types of lattice equations.
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Handlovičová Angela
2016-01-01
Full Text Available In this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.
Efficient approximation of random fields for numerical applications
Harbrecht, Helmut
2015-01-07
We consider the rapid computation of separable expansions for the approximation of random fields. We compare approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. We provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples validate and quantify the considered methods.
Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.
2007-01-01
Abstract: 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
A numerical guide to the solution of the bidomain equations of cardiac electrophysiology
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.
Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions
Directory of Open Access Journals (Sweden)
R. Jooma
2017-01-01
Full Text Available A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions.
An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Moh’d Khier Al-Srihin
2017-01-01
Full Text Available In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.
Efficient Solutions for New Homes Case Study: Savannah Gardens
Energy Technology Data Exchange (ETDEWEB)
None
2016-03-15
The Savannah Housing Department is leading sustainable and affordable housing development in Georgia. It partnered with Southface Energy Institute, a member of the U.S. Department of Energy’s Partnership for Home Innovation Building America research team, to seek cost-effective solutions for increasing the energy efficiency of the Savannah Housing Department’s standard single-family home plans in the Savannah Gardens Community. Based on engineering, cost, and constructability analyses, the combined research team chose to pilot two technologies to evaluate efficiency and comfort impacts for homeowners: a heat-pump water heater in an encapsulated attic and an insulated exterior wall sheathing.
Numerical calculation of particle collection efficiency in an ...
Indian Academy of Sciences (India)
The latter ionizes the air stream and transfers electric charge to particles which are then driven by electrostatic forces to the collecting plates on which they are deposited, and later removed. The collecting plates of ESP are often placed in tandem, one after another, to increase the total collection efficiency, as particles ...
A Numerical and Experimental Study of Local Exhaust Capture Efficiency
DEFF Research Database (Denmark)
Madsen, U.; Breum, N. O.; Nielsen, Peter Vilhelm
1993-01-01
Direct capture efficiency of a local exhaust system is defined by introducing an imaginary control box surrounding the contaminant source and the exhaust opening. The imaginary box makes it possible to distinguish between contaminants directly captured and those that escape. Two methods...
Directory of Open Access Journals (Sweden)
V. M. Mikhailov
2017-12-01
Full Text Available Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use
Directory of Open Access Journals (Sweden)
Mark A Lau
2016-09-01
Full Text Available This paper presents the implementation of numerical and analytical solutions of some of the classical partial differential equations using Excel spreadsheets. In particular, the heat equation, wave equation, and Laplace’s equation are presented herein since these equations have well known analytical solutions. The numerical solutions can be easily obtained once the differential equations are discretized via finite differences and then using cell formulas to implement the resulting recursive algorithms and other iterative methods such as the successive over-relaxation (SOR method. The graphing capabilities of spreadsheets can be exploited to enhance the visualization of the solutions to these equations. Furthermore, using Visual Basic for Applications (VBA can greatly facilitate the implementation of the analytical solutions to these equations, and in the process, one obtains Fourier series approximations to functions governing initial and/or boundary conditions.
Efficient Traveltime Solutions of the TI Acoustic Eikonal Equation
Waheed, Umair bin
2014-10-22
Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for integral imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order nonlinearity of the TI eikonal equation, which requires solving a quartic polynomial at each computational step. Using perturbation theory, we approximate the first-order discretized form of the TI eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter. Such perturbation, applied to the discretized form of the eikonal equation, does not impose any restrictions on the complexity of the perturbed parameter field. Therefore, it provides accurate traveltime solutions even for the anisotropic Marmousi model, with complex distribution of velocity and anellipticity anisotropy parameter. The formulation allows tremendous cost reduction compared to using the exact TI eikonal solver. Furthermore, comparative tests with previously developed approximations illustrate remarkable gain in accuracy of the proposed approximation, without any addition to the computational cost.
Gordeev, S. I.; Bogatova, T. F.; Ryzhkov, A. F.
2017-11-01
Raising the efficiency and environmental friendliness of electric power generation from coal is the aim of numerous research groups today. The traditional approach based on the steam power cycle has reached its efficiency limit, prompted by materials development and maneuverability performance. The rival approach based on the combined cycle is also drawing nearer to its efficiency limit. However, there is a reserve for efficiency increase of the integrated gasification combined cycle, which has the energy efficiency at the level of modern steam-turbine power units. The limit of increase in efficiency is the efficiency of NGCC. One of the main problems of the IGCC is higher costs of receiving and preparing fuel gas for GTU. It would be reasonable to decrease the necessary amount of fuel gas in the power unit to minimize the costs. The effect can be reached by raising of the heat value of fuel gas, its heat content and the heat content of cycle air. On the example of the process flowsheet of the IGCC with a power of 500 MW, running on Kuznetsk bituminous coal, by means of software Thermoflex, the influence of the developed technical solutions on the efficiency of the power plant is considered. It is received that rise in steam-air blast temperature to 900°C leads to an increase in conversion efficiency up to 84.2%. An increase in temperature levels of fuel gas clean-up to 900°C leads to an increase in the IGCC efficiency gross/net by 3.42%. Cycle air heating reduces the need for fuel gas by 40% and raises the IGCC efficiency gross/net by 0.85-1.22%. The offered solutions for IGCC allow to exceed net efficiency of analogous plants by 1.8-2.3%.
Platzek, F.W.
2017-01-01
A river engineer is challenged with the task of setting up an appropriate model for a certain application. The model needs to provide suitable answers to the questions asked (i.e. be effective) and needs to do this within the available time (i.e. be efficient). To set up such a model with sufficient
Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem
Directory of Open Access Journals (Sweden)
Susmita Paul
2016-01-01
Full Text Available We try to compare the solutions by some numerical techniques when we apply the methods on some mathematical biology problems. The Runge-Kutta-Fehlberg (RKF method is a promising method to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for insect population, one-species Lotka-Volterra model. The technique is described and illustrated by numerical examples. We modify the population models by taking the Holling type III functional response and intraspecific competition term and hence we solve it by this numerical technique and show that RKF method gives good results. We try to compare this method with the Laplace Adomian Decomposition Method (LADM and with the exact solutions.
Oscillating solutions of the Vlasov-Poisson system-A numerical investigation
Ramming, Tobias; Rein, Gerhard
2018-02-01
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in time or damped. Along one-parameter families of polytropic steady states we establish an Eddington-Ritter type relation which relates the period of the oscillation to the central density of the steady state. The numerically obtained periods are used to estimate possible periods for typical elliptical galaxies.
Numerical Solution of The Linear Fredholm Integral Equations of the Second Kind
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N. Parandin
2010-03-01
Full Text Available The theory of integral equation is one of the major topics of applied mathematics. The main purpose of this paper is to introduce a numerical method based on the interpolation for approximating the solution of the second kind linear Fredholm integral equation. In this case, the divided differences method is applied. At last, two numerical examples are presented to show the accuracy of the proposed method
An efficient numerical method for solving the Boltzmann equation in multidimensions
Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas
2018-01-01
In this paper we deal with the extension of the Fast Kinetic Scheme (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The scheme combines a robust and fast method for treating the transport part based on an innovative Lagrangian technique supplemented with conservative fast spectral schemes to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is numerically tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different numerical methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.
Higher-order numerical solutions using cubic splines. [for partial differential equations
Rubin, S. G.; Khosla, P. K.
1975-01-01
A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-
2nd International Workshop on the Numerical Solution of Markov Chains
1995-01-01
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Nacozy, P. E.
1984-01-01
The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.
Solutions manual to accompany An introduction to numerical methods and analysis
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
Use of Green's functions in the numerical solution of two-point boundary value problems
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.
Finite analytic numerical solution of two-dimensional channel flow over a backward-facing step
Ho, K.-S.; Chen, C.-J.
1986-01-01
Laminar channel flow over a backward-facing step is investigated. The finite analytic (FA) method is used to obtain the numerical solution. The FA solutions predict the recirculation zone lengths and the recirculated mass flow rates for Reynolds numbers, Re, of 25, 50, 73, 125, 191 and 229 which correlate well with experimental measurements. The general flow patterns of the recirculation region flows for the Reynolds numbers considered in this study are similar to each other.
Analytical solutions and numerical modeling for a dam-break problem in inclined channels
Pelinovsky, Efim; Didenkulova, Ira; Didenkulov, Oleg; Rodin, Artem
2016-04-01
Here we obtain different analytical solutions of the shallow-water equations for inviscid nonlinear waves in inclined channels. (i) The first solution describes Riemann wave moving up or down alone the channel slope. It requires the initial fluid flow, which often accompanies waves generated by landslides. This solution is valid for a finite time before the wave breaks. (ii) The second solution generalizes the classical dam-break problem for the case of a dam located in the inclined channel. In this case the cross-section of the channel influences the speed of wave propagation inside the channel, and therefore changes wave dynamics inside the channel compare to the plane beach. (iii) The third solution describes the intermediate stage of the wave front dynamics for a dam of a large height. This solution is derived with the use of generalized Carrier-Greenspan approach developed early by Didenkulova & Pelinovsky (2011) and Rybkin et al (2014). Some of the analytical solutions are tested with the means of numerical modeling. The numerical modeling is carried out using the CLAWPACK software based on nonlinear shallow water equations. Application of the described solutions to possible laboratory experiments is discussed.
Numerical investigation of the thrust efficiency of a laser propelled vehicle
Energy Technology Data Exchange (ETDEWEB)
mulroy jr
1990-08-01
The flow situation for a thruster propelled by ablated gas which is energized by a laser pulse is numerically simulated. The flow is axisymmetric and nonsteady, and is assumed to be inviscid due to its high Reynolds number. The high pressure expansion of the laser heated gas generates thrust as it pushes against the vehicle. Gas expansion lateral to the thrust vector causes performance to decrease. The vehicle geometry and the laser pulse characteristics determine the degree to which the flow is one dimensional. As the thruster's parameters are varied, its impulse is calculated and compared to the limiting impulse of a one-dimensional system, and thus the thrust efficiency is computed. Lateral expansion losses computed by simulating the flow of the expanding gas time-accurately on a computer are far less than losses predicted using the method of characteristics, which is the best alternate means of computation. Flows which exhibit a substantial amount of lateral expansion can still yield an expansion efficiency which exceeds 70%. This finding has significant implications on the eventual design of flight hardware. Steger and Warming's flux split numerics for the Euler equations are modified for blast simulations into near vacuum ambient conditions. At the interface between the near vacuum ambient and the wave front, the solution is first order accurate but sufficiently robust to handle pressure ratios exceeding one million and density ratios exceeding 10,000 between the thrust gas and the ambient gas. Elsewhere the solution is second order accurate. The majority of the calculations performed assume an ideal gas equation of state with {gamma} = 1.2. The propellant Lithium Hydride has shown excellent promise in the laboratory, yielding I{sub sp} = 800-1000 sec. Equilibrium and kinetic modeling of LiH is undertaken, with a variable {gamma} of from 1.25 to 1.66 resulting from the kinetic assumptions of ionization equilibrium and frozen chemistry. These
Efficient planning and numerical analysis of industrial hemming processes
Burchitz, Igor; Fritsche, David; Grundmann, Göran; Hillmann, Matthias
2011-08-01
Hemming is a forming operation used in the automotive industry to join inner and outer components during the assembly of closures. These are typically opening parts of the body-in-white with additional requirements to their visual appearance. A suitable production concept of hemming operation which satisfies quality, capacity and cost requirements is determined during hemming planning activities. A digital tool to facilitate these activities and minimize the amount of trial and error iterations in try-out phase is presented in this paper. This tool can be used to define process plan, active tool surfaces and suitable process parameters for both die hemming and roll hemming operations. In case of early feasibility studies, when the die layout of the drawing operation is still not available, 3D part geometry is used directly to develop the concept of hemming process. Advanced validation studies, aimed at process optimization and controlling defects associated with hemming, can be based on complete simulation of all forming operations. Validation and analysis of developed concepts of hemming operation is done using the standard AutoForm-Incremental solver. Submesh strategy and special algorithm for contact description between inner and outer parts were implemented to ensure that accurate simulation results can be obtained within reasonable calculation time. Performance of the new software tool for hemming planning and accuracy of simulation results are demonstrated using several simple benchmarks and a real industrial part. It is shown that the new software tool can help to secure the efficient production launch by providing adequate support in try-out phase.
Efficient Solution of the Electronic Eigenvalue Problem Using Wavepacket Propagation.
Neville, Simon P; Schuurman, Michael S
2018-02-15
We report how imaginary time wavepacket propagation may be used to efficiently calculate the lowest-lying eigenstates of the electronic Hamiltonian. This approach, known as the relaxation method in the quantum dynamics community, represents a fundamentally different approach to the solution of the electronic eigenvalue problem in comparison to traditional iterative subspace diagonalization schemes such as the Davidson and Lanczos methods. In order to render the relaxation method computationally competitive with existing iterative subspace methods, an extended short iterative Lanczos wavepacket propagation scheme is proposed and implemented. In the examples presented here, we show that by using an efficient wavepacket propagation algorithm the relaxation method is, at worst, as computationally expensive as the commonly used block Davidson-Liu algorithm, and in certain cases, significantly less so.
On the limits of numerical astronomical solutions used in paleoclimate studies
Zeebe, Richard E.
2017-04-01
Numerical solutions of the equations of the Solar System estimate Earth's orbital parameters in the past and represent the backbone of cyclostratigraphy and astrochronology, now widely applied in geology and paleoclimatology. Given one numerical realization of a Solar System model (i.e., obtained using one code or integrator package), various parameters determine the properties of the solution and usually limit its validity to a certain time period. Such limitations are denoted here as "internal" and include limitations due to (i) the underlying physics/physical model and (ii) numerics. The physics include initial coordinates and velocities of Solar System bodies, treatment of the Moon and asteroids, the Sun's quadrupole moment, and the intrinsic dynamics of the Solar System itself, i.e., its chaotic nature. Numerical issues include solver algorithm, numerical accuracy (e.g., time step), and round-off errors. At present, internal limitations seem to restrict the validity of astronomical solutions to perhaps the past 50 or 60 myr. However, little is currently known about "external" limitations, that is, how do different numerical realizations compare, say, between different investigators using different codes and integrators? Hitherto only two solutions for Earth's eccentricity appear to be used in paleoclimate studies, provided by two different groups that integrated the full Solar System equations over the past >100 myr (Laskar and coworkers and Varadi et al. 2003). In this contribution, I will present results from new Solar System integrations for Earth's eccentricity obtained using the integrator package HNBody (Rauch and Hamilton 2002). I will discuss the various internal limitations listed above within the framework of the present simulations. I will also compare the results to the existing solutions, the details of which are still being sorted out as several simulations are still running at the time of writing.
Macomber, B.; Woollands, R. M.; Probe, A.; Younes, A.; Bai, X.; Junkins, J.
2013-09-01
Modified Chebyshev Picard Iteration (MCPI) is an iterative numerical method for approximating solutions of linear or non-linear Ordinary Differential Equations (ODEs) to obtain time histories of system state trajectories. Unlike other step-by-step differential equation solvers, the Runge-Kutta family of numerical integrators for example, MCPI approximates long arcs of the state trajectory with an iterative path approximation approach, and is ideally suited to parallel computation. Orthogonal Chebyshev Polynomials are used as basis functions during each path iteration; the integrations of the Picard iteration are then done analytically. Due to the orthogonality of the Chebyshev basis functions, the least square approximations are computed without matrix inversion; the coefficients are computed robustly from discrete inner products. As a consequence of discrete sampling and weighting adopted for the inner product definition, Runge phenomena errors are minimized near the ends of the approximation intervals. The MCPI algorithm utilizes a vector-matrix framework for computational efficiency. Additionally, all Chebyshev coefficients and integrand function evaluations are independent, meaning they can be simultaneously computed in parallel for further decreased computational cost. Over an order of magnitude speedup from traditional methods is achieved in serial processing, and an additional order of magnitude is achievable in parallel architectures. This paper presents a new MCPI library, a modular toolset designed to allow MCPI to be easily applied to a wide variety of ODE systems. Library users will not have to concern themselves with the underlying mathematics behind the MCPI method. Inputs are the boundary conditions of the dynamical system, the integrand function governing system behavior, and the desired time interval of integration, and the output is a time history of the system states over the interval of interest. Examples from the field of astrodynamics are
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
Directory of Open Access Journals (Sweden)
H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach
Geng, Xiaolong; Boufadel, Michel C.; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L.; Miller, Richard S.
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach.
Geng, Xiaolong; Boufadel, Michel C; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L; Miller, Richard S
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies. Copyright © 2014 Elsevier B.V. All rights reserved.
Directory of Open Access Journals (Sweden)
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.
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.
COMPARING NUMERICAL METHODS FOR THE SOLUTION OF THE DAMPED FORCED OSCILLATOR PROBLEM
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A. R. Vahidi
2009-07-01
Full Text Available In this paper, we present a comparative study between the Adomian decomposition method and two classical well-known Runge-Kutta and central difference methods for the solution of damped forced oscillator problem. We show that the Adomian decomposition method for this problem gives more accurate approximations relative to other numerical methods and is easier to apply.
Symmetry and Numerical Solutions for Systems of Non-linear Reaction Diffusion Equations
KUMAR,SANJEEV; Singh, Ravendra
2007-01-01
Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion equation with respect to one-dimensional Algebra is carried out in this work. Some classes of analytical and numerical solutions are obtained and expressed using suitable graphs.
On the numerical solution of diffusion-reaction equations with singular source terms
Ashyraliyev, M.; Blom, J.G.; Verwer, J.G.
2008-01-01
A numerical study is presented of reaction-diffusion problems having singular reaction source terms, singular in the sense that within the spatial domain the source is defined by a Dirac delta function expression on a lower dimensional surface.A consequence is that solutions will be continuous, but
On the numerical solution of diffusion-reaction equations with singular source terms
M. Ashyraliyev (Maksat); J.G. Blom (Joke); J.G. Verwer (Jan)
2008-01-01
htmlabstractA numerical study is presented of reaction–diffusion problems having singular reaction source terms, singular in the sense that within the spatial domain the source is defined by a Dirac delta function expression on a lower dimensional surface. A consequence is that solutions will be
A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
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.
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...
Three numerical algorithms were compared to provide a solution of a radiative transfer equation (RTE) for plane albedo (hemispherical reflectance) in semi-infinite one-dimensional plane-parallel layer. Algorithms were based on the invariant imbedding method and two different var...
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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.
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.
Efficient removal of mercury from aqueous solutions and industrial effluent.
Dos Santos, Maria B P; Leal, Katia Z; Oliveira, Fernando J S; Sella, Silvia M; Vieira, Méri D; Marques, Elisa M D; Gomes, Vanessa A C
2015-01-01
The objective of this study was to examine the ability of a solid waste produced during beneficiation of ornamental rocks to remove mercury (Hg) from an industrial effluent and aqueous solutions under various conditions. Batch studies have been carried out by observing the effects of pH, concentration of the adsorbate, contact time, and so on. Various sorption isotherm models such as Langmuir, Freundlich, and Tóth have been applied for the adsorbent. Film and intraparticle diffusion were both found to be rate-limiting steps. Adsorption was properly described by the Freundlich model (capacity constant of 0.3090 (mg g(-1))(mg L(-1))(-1/n) and adsorption intensity indicator of 2.2939), which indicated a favorable sorption and encouraged subsequent studies for treatment of Hg-containing industrial effluent. Industrial effluent treatment efficiency reached Hg removals greater than 90% by using ornamental rock solid waste (ORSW). Besides, desorption studies indicated that the maximum recovery of mercury was 100 ± 2% for 1 mol L(-1) HNO3 and 74 ± 8% for 0.1 mol L(-1) HNO3. The ORSW could be reused thrice without significant difference on the Hg removal rate from industrial effluent. These findings place ORSW as a promising efficient and low-cost adsorbent for the removal of Hg from aqueous solutions and industrial effluent.
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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.
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model
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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.
NUMERICAL SOLUTION OF THE GODUNOV - SULTANGAZIN SYSTEM OF EQUATIONS. PERIODIC CASE
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Vasil’eva Ol’ga Aleksandrovna
2016-04-01
Full Text Available The Cauchy problem of the Godunov - Sultangazin system of equations with periodic initial conditions is considered in the article. The Godunov - Sultangazin system of equations is a model problem of the kinetic theory of gases. It is a discrete kinetic model of one-dimensional gas consisting of identical monatomic molecules. The molecules can have one of three speeds. So, there are three groups of molecules. The molecules of the first two groups have the speeds equal in values and opposite in directions. The molecules of the third group have zero speed. The considered mathematical model has a number of properties of Boltzmann equation. This system of the equations is a quasi-linear system of partial differential equations. There is no analytic solution for this problem in the general case. So, numerical investigation of the Cauchy problem of the Godunov - Sultangazin system is very important. The finite-difference method of the first order is used for numerical investigation of the Cauchy problem of the Godunov - Sultangazin system of equations. The paper presents and discusses the results of numerical investigation of the Cauchy problem for the studied system solution with periodic initial condition. The dependence of the time of stabilization of the Cauchy problem solution of Godunov - Sultangazin system of equations from the decreasing parameter of system are obtained. The paper presents the dependence of time of energy exchange from the decreasing parameter. The solution stabilization to the equilibrium state is obtained. The stabilization time of Godunov - Sultangazin system solution is compared to the stabilization time of Carleman system solution in periodic case. The results of numerical investigation are in good agreement with the theoretical results obtained previously.
Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium
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M. A. Castro
2013-01-01
conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.
Quintic B-spline for the numerical solution of the good Boussinesq equation
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Shahid S. Siddiqi
2014-07-01
Full Text Available A numerical method is developed to solve the nonlinear Boussinesq equation using the quintic B-spline collocation method. Applying the Von Neumann stability analysis, the proposed method is shown to be unconditionally stable. An example has been considered to illustrate the efficiency of the method developed.
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.
Velocity-induced numerical solutions of reaction-diffusion systems on continuously growing domains
Madzvamuse, Anotida; Maini, Philip K.
2007-07-01
Reaction-diffusion systems have been widely studied in developmental biology, chemistry and more recently in financial mathematics. Most of these systems comprise nonlinear reaction terms which makes it difficult to find closed form solutions. It therefore becomes convenient to look for numerical solutions: finite difference, finite element, finite volume and spectral methods are typical examples of the numerical methods used. Most of these methods are locally based schemes. We examine the implications of mesh structure on numerically computed solutions of a well-studied reaction-diffusion model system on two-dimensional fixed and growing domains. The incorporation of domain growth creates an additional parameter - the grid-point velocity - and this greatly influences the selection of certain symmetric solutions for the ADI finite difference scheme when a uniform square mesh structure is used. Domain growth coupled with grid-point velocity on a uniform square mesh stabilises certain patterns which are however very sensitive to any kind of perturbation in mesh structure. We compare our results to those obtained by use of finite elements on unstructured triangular elements.
Sun, Hui; Zhou, Shenggao; Moore, David K; Cheng, Li-Tien; Li, Bo
2016-05-01
We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.
A Cell-Based Finite Difference Method for the Numerical Solution of PDEs
Salih, A.; Barron, R. M.; Friedl, J.
2011-11-01
The governing partial differential equations of fluid motion are usually numerically approximated using one of three methods: Finite Difference (FD), Finite Volume (FV) or Finite Element (FE). Finding practical solutions to the governing equations of fluid mechanics is one of the most challenging problems in engineering because these equations, in most cases, form a set of coupled non-linear partial differential equations. In this research, a new cell-centred Finite Difference (CCFD) formulation is developed that is applied in each individual cell of an arbitrary mesh discretizing the solution domain. This feature allows the application of the proposed FD numerical formulation on arbitrary mesh topologies, i.e., structured, unstructured or hybrid meshes. Initially, a simple test case is investigated to illustrate this method. The numerical results are compared with the analytical solution and/or a traditional FD solution. Lastly, two additional test cases are conducted to illustrate the ability of the CCFD method to handle mixed boundary types and its extendibility to other types of elliptic boundary value problems.
A New Method to Solve Numeric Solution of Nonlinear Dynamic System
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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.
A Hybrid Analytical-Numerical Solution to the Laminar Flow inside Biconical Ducts
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Thiago Antonini Alves
2015-10-01
Full Text Available In this work was presented a hybrid analytical-numerical solution to hydrodynamic problem of fully developed Newtonian laminar flow inside biconical ducts employing the Generalized Integral Transform Technique (GITT. In order to facilitate the analytical treatment and the application of the boundary conditions, a Conformal Transform was used to change the domain into a more suitable coordinate system. Thereafter, the GITT was applied on the momentum equation to obtain the velocity field. Numerical results were obtained for quantities of practical interest, such as maximum and minimum velocity, Fanning friction factor, Poiseuille number, Hagenbach factor and hydrodynamic entry length.
Numerical solution of continuous-time DSGE models under Poisson uncertainty
DEFF Research Database (Denmark)
Posch, Olaf; Trimborn, Timo
then use the Waveform Relaxation algorithm to provide a guess of the policy function and solve the resulting system of ordinary differential equations by standard methods and fix-point iteration. Analytical solutions are provided as a benchmark from which our numerical method can be used to explore broader......We propose a simple and powerful method for determining the transition process in continuous-time DSGE models under Poisson uncertainty numerically. The idea is to transform the system of stochastic differential equations into a system of functional differential equations of the retarded type. We...
A numerical solution of a singular boundary value problem arising in boundary layer theory.
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.
Directory of Open Access Journals (Sweden)
N. A. Ahmad
2017-01-01
Full Text Available A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK methods.
System solution to improve energy efficiency of HVAC systems
Chretien, L.; Becerra, R.; Salts, N. P.; Groll, E. A.
2017-08-01
According to recent surveys, heating and air conditioning systems account for over 45% of the total energy usage in US households. Three main types of HVAC systems are available to homeowners: (1) fixed-speed systems, where the compressor cycles on and off to match the cooling load; (2) multi-speed (typically, two-speed) systems, where the compressor can operate at multiple cooling capacities, leading to reduced cycling; and (3) variable-speed systems, where the compressor speed is adjusted to match the cooling load of the household, thereby providing higher efficiency and comfort levels through better temperature and humidity control. While energy consumption could reduce significantly by adopting variable-speed compressor systems, the market penetration has been limited to less than 10% of the total HVAC units and a vast majority of systems installed in new construction remains single speed. A few reasons may explain this phenomenon such as the complexity of the electronic circuitry required to vary compressor speed as well as the associated system cost. This paper outlines a system solution to boost the Seasonal Energy Efficiency Rating (SEER) of a traditional single-speed unit through using a low power electronic converter that allows the compressor to operate at multiple low capacity settings and is disabled at high compressor speeds.
Lian, Chenzhou
The focus of the research is to gain a better understanding of the mixing and combustion of propellants in a confined single element rocket engine combustor. The approach taken is to use the unsteady computational simulations of both liquid and gaseous oxygen reacting with gaseous hydrogen to study the effects of transient processes, recirculation regions and density variations under supercritical conditions. The physics of combustion involve intimate coupling between fluid dynamics, chemical kinetics and intense energy release and take place over an exceptionally wide range of scales. In the face of these monumental challenges, it remains the engineer's task to find acceptable simulation approach and reliable CFD algorithm for combustion simulations. To provide the computational robustness to allow detailed analyses of such complex problems, we start by investigating a method for enhancing the reliability of implicit computational algorithms and decreasing their sensitivity to initial conditions without adversely impacting their efficiency. Efficient convergence is maintained by specifying a large global CFL number while reliability is improved by limiting the local CFL number such that the solution change in any cell is less than a specified tolerance. The magnitude of the solution change is estimated from the calculated residual in a manner that requires negligible computational time. The method precludes unphysical excursions in Newton-like iterations in highly non-linear regions where Jacobians are changing rapidly as well as non-physical results during the computation. The method is tested against a series of problems to identify its characteristics and to verify the approach. The results reveal a substantial improvement in convergence reliability of implicit CFD applications that enables computations starting from simple initial conditions. The method is applied in the unsteady combustion simulations and allows long time running of the code without user
Numerical time-dependent solutions of the Schrödinger equation with piecewise continuous potentials
van Dijk, Wytse
2016-06-01
We consider accurate numerical solutions of the one-dimensional time-dependent Schrödinger equation when the potential is piecewise continuous. Spatial step sizes are defined for each of the regions between the discontinuities and a matching condition at the boundaries of the regions is employed. The Numerov method for spatial integration is particularly appropriate to this approach. By employing Padé approximants for the time-evolution operator, we obtain solutions with significantly improved precision without increased CPU time. This approach is also appropriate for adaptive changes in spatial step size even when there is no discontinuity of the potential.
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C. A. Raposo
2013-08-01
Full Text Available In this work we study the asymptotic behavior as t → ∞ of the solution for the Timoshenko system with delay term in the feedback. We use the semigroup theory for to prove the well-posedness of the system and for to establish the exponential stability. As far we know, there exist few results for problems with delay, where the asymptotic behavior is based on the Gearhart- Herbst-Pruss-Huang theorem to dissipative system. See [4], [5], [6]. Finally, we present numerical results of the solution of the system.
Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior
Directory of Open Access Journals (Sweden)
F. Ghomanjani
2014-01-01
Full Text Available We present a numerical method to solve boundary value problems (BVPs for singularly perturbed differential-difference equations with negative shift. In recent papers, the term negative shift has been used for delay. The Bezier curves method can solve boundary value problems for singularly perturbed differential-difference equations. The approximation process is done in two steps. First we divide the time interval, into k subintervals; second we approximate the trajectory and control functions in each subinterval by Bezier curves. We have chosen the Bezier curves as piecewise polynomials of degree n and determined Bezier curves on any subinterval by n+1 control points. The proposed method is simple and computationally advantageous. Several numerical examples are solved using the presented method; we compared the computed result with exact solution and plotted the graphs of the solution of the problems.
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H. Khalil
2015-06-01
Full Text Available We study shifted Legendre polynomials and develop some operational matrices of integrations. We use these operational matrices and develop new sophisticated technique for numerical solutions to the following coupled system of fredholm integro differential equations DU(x = f(x + 11 Z 1 0 K11(x, tU(tdt + 12 Z 1 0 K12(x, tV (tdt, DV (x = g(x + 21 Z 1 0 K21(x, tU(tdt + 22 Z 1 0 K22(x, tV (tdt, U(0 = C1, V (0 = C2, where D is fractional derivative of order with respect to x, 0 < 6 1, 11, 12, 21, 22 are real constants, f, g 2 C([0, 1] and K11, K12, K21, K22 2 C([0, 1]×[0, 1]. We develop simple procedure to reduce the coupled system of equations to a system of algebraic equations without discretizing the system. We provide examples and numerical simulations to show the applicability and simplicity of our results and to demonstrate that the results obtained using the new technique matches well with the exact solutions of the problem. We also provide error analysis.
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.
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
Halil Özer; Özkan Öz
2014-01-01
This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using fou...
Shiralashetti, S. C.; Deshi, A. B.
Wavelet analysis is a recently developed mathematical tool for many problems. One of its main attractive features is the ability to accurately represent general functions with small number of adaptively chosen wavelet coefficients. In this paper, the Legendre wavelet collocation method (LWCM) for the numerical solution of differential equations is presented. The proposed method gives better results than the existing ones. Some of the illustrative examples are included to observe the performance of the proposed scheme.
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 solutions of the Kawahara equation by the septic B-spline collocation method
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Battal Gazi Karakoc
2014-08-01
Full Text Available In this article, a numerical solution of the Kawahara equation is presented by septic B-spline collocation method. Applying the Von-Neumann stability analysis, the present method is shown to be unconditionally stable. The accuracy of the proposed method is checked by two test problems. L2 and L1 error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results.
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Andreas Ruffing
2001-01-01
Full Text Available We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.
The numerical solution of differential-algebraic systems by Runge-Kutta methods
Hairer, Ernst; Lubich, Christian
1989-01-01
The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.
A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation
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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.
Thin Film Packaging Solutions for High Efficiency OLED Lighting Products
Energy Technology Data Exchange (ETDEWEB)
None
2008-06-30
The objective of the 'Thin Film Packaging Solutions for High Efficiency OLED Lighting Products' project is to demonstrate thin film packaging solutions based on SiC hermetic coatings that, when applied to glass and plastic substrates, support OLED lighting devices by providing longer life with greater efficiency at lower cost than is currently available. Phase I Objective: Demonstrate thin film encapsulated working phosphorescent OLED devices on optical glass with lifetime of 1,000 hour life, CRI greater than 75, and 15 lm/W. Phase II Objective: Demonstrate thin film encapsulated working phosphorescent OLED devices on plastic or glass composite with 25 lm/W, 5,000 hours life, and CRI greater than 80. Phase III Objective: Demonstrate 2 x 2 ft{sup 2} thin film encapsulated working phosphorescent OLED with 40 lm/W, 10,000 hour life, and CRI greater than 85. This report details the efforts of Phase III (Budget Period Three), a fourteen month collaborative effort that focused on optimization of high-efficiency phosphorescent OLED devices and thin-film encapsulation of said devices. The report further details the conclusions and recommendations of the project team that have foundation in all three budget periods for the program. During the conduct of the Thin Film Packaging Solutions for High Efficiency OLED Lighting Products program, including budget period three, the project team completed and delivered the following achievements: (1) a three-year marketing effort that characterized the near-term and longer-term OLED market, identified customer and consumer lighting needs, and suggested prototype product concepts and niche OLED applications lighting that will give rise to broader market acceptance as a source for wide area illumination and energy conservation; (2) a thin film encapsulation technology with a lifetime of nearly 15,000 hours, tested by calcium coupons, while stored at 16 C and 40% relative humidity ('RH'). This encapsulation technology
An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere
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.
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)
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2014-03-01
Full Text Available In this paper, an implicit logarithmic finite difference method (I-LFDM is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.
Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report
Energy Technology Data Exchange (ETDEWEB)
Prinja, Anil K.
2000-12-31
The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset are amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but
Efficient scheme for numerical simulations of the spin-bath decoherence
Dobrovitski, VV; De Raedt, HA
We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of a few coupled spins: (i) determining the pointer states of
Li, Tiexiang; Huang, Tsung-Ming; Lin, Wen-Wei; Wang, Jenn-Nan
2017-03-01
We propose an efficient eigensolver for computing densely distributed spectra of the two-dimensional transmission eigenvalue problem (TEP), which is derived from Maxwell’s equations with Tellegen media and the transverse magnetic mode. The governing equations, when discretized by the standard piecewise linear finite element method, give rise to a large-scale quadratic eigenvalue problem (QEP). Our numerical simulation shows that half of the positive eigenvalues of the QEP are densely distributed in some interval near the origin. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Extensive numerical simulations show that our proposed method processes the convergence efficiently, even when it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by nonlinear functions, which can be applied to estimate the denseness of the eigenvalues for the TEP.
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.
Sun, Shuyu
2012-09-01
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 MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J.; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions.
He, Cairong; Wang, Tongke; Zhao, Zhixue; Hao, Yonghong; Yeh, Tian-Chyi J; Zhan, Hongbin
2017-11-01
Submarine groundwater discharge (SGD) has been recognized as a major pathway of groundwater flow to coastal oceanic environments. It could affect water quality and marine ecosystems due to pollutants and trace elements transported through groundwater. Relations between different characteristics of aquifers and SGD have been investigated extensively before, but the role of fractures in SGD still remains unknown. In order to better understand the mechanism of groundwater flow and solute transport through fractures in SGD, one-dimensional analytical solutions of groundwater hydraulic head and velocity through a synthetic horizontal fracture with periodic boundary conditions were derived using a Laplace transform technique. Then, numerical solutions of solute transport associated with the given groundwater velocity were developed using a finite-difference method. The results indicated that SGD associated with groundwater flow and solute transport was mainly controlled by sea level periodic fluctuations, which altered the hydraulic head and the hydraulic head gradient in the fracture. As a result, the velocity of groundwater flow associated with SGD also fluctuated periodically. We found that the pollutant concentration associated with SGD oscillated around a constant value, and could not reach a steady state. This was particularly true at locations close to the seashore. This finding of the role of fracture in SGD will assist pollution remediation and marine conservation in coastal regions. Copyright © 2017 Elsevier B.V. All rights reserved.
A Comparative Evaluation of Numerical and Analytical Solutions to the Biadhesive Single-Lap Joint
Directory of Open Access Journals (Sweden)
Halil Özer
2014-01-01
Full Text Available This paper attempts to address the detailed verification of Zhao’s analytical solution including the moment effect with the two- and three-dimensional finite element results. Zhao compared the analytical results with only the 2D FEA results and used the constant bond-length ratio for the biadhesive bondline. In this study, overlap surfaces of the adherends and the adhesives were modelled using surface-to-surface contact elements. Both analytical and numerical analyses were performed using four different biadhesive bondline configurations. The 3D FEA results reveal the existence of complex stress state at the overlap ends. However, the general results show that analytical and numerical results were in a good agreement.
An efficient algorithm for classical density functional theory in three dimensions: ionic solutions.
Knepley, Matthew G; Karpeev, Dmitry A; Davidovits, Seth; Eisenberg, Robert S; Gillespie, Dirk
2010-03-28
Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O(N log N) operations and O(N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the "bulk-fluid" functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses O(N log N) operations. The other is for the "reference fluid density" (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O(N(2)) operations.
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Jafar Biazar
2015-01-01
Full Text Available We combine the Adomian decomposition method (ADM and Adomian’s asymptotic decomposition method (AADM for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.
Numerical simulation of the limiting efficiency of the graded bandgap solar cell
Energy Technology Data Exchange (ETDEWEB)
Rafat, N.H. [Department of Mathematics and Engineering Physics, Faculty of Engineering, Cairo University, Giza (Egypt); Abdel Haleem, A.M. [Department of Mathematics and Engineering Physics, Faculty of Engineering, El Fayoum University, El Fayoum (Egypt); Habib, S.E.-D. [Electronics and Communication Department, Faculty of Engineering, Cairo University, Giza (Egypt)
2007-01-15
The limiting efficiency of the compositionally graded bandgap solar cell is calculated using a 1-D numerical simulator. Our simulator calculates the limiting efficiency by solving the coupled semiconductor equations, namely, Poisson's equation, the current continuity equations, together with the Boltzmann photon equation, rather than the detailed balance equations that are usually used in such calculations. The non-avoidable radiative and Auger bulk losses are the only losses considered in the calculations. The effect of photon recycling on the cell's parameters is included in the calculations of radiative recombination rates. We verified numerically that bandgap grading, under optimum profile, increases the limiting efficiency of the solar cell, over the previously published values. The effect of the bandgap grading on desensitizing the surface of the cell is discussed. (author)
Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem
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
Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations
Directory of Open Access Journals (Sweden)
Yongjin Li
2017-01-01
Full Text Available We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs. We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.
Directory of Open Access Journals (Sweden)
R. C. Mittal
2014-01-01
Full Text Available We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.
Human-computer interfaces applied to numerical solution of the Plateau problem
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.
Numerical Solution of Problem for Non-Stationary Heat Conduction in Multi-Layer Bodies
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R. I. Еsman
2007-01-01
Full Text Available A mathematical model for non-stationary heat conduction of multi-layer bodies has been developed. Dirac’s δ-function is used to take into account phase and chemical transformations in one of the wall layers. While formulating a problem non-linear heat conduction equations have been used with due account of dependence of thermal and physical characteristics on temperature. Solution of the problem is realized with the help of methods of a numerical experiment and computer modeling.
Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.
1982-01-01
A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.
A Numerical Algorithm for the Solution of a Phase-Field Model of Polycrystalline Materials
Energy Technology Data Exchange (ETDEWEB)
Dorr, M R; Fattebert, J; Wickett, M E; Belak, J F; Turchi, P A
2008-12-04
We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton-Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton-Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.
Mustafa, Meraj; Farooq, Muhammad A; Hayat, Tasawar; Alsaedi, Ahmed
2013-01-01
This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies.
Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.
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.
Karami-Lakeh, Hossein; Hosseini-Abardeh, Reza; Kaatuzian, Hassan
2017-05-01
One major problem of solar cells is the decrease in efficiency due to an increase in temperature when operating under constant irradiation of solar energy. The combination of solar cell and a thermoelectric generator is one of the methods proposed to solve this problem. In this paper, the performance of thermo-photovoltaic system is studied experimentally as well as through numerical simulation. In the experimental part, design, manufacture and test of a novel thermo-photovoltaic system assembly are presented. Results of the assembled system showed that with reduction of one degree (Centigrade) in the temperature of solar cell under investigation, and about 0.2 % increase in the efficiency will be obtained in comparison with given efficiency at that specified temperature. The solar cell in a hybrid-assembled system under two cooling conditions (air cooling and water cooling) obtained an efficiency of 8 % and 9.5 %, respectively, while the efficiency of a single cell under the same radiation condition was 6 %. In numerical simulation part, photo-thermoelectric performance of system was analyzed. Two methods for evaluation of thermoelectric performance were used: average properties and finite element method. Results of simulation also demonstrate an increase in solar cell efficiency in the combined system in comparison with that of the single cell configuration.
DeChant, Lawrence Justin
1998-01-01
In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have
Numerical solution of an elastic and viscoelastic gravitational models by the finite element method
Arjona Almodóvar, A.; Chacón Rebollo, T.; Gómez Marmol, M.
2014-12-01
Volcanic areas present a lower effective viscosity than usually in the Earth's crust. Both the elastic-gravitational and the viscoelastic-gravitational models allow the computation of gravity, deformation, and gravitational potential changes in order to investigate crustal deformations of Earth (see for instance Battaglia & Segall, 2004; Fernández et al. 1999, 2001; Rundle 1980 and 1983). These models can be represented by a coupled system of linear parabolic (for the elastic deformations), hyperbolic (for the viscoelastic deformations) and elliptic partial differential equations (for gravitational potential changes) (see for instance Arjona et al. 2008 and 2010). The existence and uniqueness of weak solutions for both the elastic-gravitational and viscoelastic-gravitational problem was demonstrated in Arjona et al. (2008 and 2014). The stabilization to solutions of the associated stationary system was proved in Arjona and Díaz (2007). Here we consider the internal source as response to the effect of a pressurized magma reservoir into a multilayered, elastic-gravitational and viscoelastic-gravitational earth model. We introduce the numerical analysis of a simplified steady elastic-gravitational model, solved by means of the finite element method. We also present some numerical tests in realistic situations that confirm the predictions of theoretical order of convergence. Finally, we describe the methodology for both the elastic-gravitational and the viscoelastic-gravitational models using 2D and 3D test examples performed with FreeFEM++.
Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models
Directory of Open Access Journals (Sweden)
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 modeling of solute transport in deformable unsaturated layered soil
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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.
On the numerical solution of the diffusion equation with a nonlocal boundary condition
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Dehghan Mehdi
2003-01-01
Full Text Available Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs. The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.
Wang, Jinting; Lu, Liqiao; Zhu, Fei
2018-01-01
Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.
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 .
He, Qiaolin
2011-06-01
In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
DEFF Research Database (Denmark)
Hyun, Jaeyub; Kook, Junghwan; Wang, Semyung
2015-01-01
This study proposes an efficient and stable model reduction scheme for the numerical simulation of broadband, inhomogeneous, and anisotropic acoustic systems. Unlike a conventional model reduction scheme, the proposed model reduction scheme uses the adaptive quasi-static Ritz vector (AQSRV...... using the error indicator. "Multiple frequency subintervals" means to divide the frequency band of interest into several frequency bands from the computational time viewpoint. "Adaptive selection of the subinterval information and basis vector" means to select a different number of subintervals...... and basis vectors for use according to the target system. The proposed model reduction scheme is applied to the numerical simulation of the simple mass-damping-spring system and the acoustic metamaterial systems (i.e., acoustic lens and acoustic cloaking device) for the first time. Through these numerical...
Covaci, L.; Peeters, F. M.; Berciu, M.
2010-10-01
We propose a highly efficient numerical method to describe inhomogeneous superconductivity by using the kernel polynomial method in order to calculate the Green’s functions of a superconductor. Broken translational invariance of any type (impurities, surfaces, or magnetic fields) can be easily incorporated. We show that limitations due to system size can be easily circumvented and therefore this method opens the way for the study of scenarios and/or geometries that were unaccessible before. The proposed method is highly efficient and amenable to large scale parallel computation. Although we only use it in the context of superconductivity, it is applicable to other inhomogeneous mean-field theories.
Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification
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 Series Solution for Fractional Differential Equations
Directory of Open Access Journals (Sweden)
Mohammed Al-Refai
2014-01-01
where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.
DEFF Research Database (Denmark)
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
To facilitate the validation of the numerical Method of Auxiliary Sources an analytical Method of Auxiliary Sources solution is derived in this paper. The Analytical solution is valid for transverse magnetic, and electric, plane wave scattering by circular impedance Cylinders, and it is derived...... of the numerical Method of Auxiliary Sources for a range of scattering configurations....... with their singularities at different positions away from the origin. The transformation necessitates a truncation of the wave transformation but the inaccuracy introduced hereby is shown to be negligible. The analytical Method of Auxiliary Sources solution is employed as a reference to investigate the accuracy...
Improving Efficiency of CCS Numerical Simulations Through Use of Parallel Processing
Directory of Open Access Journals (Sweden)
Konopka K.
2015-04-01
Full Text Available The study presents the findings of research concerning the possibilities for application of parallel processing in order to reduce the computing time of numerical simulations of the steel continuous casting process. The computing efficiency for a CCS model covering the mould and a strand fragment was analysed. The calculations were performed with the ProCAST software package using the finite element method. Two computing environments were used: the PL-Grid infrastructure and cloud computing platform.
Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach
Kiris, Cetin; Kwak, Dochan
1999-01-01
A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.
Cilfone, Nicholas A; Kirschner, Denise E; Linderman, Jennifer J
2015-03-01
Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.
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M. Boumaza
2015-07-01
Full Text Available Transient convection heat transfer is of fundamental interest in many industrial and environmental situations, as well as in electronic devices and security of energy systems. Transient fluid flow problems are among the more difficult to analyze and yet are very often encountered in modern day technology. The main objective of this research project is to carry out a theoretical and numerical analysis of transient convective heat transfer in vertical flows, when the thermal field is due to different kinds of variation, in time and space of some boundary conditions, such as wall temperature or wall heat flux. This is achieved by the development of a mathematical model and its resolution by suitable numerical methods, as well as performing various sensitivity analyses. These objectives are achieved through a theoretical investigation of the effects of wall and fluid axial conduction, physical properties and heat capacity of the pipe wall on the transient downward mixed convection in a circular duct experiencing a sudden change in the applied heat flux on the outside surface of a central zone.
Energy efficiency and reliability solutions for rail operations and facilities.
2014-11-01
The objectives of the study included examining energy consumption of : the facilities comprising the three major rail yards on the New Haven Rail Line as : well as platform stations and identifying energy efficiency and cost savings : opportunities f...
Ha, Sanghyun; Park, Junshin; You, Donghyun
2017-11-01
Utility of the computational power of modern Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. Due to its serial and bandwidth-bound nature, the present choice of numerical methods is considered to be a good candidate for evaluating the potential of GPUs for solving Navier-Stokes equations using non-explicit time integration. An efficient algorithm is presented for GPU acceleration of the Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution method used in the semi-implicit fractional-step method. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while Navier-Stokes equations are computed on a GPU. Extension to multiple NVIDIA GPUs is implemented using NVLink supported by the Pascal architecture. Performance of the present method is experimented on multiple Tesla P100 GPUs compared with a single-core Xeon E5-2650 v4 CPU in simulations of boundary-layer flow over a flat plate. Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (Ministry of Science, ICT and Future Planning NRF-2016R1E1A2A01939553, NRF-2014R1A2A1A11049599, and Ministry of Trade, Industry and Energy 201611101000230).
Venturi, Daniele
2016-11-01
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics, quantum field theory and statistical physics. For example, in the context of fluid dynamics, the Hopf characteristic functional equation was deemed by Monin and Yaglom to be "the most compact formulation of the turbulence problem", which is the problem of determining the statistical properties of the velocity and pressure fields of Navier-Stokes equations given statistical information on the initial state. However, no effective numerical method has yet been developed to compute the solution to functional differential equations. In this talk I will provide a new perspective on this general problem, and discuss recent progresses in approximation theory for nonlinear functionals and functional equations. The proposed methods will be demonstrated through various examples.
Directory of Open Access Journals (Sweden)
M. Hatami
2016-06-01
Full Text Available In this study, a simple and high accurate series-based method called Differential Transformation Method (DTM is used for solving the coupled nonlinear differential equations in fluids mechanic problems. The concept of the DTM is briefly introduced, and its application on two different cases, natural convection of a non-Newtonian nanofluid between two vertical plates and Newtonian nanofluid flow between two horizontal plates, has been studied. DTM results are compared with those obtained by a numerical solution (Fourth-order Runge–Kutta to show the accuracy of the proposed method. Results reveal that DTM is very effective and convenient which can achieve more reliable results compared to other analytical methods in solving some engineering and sciences problems.
Riemannian Gradient Algorithm for the Numerical Solution of Linear Matrix Equations
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Xiaomin Duan
2014-01-01
Full Text Available A Riemannian gradient algorithm based on geometric structures of a manifold consisting of all positive definite matrices is proposed to calculate the numerical solution of the linear matrix equation Q=X+∑i=1mAiTXAi. In this algorithm, the geodesic distance on the curved Riemannian manifold is taken as an objective function and the geodesic curve is treated as the convergence path. Also the optimal variable step sizes corresponding to the minimum value of the objective function are provided in order to improve the convergence speed. Furthermore, the convergence speed of the Riemannian gradient algorithm is compared with that of the traditional conjugate gradient method in two simulation examples. It is found that the convergence speed of the provided algorithm is faster than that of the conjugate gradient method.
Numerical simulation on vapor absorption by wavy lithium bromide aqueous solution films
Bo, Shoushi; Ma, Xuehu; Chen, Hongxia; Lan, Zhong
2011-12-01
Numerical simulation has been made on heat and mass transfer of vapor absorption by wavy lithium bromide aqueous solution films. The velocity fields and interface positions are obtained by VOF model. Solitary waves are generated by periodically disturbed inflow boundary. Based on these, the temperature and concentration fields are obtained with a stationary interface shape. The effect of solitary waves on the heat and mass transfer across the film is investigated. It is shown that due to the mixing of circulation and stretch of large film thickness, the gradient of concentration and absorption rate decrease for solitary wave region. The region of capillary waves shows a significant amount of absorption enhancement. The percentage of absorption for the different regions is quantified.
Zhu, Shichen; Yu, Xiaoyue; Xiong, Shanbai; Liu, Ru; Gu, Zhipeng; You, Juan; Yin, Tao; Hu, Yang
2017-09-01
The elaboration of the rheological behaviors of alginate dialdehyde (ADA) crosslinked collagen solutions, along with the quantitative analysis via numerical models contribute to the controllable design of ADA crosslinked solution system's fluid mechanics performance during manufacturing process for collagen biomaterials. In the present work, steady shear flow, dynamical viscoelasticity, creep-recovery, thixotropy tests were performed to characterize the rheological behaviors of the collagen solutions incorporating of ADA from the different aspects and fitted with corresponding numerical models. It was found that pseudoplastic properties of all samples enhanced with increasing amounts of ADA, which was confirmed by the parameters calculated from the Ostwald-de Waele model, Carreau and Cross model, for instance, the non-Newtonian index (n) decreased from 0.786 to 0.201 and a great increase by 280 times in value of viscosity index (K) was obtained from Ostwald-de Waele model. The forth-mode Leonov model was selected to fit all dynamic modulus-frequency curves due to its higher fitting precision (R 2 >0.99). It could be found that the values of correlation shear viscosity (η k ) increased and the values of relaxation time (θ k ) decreased with increasing ADA at the fixed k value, suggesting that the incorporation of ADA accelerated the transformation of the collagen solutions from liquid-like to gel-like state due to more formation of CN linkages between aldehyde groups and lysine residues. Also, the curves of creep and recovery phase of the native and crosslinked collagen solutions were simulated well using Burger model and a semi-empirical model, respectively. The ability to resist to deformation and elasticity strengthened for the samples with higher amounts of ADA, accompanied with the important fact that compliance value (J 50 ) decreased from 56.317Pa -1 to 2.135Pa -1 and the recovery percentage (R creep ) increased from 2.651% to 28.217%. Finally, it was found
Numerical Simulation of the Thermal Efficiency During Laser Deep Penetration Welding
Ganser, A.; Pieper, J.; Liebl, S.; Zaeh, M. F.
The advantages of laser beam welding, such as its high flexibility, its high local energy input, and its fast processing speed, led to a substantial increase of industrial applications of the technology. High losses can be observed during laser welding of materials with a high thermal conductivity, such as aluminum or copper. This is caused by the heat conduction losses in the surrounding area of the process zone and due to reflections. These energy losses lead to a reduced efficiency of the laser welding process. A numerical model based on a CFD simulation is presented, which enables to calculate the molten pool isotherms. The thermal efficiency is determined for different keyhole geometries and welding velocities. This efficiency is defined as the ratio between the energy which is required to melt the volume of metal in the fusion zone and the absorbed laser beam power.
An efficient algorithm for computation of solitary wave solutions to ...
Indian Academy of Sciences (India)
KAMRAN AYUB
2017-09-08
Sep 8, 2017 ... Various phenomena in mathematics and physics are modelled by differential equations. In nonlinear science it is of great importance and interest to explain physical models and attain analyt- ical solutions. In the recent past, large series of chemical, biological, physical singularities are feint by nonlinear.
An efficient algorithm for computation of solitary wave solutions to ...
Indian Academy of Sciences (India)
2017-09-08
Sep 8, 2017 ... ... reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.
Zhang, Bo; Chen, Tianning; Zhao, Yuyuan; Zhang, Weiyong; Zhu, Jian
2012-09-01
On the basis of the work of Wilson et al. [J. Acoust. Soc. Am. 84, 350-359 (1988)], a more exact numerical approach was constructed for predicting the nonlinear sound propagation and absorption properties of rigid porous media at high sound pressure levels. The numerical solution was validated by the experimental results for sintered fibrous porous steel samples and its predictions were compared with the numerical solution of Wilson et al. An approximate analytical solution was further put forward for the normalized surface acoustic admittance of rigid air-saturated porous materials with infinite thickness, based on the wave perturbation method developed by Lambert and McIntosh [J. Acoust. Soc. Am. 88, 1950-1959 (1990)]. Comparisons were made with the numerical results.
Directory of Open Access Journals (Sweden)
Nilson C. Roberty
2011-01-01
Full Text Available We introduce algorithms marching over a polygonal mesh with elements consistent with the propagation directions of the particle (radiation flux. The decision for adopting this kind of mesh to solve the one-speed Boltzmann transport equation is due to characteristics of the domain of the transport operator which controls derivatives only in the direction of propagation of the particles (radiation flux in the absorbing and scattering media. This a priori adaptivity has the advantages that it formulates a consistent scheme which makes appropriate the application of the Lax equivalence theorem framework to the problem. In this work, we present the main functional spaces involved in the formalism and a description of the algorithms for the mesh generation and the transport equation solution. Some numerical examples related to the solution of a transmission problem in a high-contrast model with absorption and scattering are presented. Also, a comparison with benchmarks problems for source and reactor criticality simulations shows the compatibility between calculations with the algorithms proposed here and theoretical results.
Directory of Open Access Journals (Sweden)
Peng Wang
2013-01-01
Full Text Available This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO. The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions.
Wang, Peng; Zhu, Zhouquan; Huang, Shuai
2013-01-01
This paper presents a novel biologically inspired metaheuristic algorithm called seven-spot ladybird optimization (SLO). The SLO is inspired by recent discoveries on the foraging behavior of a seven-spot ladybird. In this paper, the performance of the SLO is compared with that of the genetic algorithm, particle swarm optimization, and artificial bee colony algorithms by using five numerical benchmark functions with multimodality. The results show that SLO has the ability to find the best solution with a comparatively small population size and is suitable for solving optimization problems with lower dimensions.
New numerical methods for open-loop and feedback solutions to dynamic optimization problems
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
The Numerical Solutions of a Two-Dimensional Space-Time Riesz-Caputo Fractional Diffusion Equation
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Necati Ozdemir
2011-07-01
Full Text Available This paper is concerned with the numerical solutions of a two-dimensional space-timefractional differential equation used to model the dynamic properties of complex systems governedby anomalous diffusion. The space-time fractional anomalous diffusion equation is definedby replacing the second order space and the first order time derivatives with Riesz and Caputooperators, respectively. Using the Laplace and Fourier transforms, a general representation ofanalytical solution is obtained in terms of the Mittag-Leffler function. Gr¨unwald-Letnikov (GLapproximation is also used to find numerical solution of the problem. Finally, simulation resultsfor two examples illustrate the comparison of the analytical and numerical solutions and alsovalidity of the GL approach to this problem.
Tian, Heng; Chen, GuanHua
2012-11-28
Application of quantum dissipation theory to electronic dynamics has been limited to model systems with few energy levels, and its numerical solutions are mostly restricted to high temperatures. A highly accurate and efficient numerical algorithm, which is based on the Chebyshev spectral method, is developed to integrate a single-particle Liouville-von Neumann equation, and the two long-standing limitations of quantum dissipation theory are resolved in the context of quantum transport. Its computational time scales to O(N(3)) with N being the number of orbitals involved, which leads to a reality for the quantum mechanical simulation of real open systems containing hundreds or thousands of atomic orbitals. More importantly, the algorithm spans both finite and zero temperatures. Numerical calculations are carried out to simulate the transient current through a metallic wire containing up to 1000 orbitals.
Encapsulation Efficiency and Micellar Structure of Solute-Carrying Block Copolymer Nanoparticles
Woodhead, Jeffrey L.; Hall, Carol K.
2011-01-01
We use discontinuous molecular dynamics (DMD) computer simulation to investigate the encapsulation efficiency and micellar structure of solute-carrying block copolymer nanoparticles as a function of packing fraction, polymer volume fraction, solute mole fraction, and the interaction parameters between the hydrophobic head blocks and between the head and the solute. The encapsulation efficiency increases with increasing polymer volume fraction and packing fraction but decreases with increasing head-head interaction strength. The latter is due to an increased tendency for the solute to remain on the micelle surface. We compared two different nanoparticle assembly methods, one in which the solute and copolymer co-associate and the other in which the copolymer micelle is formed before the introduction of solute. The assembly method does not affect the encapsulation efficiency but does affect the solute uptake kinetics. Both head-solute interaction strength and head-head interaction strength affect the density profile of the micelles; increases in the former cause the solute to distribute more evenly throughout the micelle, while increases in the latter cause the solute to concentrate further from the center of the micelle. We explain our results in the context of a model of drug insertion into micelles formulated by Kumar and Prud’homme; as conditions become more conducive to micelle formation, a stronger energy barrier to solute insertion forms which in turn decreases the encapsulation efficiency of the system. PMID:21918582
Bergues Pupo, Ana E; Reyes, Juan Bory; Bergues Cabrales, Luis E; Bergues Cabrales, Jesús M
2011-09-24
Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model) generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola). Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic). Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.
Directory of Open Access Journals (Sweden)
Bergues Cabrales Jesús M
2011-09-01
Full Text Available Abstract Background Electrotherapy is a relatively well established and efficient method of tumor treatment. In this paper we focus on analytical and numerical calculations of the potential and electric field distributions inside a tumor tissue in a two-dimensional model (2D-model generated by means of electrode arrays with shapes of different conic sections (ellipse, parabola and hyperbola. Methods Analytical calculations of the potential and electric field distributions based on 2D-models for different electrode arrays are performed by solving the Laplace equation, meanwhile the numerical solution is solved by means of finite element method in two dimensions. Results Both analytical and numerical solutions reveal significant differences between the electric field distributions generated by electrode arrays with shapes of circle and different conic sections (elliptic, parabolic and hyperbolic. Electrode arrays with circular, elliptical and hyperbolic shapes have the advantage of concentrating the electric field lines in the tumor. Conclusion The mathematical approach presented in this study provides a useful tool for the design of electrode arrays with different shapes of conic sections by means of the use of the unifying principle. At the same time, we verify the good correspondence between the analytical and numerical solutions for the potential and electric field distributions generated by the electrode array with different conic sections.
Thompson, J. F.; Mastin, C. W.; Thames, F. C.; Shanks, S. P.
1975-01-01
A procedure for numerical solution of the time-dependent, two-dimensional incompressible Navier-Stokes equations that can treat the unsteady laminar flow about bodies of arbitrary shape, such as two-dimensional airfoils, multiple airfoils, and submerged hydrofoils, as naturally as it can deal with the flow about simple bodies. The solution is based on a method of automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multiconnected region containing any number of arbitrarily shaped bodies. The curvilinear coordinates are generated as the solution of two elliptical partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other being specified along the boundaries. The solution compares excellently with the Blasius boundary layer solution for the flow past a semiinfinite flat plate.
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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.
Energy Technology Data Exchange (ETDEWEB)
Conway, A; Wang, T; Deo, N; Cheung, C; Nikolic, R
2008-06-24
This work reports numerical simulations of a novel three-dimensionally integrated, {sup 10}boron ({sup 10}B) and silicon p+, intrinsic, n+ (PIN) diode micropillar array for thermal neutron detection. The inter-digitated device structure has a high probability of interaction between the Si PIN pillars and the charged particles (alpha and {sup 7}Li) created from the neutron - {sup 10}B reaction. In this work, the effect of both the 3-D geometry (including pillar diameter, separation and height) and energy loss mechanisms are investigated via simulations to predict the neutron detection efficiency and gamma discrimination of this structure. The simulation results are demonstrated to compare well with the measurement results. This indicates that upon scaling the pillar height, a high efficiency thermal neutron detector is possible.
SOLA-DM: A numerical solution algorithm for transient three-dimensional flows
Energy Technology Data Exchange (ETDEWEB)
Wilson, T.L.; Nichols, B.D.; Hirt, C.W.; Stein, L.R.
1988-02-01
SOLA-DM is a three-dimensional time-explicit, finite-difference, Eulerian, fluid-dynamics computer code for solving the time-dependent incompressible Navier-Stokes equations. The solution algorithm (SOLA) evolved from the marker-and-cell (MAC) method, and the code is highly vectorized for efficient performance on a Cray computer. The computational domain is discretized by a mesh of parallelepiped cells in either cartesian or cylindrical geometry. The primary hydrodynamic variables for approximating the solution of the momentum equations are cell-face-centered velocity components and cell-centered pressures. Spatial accuracy is selected by the user to be first or second order; the time differencing is first-order accurate. The incompressibility condition results in an elliptic equation for pressure that is solved by a conjugate gradient method. Boundary conditions of five general types may be chosen: free-slip, no-slip, continuative, periodic, and specified pressure. In addition, internal mesh specifications to model obstacles and walls are provided. SOLA-DM also solves the equations for discrete particle dynamics, permitting the transport of marker particles or other solid particles through the fluid to be modeled. 7 refs., 7 figs.
Schöpfer, Martin; Lehner, Florian; Grasemann, Bernhard; Kaserer, Klemens; Hinsch, Ralph
2017-04-01
John G. Ramsay's sketch of structures developed in a layer progressively folded and deformed by tangential longitudinal strain (Figure 7-65 in Folding and Fracturing of Rocks) and the associated strain pattern analysis have been reproduced in many monographs on Structural Geology and are referred to in numerous publications. Although the origin of outer-arc extension fractures is well-understood and documented in many natural examples, geomechanical factors controlling their (finite or saturation) spacing are hitherto unexplored. This study investigates the formation of bending-induced fractures during constant-curvature forced folding using Distinct Element Method (DEM) numerical modelling. The DEM model comprises a central brittle layer embedded within weaker (low modulus) elastic layers; the layer interfaces are frictionless (free slip). Folding of this three-layer system is enforced by a velocity boundary condition at the model base, while a constant overburden pressure is maintained at the model top. The models illustrate several key stages of fracture array development: (i) Prior to the onset of fracture, the neutral surface is located midway between the layer boundaries; (ii) A first set of regularly spaced fractures develops once the tensile stress in the outer-arc equals the tensile strength of the layer. Since the layer boundaries are frictionless, these bending-induced fractures propagate through the entire layer; (iii) After the appearance of the first fracture set, the rate of fracture formation decreases rapidly and so-called infill fractures develop approximately midway between two existing fractures (sequential infilling); (iv) Eventually no new fractures form, irrespective of any further increase in fold curvature (fracture saturation). Analysis of the interfacial normal stress distributions suggests that at saturation the fracture-bound blocks are subjected to a loading condition similar to three-point bending. Using classical beam theory an
Numerical Investigations of Vadose Zone Transport of Saturated Sodium Thiosulfate Solutions
White, M. D.; Ward, A. L.
2001-12-01
Compared with water, hypersaline liquid wastes ([NaNO3] > 10 N) from the reduction-oxidation (REDOX) process at the Hanford site have elevated viscosity (μ > 1.2 cP), density (ρ > 1.4 gm/cm3), and surface tension (σ > 100 dyn/cm). Such liquids have infiltrated into the vadose zone at Hanford from leaking underground storage tanks. The migration behavior of saturated or hypersaline salt solutions through unsaturated soils is largely unknown. Laboratory tests with tank-waste simulants suggest that the elevated density, viscosity, and surface tension properties of these liquids can influence the wetting front behavior, altering its shape and migration rate. Conditions under which these mechanisms are active in the field and the extent to which they contribute to transport through the vadose zone are largely unknown, making it impossible to accurately predict the post-leak distribution of these fluids in the field. To investigate the effects of fluid properties on subsurface migration of hypersaline saline solutions, numerical simulations were conducted of a field-scale, tank-leak experiment. The field experiments consisted of five 4000-L injections, at a depth of 5 m, of saturated sodium thiosulfate brine (used as a surrogate for REDOX type wastes) over a 5-week period, followed by three 4000-L injections of Columbia River water. Pre-test modeling of river water injections at this Hanford field site predicted significant lateral spreading of the moisture plume and were confirmed by geophysical logging. A series of three-dimensional, multifluid (i.e., aqueous and gas phases) numerical simulations were conducted that systematically considered the effects of elevated density, viscosity, and surface tension, and reduced vapor pressure on vadose-zone transport. Hydrologic properties were determined from cores collected at the field site and calibrated using river-water injection experiments. Isothermal conditions were assumed for the simulations, however, the effects of
On the formation, growth, and shapes of solution pipes - insights from numerical modeling
Szymczak, Piotr; Tredak, Hanna; Upadhyay, Virat; Kondratiuk, Paweł; Ladd, Anthony J. C.
2015-04-01
Cylindrical, vertical structures called solution pipes are a characteristic feature of epikarst, encountered in different parts of the world, both in relatively cold areas such as England and Poland (where their formation is linked to glacial processes) [1] and in coastal areas in tropical or subtropical climate (Bermuda, Australia, South Africa, Caribbean, Mediterranean) [2,3]. They are invariably associated with weakly cemented, porous limestones and relatively high groundwater fluxes. Many of them develop under the colluvial sandy cover and contain the fill of clayey silt. Although it is widely accepted that they are solutional in origin, the exact mechanism by which the flow becomes focused is still under debate. The hypotheses include the concentration of acidified water around stems and roots of plants, or the presence of pre-existing fractures or steeply dipping bedding planes, which would determine the points of entry for the focused groundwater flows. However, there are field sites where neither of this mechanisms was apparently at play and yet the pipes are formed in large quantities [1]. In this communication we show that the systems of solution pipes can develop spontaneously in nearly uniform matrix due to the reactive-infiltration instability: a homogeneous porous matrix is unstable with respect to small variations in local permeability; regions of high permeability dissolve faster because of enhanced transport of reactants, which leads to increased rippling of the front. This leads to the formation of a system of solution pipes which then advance into the matrix. We study this process numerically, by a combination of 2d- and 3d-simulations, solving the coupled flow and transport equations at the Darcy scale. The relative simplicity of this system (pipes developing in a uniform porous matrix, without any pre-existing structure) makes it very attractive from the modeling standpoint. We quantify the factors which control the pipe diameters and the
Numerical Research of Steam and Gas Plant Efficiency of Triple Cycle for Extreme North Regions
Directory of Open Access Journals (Sweden)
Galashov Nikolay
2016-01-01
Full Text Available The present work shows that temperature decrease of heat rejection in a cycle is necessary for energy efficiency of steam turbine plants. Minimum temperature of heat rejection at steam turbine plant work on water steam is 15°C. Steam turbine plant of triple cycle where lower cycle of steam turbine plant is organic Rankine cycle on low-boiling substance with heat rejection in air condenser, which safely allows rejecting heat at condensation temperatures below 0°C, has been offered. Mathematical model of steam and gas plant of triple cycle, which allows conducting complex researches with change of working body appearance and parameters defining thermodynamic efficiency of cycles, has been developed. On the basis of the model a program of parameters and index cycles design of steam and gas plants has been developed in a package of electron tables Excel. Numerical studies of models showed that energy efficiency of steam turbine plants of triple cycle strongly depend on low-boiling substance type in a lower cycle. Energy efficiency of steam and gas plants net 60% higher can be received for steam and gas plants on the basis of gas turbine plant NK-36ST on pentane and its condensation temperature below 0°C. It was stated that energy efficiency of steam and gas plants net linearly depends on condensation temperature of low-boiling substance type and temperature of gases leaving reco very boiler. Energy efficiency increases by 1% at 10% decrease of condensation temperature of pentane, and it increases by 0.88% at 15°C temperature decrease of gases leaving recovery boiler.
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.
Ren, Qiang; Nagar, Jogender; Kang, Lei; Bian, Yusheng; Werner, Ping; Werner, Douglas H
2017-05-18
A highly efficient numerical approach for simulating the wideband optical response of nano-architectures comprised of Drude-Critical Points (DCP) media (e.g., gold and silver) is proposed and validated through comparing with commercial computational software. The kernel of this algorithm is the subdomain level discontinuous Galerkin time domain (DGTD) method, which can be viewed as a hybrid of the spectral-element time-domain method (SETD) and the finite-element time-domain (FETD) method. An hp-refinement technique is applied to decrease the Degrees-of-Freedom (DoFs) and computational requirements. The collocated E-J scheme facilitates solving the auxiliary equations by converting the inversions of matrices to simpler vector manipulations. A new hybrid time stepping approach, which couples the Runge-Kutta and Newmark methods, is proposed to solve the temporal auxiliary differential equations (ADEs) with a high degree of efficiency. The advantages of this new approach, in terms of computational resource overhead and accuracy, are validated through comparison with well-known commercial software for three diverse cases, which cover both near-field and far-field properties with plane wave and lumped port sources. The presented work provides the missing link between DCP dispersive models and FETD and/or SETD based algorithms. It is a competitive candidate for numerically studying the wideband plasmonic properties of DCP media.
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.
Uncoupled continuous-time random walk model: analytical and numerical solutions.
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Uncoupled continuous-time random walk model: Analytical and numerical solutions
Fa, Kwok Sau
2014-05-01
Solutions for the continuous-time random walk (CTRW) model are known in few cases. In this work, the uncoupled CTRW model is investigated analytically and numerically. In particular, the probability density function (PDF) and n-moment are obtained and analyzed. Exponential and Gaussian functions are used for the jump length PDF, whereas the Mittag-Leffler function and a combination of exponential and power-laws function is used for the waiting time PDF. The exponential and Gaussian jump length PDFs have finite jump length variances and they give the same second moment; however, their distribution functions present different behaviors near the origin. The combination of exponential and power-law function for the waiting time PDF can generate a crossover from anomalous regime to normal regime. Moreover, the parameter of the exponential jump length PDF does not change the behavior of the n-moment for all time intervals, and for the Gaussian jump length PDF the n-moment also indicates a similar behavior.
Pandey, Rishi Kumar; Mishra, Hradyesh Kumar
2017-11-01
In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning.
Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem
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Vladimir A. Emelichev
2002-11-01
Full Text Available We consider a multiple criterion Boolean programming problem with MINMAX partial criteria. The extreme level of independent perturbations of partial criteria parameters such that efficient (Pareto optimal solution preserves optimality was obtained.
DEFF Research Database (Denmark)
Celia, Michael A.; Binning, Philip John
1992-01-01
A numerical algorithm for simulation of two-phase flow in porous media is presented. The algorithm is based on a modified Picard linearization of the governing equations of flow, coupled with a lumped finite element approximation in space and dynamic time step control. Numerical results indicate...... 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...... that describe two-phase flow in porous media....
Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics
Kakhktsyan, V. M.; Khachatryan, A. Kh.
2013-07-01
A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.
Public-domain-software solution to data-access problems for numerical modelers
Jenter, Harry; Signell, Richard
1992-01-01
Unidata's network Common Data Form, netCDF, provides users with an efficient set of software for scientific-data-storage, retrieval, and manipulation. The netCDF file format is machine-independent, direct-access, self-describing, and in the public domain, thereby alleviating many problems associated with accessing output from large hydrodynamic models. NetCDF has programming interfaces in both the Fortran and C computer language with an interface to C++ planned for release in the future. NetCDF also has an abstract data type that relieves users from understanding details of the binary file structure; data are written and retrieved by an intuitive, user-supplied name rather than by file position. Users are aided further by Unidata's inclusion of the Common Data Language, CDL, a printable text-equivalent of the contents of a netCDF file. Unidata provides numerous operators and utilities for processing netCDF files. In addition, a number of public-domain and proprietary netCDF utilities from other sources are available at this time or will be available later this year. The U.S. Geological Survey has produced and is producing a number of public-domain netCDF utilities.
Simos, T. E.
2017-11-01
A family of four stages high algebraic order embedded explicit six-step methods, for the numerical solution of second order initial or boundary-value problems with periodical and/or oscillating solutions, are studied in this paper. The free parameters of the new proposed methods are calculated solving the linear system of equations which is produced by requesting the vanishing of the phase-lag of the methods and the vanishing of the phase-lag's derivatives of the schemes. For the new obtained methods we investigate: • Its local truncation error (LTE) of the methods.• The asymptotic form of the LTE obtained using as model problem the radial Schrödinger equation.• The comparison of the asymptotic forms of LTEs for several methods of the same family. This comparison leads to conclusions on the efficiency of each method of the family.• The stability and the interval of periodicity of the obtained methods of the new family of embedded finite difference pairs.• The applications of the new obtained family of embedded finite difference pairs to the numerical solution of several second order problems like the radial Schrödinger equation, astronomical problems etc. The above applications lead to conclusion on the efficiency of the methods of the new family of embedded finite difference pairs.
Method of independent timesteps in the numerical solution of initial value problems
Energy Technology Data Exchange (ETDEWEB)
Porter, A.P.
1976-07-21
In the numerical solution of initial-value problems in several independent variables, the timestep is controlled, especially in the presence of shocks, by a small portion of the logical mesh, what one may call the crisis zone. One is frustrated by the necessity of doing in the whole mesh frequent calculations required by only a small part of the mesh. It is shown that it is possible to choose different timesteps natural to different parts of the mesh and to advance each zone in time only as often as is appropriate to that zone's own natural timestep. Prior work is reviewed and for the first time an investigation of the conditions for well-posedness, consistency and stability in independent timesteps is presented; a new method results. The prochronic and parachronic Cauchy surfaces are identified; and the reasons (well-posedness) for constraining the Cauchy surfaces to be prochronic (as distinct from the method of Grandey), that is, to lie prior to the time of the crisis zone (the zone of least timestep), are indicated. Stability (in the maximum norm) of parabolic equations and (in the L2 norm) of hyperbolic equations is reviewed, without restricting the treatment to linear equations or constant coefficients, and stability of the new method is proven in this framework. The details of the method of independent timesteps, the rules for choosing timesteps and for deciding when to update and when to skip zones, and the method of joining adjacent regions of differing timestep are described. The stability of independent timestep difference schemes is analyzed and exhibited. The economic advantages of the method, which often amount to an order-of-magnitude decrease in running time relative to conventional or implicit difference methods, are noted.
Kaiser, Franz-Joachim; Bassler, Niels; Tölli, Heikki; Jäkel, Oliver
2012-03-01
Modern particle therapy facilities enable sub-millimeter precision in dose deposition. Here, also ionization chambers (ICs) are used, which requires knowledge of the recombination effects. Up to now, recombination is corrected using phenomenological approaches for practical reasons. In this study the effect of the underlying dose distribution on columnar recombination, a quantitative model for initial recombination, is investigated. Jaffé's theory, formulated in 1913 quantifies initial recombination by elemental processes, providing an analytical (closed) solution. Here, we investigate the effect of the underlying charged carrier distribution around a carbon ion track. The fundamental partial differential equation, formulated by Jaffé, is solved numerically taking into account more realistic charge carrier distributions by the use of a computer program (Gascoigne 3D). The investigated charge carrier distributions are based on track structure models, which follow a 1/r(2) behavior at larger radii and show a constant value at small radii. The results of the calculations are compared to the initial formulation and to data obtained in experiments using carbon ion beams. The comparison between the experimental data and the calculations shows that the initial approach made by Jaffé is able to reproduce the effects of initial recombination. The amorphous track structure based charge carrier distribution does not reproduce the experimental data well. A small additional correction in the assessment of the saturation current or charge is suggested by the data. The established model of columnar recombination reproduces the experimental data well, whereas the extensions using track structure models do not show such an agreement. Additionally, the effect of initial recombination on the saturation curve (i.e. Jaffé plot) does not follow a linear behavior as suggested by current dosimetry protocols, therefore higher order corrections (such as the investigated ones) might be
Numerical Analysis of Novel Back Surface Field for High Efficiency Ultrathin CdTe Solar Cells
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M. A. Matin
2013-01-01
Full Text Available This paper numerically explores the possibility of high efficiency, ultrathin, and stable CdTe cells with different back surface field (BSF using well accepted simulator AMPS-1D (analysis of microelectronics and photonic structures. A modified structure of CdTe based PV cell SnO2/Zn2SnO4/CdS/CdTe/BSF/BC has been proposed over reference structure SnO2/Zn2SnO4/CdS/CdTe/Cu. Both higher bandgap materials like ZnTe and Cu2Te and low bandgap materials like As2Te3 and Sb2Te3 have been used as BSF to reduce minority carrier recombination loss at the back contact in ultra-thin CdTe cells. In this analysis the highest conversion efficiency of CdTe based PV cell without BSF has been found to be around 17% using CdTe absorber thickness of 5 μm. However, the proposed structures with different BSF have shown acceptable efficiencies with an ultra-thin CdTe absorber of only 0.6 μm. The proposed structure with As2Te3 BSF showed the highest conversion efficiency of 20.8% ( V, mA/cm2, and . Moreover, the proposed structures have shown improved stability in most extents, as it was found that the cells have relatively lower negative temperature coefficient. However, the cell with ZnTe BSF has shown better overall stability than other proposed cells with temperature coefficient (TC of −0.3%/°C.
A Robust and Efficient Numerical Method for RNA-Mediated Viral Dynamics
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Vladimir Reinharz
2017-10-01
Full Text Available The multiscale model of hepatitis C virus (HCV dynamics, which includes intracellular viral RNA (vRNA replication, has been formulated in recent years in order to provide a new conceptual framework for understanding the mechanism of action of a variety of agents for the treatment of HCV. We present a robust and efficient numerical method that belongs to the family of adaptive stepsize methods and is implicit, a Rosenbrock type method that is highly suited to solve this problem. We provide a Graphical User Interface that applies this method and is useful for simulating viral dynamics during treatment with anti-HCV agents that act against HCV on the molecular level.
Wen Wan Xin
2002-01-01
The energy resolution and time resolution of two phi 75 x 100 BGO detectors for high energy gamma ray newly made were measured with sup 1 sup 3 sup 7 Cs and sup 6 sup 0 Co resources. The two characteristic gamma rays of high energy emitted from the thermal neutron capture of germanium in BGO crystal were used for the energy calibration of gamma spectra. The intrinsic photopeak efficiency, single escape probability and double escape probabilities of BGO detectors in photon energy range of 4-30 MeV are numerically calculated with GEANT code. The real count response and count ratio of the uniformly distributed incident photons in energy range of 0-30 MeV are also calculated. The distortion of gamma spectra caused by the photon energy loss extension to lower energy in detection medium is discussed
Energy Technology Data Exchange (ETDEWEB)
Buscaglia, G.C.; Lopez, A. [Centro Atomico Bariloche and Inst. Balseiro, Bariloche (Argentina); Bolech, C. [Rutgers - the State Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy
2000-07-01
A numerical method for the solution of the time-dependent Ginzburg-Landau equations is detailed. The method is based on the popular technique of gauge invariant variables. Extension of the method to multiply connected domains is addressed. An implementation of the method is made available through the Web. (orig.)
El-Tom, M E A
1974-01-01
A procedure, using spine functions of degree m, deficiency k-1, for obtaining approximate solutions to nonlinear Volterra integral equations of the second kind is presented. The paper is an investigation of the numerical stability of the procedure for various values of m and k. (5 refs).
DEFF Research Database (Denmark)
For solving partial differential equations (or distributed dynamic systems), the method of lines (MOL) and the space-time conservation element and solution element (CE/SE) method are compared in terms of computational efficiency, solution accuracy and stability. Several representative examples....... It is concluded that the CE/SE method is adequate to capturing shocks in PDEs but for diffusion-dominated stiff PDEs, the MOL with an ODE time integrator is complementary to the CE/SE method....
Confocal signal evaluation algorithms for surface metrology: uncertainty and numerical efficiency.
Rahlves, Maik; Roth, Bernhard; Reithmeier, Eduard
2017-07-20
Confocal microscopy is one of the dominating measurement techniques in surface metrology, with an enhanced lateral resolution compared to alternative optical methods. However, the axial resolution in confocal microscopy is strongly dependent on the accuracy of signal evaluation algorithms, which are limited by random noise. Here, we discuss the influence of various noise sources on confocal intensity signal evaluating algorithms, including center-of-mass, parabolic least-square fit, and cross-correlation-based methods. We derive results in closed form for the uncertainty in height evaluation on surface microstructures, also accounting for the number of axially measured intensity values and a threshold that is commonly applied before signal evaluation. The validity of our results is verified by numerical Monte Carlo simulations. In addition, we implemented all three algorithms and analyzed their numerical efficiency. Our results can serve as guidance for a suitable choice of measurement parameters in confocal surface topography measurement, and thus lead to a shorter measurement time in practical applications.
Adaptive numerical solutions of the Euler equations in 3D using finite elements
Peraire, J.; Peiro, J.; Formaggia, L.; Morgan, K.
1989-01-01
The development of an adaptive mesh solution for a flow involving shock interaction on a swept cylinder and an initial solution for a flow past a complex fighter configuration is reported. The finite element solution algorithm, the mesh generation, and the adaptivity of the solution are described. Sample results for the flow past an F-18 configuration at Mach 0.9 and alpha of 3 deg and for shock interaction on a swept cylinder at Mach 8.04 are summarized.
NUMERICAL AND ANALYTIC SOLUTION OF PRANDTL’S EQUATION FOR SOLID BODIES WITH AGREED CONTACT SURFACES
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A. Chigarev
2013-01-01
Full Text Available The paper considers a method for problem solution pertaining to compression of elastic bodies bounded by cylindrical surfaces whose radii are almost equal. The objective aim does not allow to apply the Hertz theory and reduces to finding approximate solutions of the Prandtl’s equation. The resulting solution is compared with the solution in the ANSYS system.
Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta
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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.
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Jyoti Talwar
2012-01-01
Full Text Available In this piece of work using only three grid points, we propose two sets of numerical methods in a coupled manner for the solution of fourth-order ordinary differential equation uiv(x=f(x,u(x,u′(x,u′′(x,u′′′(x, a
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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.
An in-vitro model for comparing the efficiency of wound-rinsing solutions.
Kaehn, K
2009-06-01
To develop an in-vitro model to evaluate the efficiency of wound-rinsing solutions in removing adherent, hydrophobic, denatured proteins. We hypothesised that saline solutions would be less effective than surfactant-containing solutions in removing denatured proteins. Prepared slides containing dried blood plasma or fibrin were incubated for up to one hour in histological troughs filled with one of four test solutions: physiological saline solution, Ringer's solution, a surfactant-containing solution and an antiseptic. The concentration of dissolved proteins was measured using a modified Biuret test. Results were analysed by plotting protein concentration against the incubation time. During the incubation period, the protein concentration increased in all of the test solutions, with the lowest concentration reported in the two saline-based solutions. These stayed clear, while the surfactant-containing solution become opaque, indicating that the surfactant had encased hydrophic substances, such as denatured proteins. Ringer's solution and saline are inappropriate solvents for adhering wound coatings. A sterile, surfactant-containing wound rinsing solution contains the essential properties for thorough and gentle cleansing of chronic wounds. None.
DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems
Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske
2008-12-01
We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly
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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.
Byrnes, Steven J; Aieta, Francesco; Capasso, Federico
2015-01-01
A metasurface lens (meta-lens) is a lens that bends light with an array of nanostructures on a flat surface, rather than by refraction. Macroscopic meta-lenses (mm- to cm-scale diameter) have been quite difficult to simulate and optimize, due to the large area, the lack of periodicity, and the billions of adjustable parameters. We describe a method for designing a large-area meta-lens that allows not only prediction of the efficiency and far-field, but also optimization of the shape and position of each individual nanostructure, with a computational cost that is almost independent of the lens size. Loosely speaking, the technique consists of designing a series of metasurface beam deflectors (blazed gratings), and then gluing them together. As a test of this framework, we design some high-numerical-aperture (NA=0.94) meta-lenses for visible light, based on TiO2 nano-pillars on a glass substrate. One of our designs is predicted to focus unpolarized 580nm light with 79% predicted efficiency; another focuses 580n...
Ayub, Kamran; Khan, M. Yaqub; Mahmood-Ul-Hassan, Qazi; Ahmad, Jamshad
2017-09-01
Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the \\exp (-φ (ζ ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld-Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.
Saha Ray, S.
2013-12-01
In this paper, the modified fractional reduced differential transform method (MFRDTM) has been proposed and it is implemented for solving fractional KdV (Korteweg-de Vries) equations. The fractional derivatives are described in the Caputo sense. In this paper, the reduced differential transform method is modified to be easily employed to solve wide kinds of nonlinear fractional differential equations. In this new approach, the nonlinear term is replaced by its Adomian polynomials. Thus the nonlinear initial-value problem can be easily solved with less computational effort. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of the solutions, several fractional KdV equations with different types of nonlinearities are considered. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional KdV equations.
1993-04-01
et al. Finite Elements An Introduction. Volume I. Englewood Cliffs, New Jersey: Prentice-Hall, 1981. Chapra , Steven C. and Canale, Raymond P. Numerical...1981. 2. Chapra , Steven C. and Canale, Raymond P. Numerical Methods For Engineers. New York: McGraw-Hill Book Company, 1985 3. Chandrupatla, Tirupathi
Numerical solution of nonlinear acoustic wave problems employing a green's function approach
Huijssen, J.; Verweij, M.D.
2006-01-01
The design of phased array transducers for medical diagnostic ultrasound asks for an understanding of the nonlinear propagation of acoustic wavefields. Most existing numerical models are based on the linearized model equations, but in the recent decades several numerical models have been developed
Numerical solution of nonlinear Volterra-Fredholm integral equation by using Chebyshev polynomials
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R. Ezzati
2011-03-01
Full Text Available In this paper, we have used Chebyshev polynomials to solve linearand nonlinear Volterra-Fredholm integral equations, numerically.First we introduce these polynomials, then we use them to changethe Volterra-Fredholm integral equation to a linear or nonlinearsystem. Finally, the numerical examples illustrate the efficiencyof this method.
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.
Li, Zheng; Wang, Hong; Yang, Danping
2017-10-01
We present a space-time fractional Allen-Cahn phase-field model that describes the transport of the fluid mixture of two immiscible fluid phases. The space and time fractional order parameters control the sharpness and the decay behavior of the interface via a seamless transition of the parameters. Although they are shown to provide more accurate description of anomalous diffusion processes and sharper interfaces than traditional integer-order phase-field models do, fractional models yield numerical methods with dense stiffness matrices. Consequently, the resulting numerical schemes have significantly increased computational work and memory requirement. We develop a lossless fast numerical method for the accurate and efficient numerical simulation of the space-time fractional phase-field model. Numerical experiments shows the utility of the fractional phase-field model and the corresponding fast numerical method.
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Rekha R Warrier
2014-12-01
Full Text Available This study presents the effects of storage duration and temperature of Strychnos potatorum stock solution on its coagulation efficiency. Coagulation efficiency of the seed extracts on water samples depended on the initial turbidity of the water sample. The stock solutions could clarify only highly turbid solutions. The optimum dosage of the stock solutions was 5% and optimal time required was 50 minutes. S. potatorum stock solutions, which were kept at room temperature (28 °C, had a shelf life of only five days and were able to remove turbidity from high and low turbidity water samples and no coagulation activity was observed for medium turbidity. The highest turbidity removals were observed for stock solutions, which were kept for three days. For stock solutions which were stored in refrigerator, shelf life was extended upto seven days, and the turbidity removal efficiencies improved from 45.9 to 63.8 for low and 43.7 to 64.9 % for high turbidity water samples, respectively.
Munteanu, Mihaela; Dascălu, Gabriela
2012-01-01
Widely use of reinforced concrete frame structures highlights the elements study of this structure type. Analysis of reinforced concrete slabs is supported by technical and economic objectives that aim to obtain innovative and feasible solutions. In this respect, the solution of hollow voided slabs is analysed in comparison with classic slab floor, stating the advantages and disadvantages of these two solutions. Previous testing and study of these variant represent another factor to be achiev...
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Farshid Mirzaee
2013-09-01
Full Text Available A numerical method based on an NM-set of general, hybrid of block-pulse function and Taylor series (HBT, is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra–Fredholm integral equations into some algebraic equations. In addition, convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.
Energy Technology Data Exchange (ETDEWEB)
Teixeira, Vinicius Ligiero; Pires, Adolfo Puime; Bedrikovetsky, Pavel G. [Universidade Estadual do Norte Fluminense (UENF), Macae, RJ (Brazil). Lab. de Engenharia e Exploracao do Petroleo (LENEP)
2004-07-01
Enhanced Oil Recovery (EOR) methods include injection of different fluids into reservoirs to improve oil displacement. The EOR methods may be classified into the following kinds: injection of chemical solutions, injection of solvents and thermal methods. The chemical fluids most commonly injected are polymers, surfactants, micellar solutions, etc. Displacement of oil by any of these fluids involves complex physico-chemical processes of interphase mass transfer, phase transitions and transport properties changes. These processes can be divided into two main categories: thermodynamical and hydrodynamical ones. They occur simultaneously during the displacement, and are coupled in the modern mathematical models of EOR. The model for one-dimensional displacement of oil by polymer solutions is analyzed in this paper. The Courant number is fixed, and we compare the results of different runs of a numerical simulator with the analytical solution of this problem. Each run corresponds to a different spatial discretization. (author)
A numerically efficient technique of regional gravity field modeling using Radial Basis Functions
Shahbazi, Anahita; Safari, Abdolreza; Foroughi, Ismael; Tenzer, Robert
2016-02-01
Radial Basis Functions (RBFs) have been extensively used in regional gravity and (quasi)geoid modeling. Reliable models require the choice of an optimal number of RBFs and of their parameters. The RBF parameters are typically optimized using a regularization algorithm. Therefore, the determination of the number of RBFs is the most challenging task in the modeling procedure. For this purpose, we design a data processing scheme to optimize the number of RBFs and their parameters simultaneously. Using this scheme, the gravimetric quasi-geoid model can be validated without requiring additional information on the quasi-geoidal geometry obtained from GPS/leveling data. Furthermore, the Levenberg-Marquardt algorithm, used for regularization, is modified to enhance its numerical performance. We demonstrate that these modifications guarantee the convergence of the solution to the global minimum while substantially decreasing the number of iterations. The proposed methodology is evaluated using synthetic gravity data and compared with existing methods for validating the RBF parameterization of the gravity field.
Wang, Lingle; Friesner, Richard A; Berne, B J
2011-08-04
A small change in the Hamiltonian scaling in Replica Exchange with Solute Tempering (REST) is found to improve its sampling efficiency greatly, especially for the sampling of aqueous protein solutions in which there are large-scale solute conformation changes. Like the original REST (REST1), the new version (which we call REST2) also bypasses the poor scaling with system size of the standard Temperature Replica Exchange Method (TREM), reducing the number of replicas (parallel processes) from what must be used in TREM. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST2 is compared with TREM and with REST1 for the folding of the trpcage and β-hairpin in water. The comparisons confirm that REST2 greatly reduces the number of CPUs required by regular replica exchange and greatly increases the sampling efficiency over REST1. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water.
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M. I. Berenguer
2009-01-01
Full Text Available In this work we use analytical tools—Schauder bases and Geometric Series theorem—in order to develop a new method for the numerical resolution of the linear Volterra integral equation of the second kind.
Denisov, A. M.; Zakharov, E. V.; Kalinin, A. V.; Kalinin, V. V.
2010-07-01
A numerical method is proposed for solving an inverse electrocardiography problem for a medium with a piecewise constant electrical conductivity. The method is based on the method of boundary integral equations and Tikhonov regularization.
Numerical solution of neutral functional-differential equations with proportional delays
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Mehmet Giyas Sakar
2017-07-01
Full Text Available In this paper, homotopy analysis method is improved with optimal determination of auxiliary parameter by use of residual error function for solving neutral functional-differential equations (NFDEs with proportional delays. Convergence analysis and error estimate of method are given. Some numerical examples are solved and comparisons are made with the existing results. The numerical results show that the homotopy analysis method with residual error function is very effective and simple.
Hilbert space method for the numerical solution of reactor physics problems
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Labs.)
1983-01-01
A Hilbert space approach is used to give a unified treatment of neutron transport by finite element methods. Global solutions can be found by least squares, variational and weighted residual methods stemming from an identity. Bounds for local characteristics of solutions are found by a bi-variational method.
Dealing with unexpected events : efficient and safe solutions to emergent repair on NPP
Energy Technology Data Exchange (ETDEWEB)
Liekens Massazza, I.
2015-07-01
Nuclear Facilities are constantly challenged with unexpected events occurring on Primary Circuit components. A solution must be deployed quickly to minimize impact on the scheduled outage duration while guaranteeing safety, quality and ALARA standards. AREVA NP has demonstrated worldwide recognized capabilities and expertise through efficient management of various unexpected forced events through the time. Turnkey packaged solutions which are proposed are based on proven technics which can be quickly adapted and qualified to the specific problem, resulting in customers’ full satisfaction. (Author)
Efficient Incorporation of Mg in Solution Grown GaN Crystals
2013-10-11
Efficient Incorporation of Mg in Solution Grown GaN Crystals Jaime A. Freitas, Jr., Boris N. Feigelson, and Travis J. Anderson Naval Research...and optical spectroscopy studies carried out on GaN crystals grown in solution detect and identify Mg as the dominant shallow acceptor. Selective...selected crystal orientations.6) HVPE wafers are in general n-type (free carrier concentration of typically 5 1017/cm3), have a high dislocation
Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations
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Khaled A. Gepreel
2013-01-01
Full Text Available We implement relatively analytical techniques, the homotopy perturbation method, and variational iteration method to find the approximate solutions for time and space fractional Benjamin-Bona Mahony equation. The fractional derivatives are described in the Caputo sense. These methods are used in applied mathematics to obtain the analytic approximate solutions for the nonlinear Bejamin-Bona Mahoney (BBM partial fractional differential equation. We compare between the approximate solutions obtained by these methods. Also, we present the figures to compare between the approximate solutions. Also, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved -expansion function method to find exact solutions of nonlinear fractional BBM equation.
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Mehriban Imanova Natiq
2012-03-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE As is known, many problems of natural science are reduced mainly to the solution of nonlinear Volterra integral equations. The method of quadratures that was first applied by Volterra to solving variable boundary integral equations is popular among numerical methods for the solution of such equations. At present, there are different modifications of the method of quadratures that have bounded accuracies. Here we suggest a second derivative multistep method for constructing more exact methods.
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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.
Efficient and stable solution-processed planar perovskite solar cells via contact passivation
Tan, Hairen; Jain, Ankit; Voznyy, Oleksandr; Lan, Xinzheng; García de Arquer, F. Pelayo; Fan, James Z.; Quintero-Bermudez, Rafael; Yuan, Mingjian; Zhang, Bo; Zhao, Yicheng; Fan, Fengjia; Li, Peicheng; Quan, Li Na; Zhao, Yongbiao; Lu, Zheng-Hong; Yang, Zhenyu; Hoogland, Sjoerd; Sargent, Edward H.
2017-02-01
Planar perovskite solar cells (PSCs) made entirely via solution processing at low temperatures (efficiencies of 20.1 and 19.5% for active areas of 0.049 and 1.1 square centimeters, respectively, achieved via low-temperature solution processing. Solar cells with efficiency greater than 20% retained 90% (97% after dark recovery) of their initial performance after 500 hours of continuous room-temperature operation at their maximum power point under 1-sun illumination (where 1 sun is defined as the standard illumination at AM1.5, or 1 kilowatt/square meter).
Butet, J.; Bernasconi, G. D.; Yang, K.-Y.; Martin, O. J. F.
2016-09-01
During the last decade, important attention has been devoted to the observation of nonlinear optical processes in plasmonic nanosystems, giving rise to a new field of research called nonlinear plasmonics. The cornerstone of nonlinear plasmonics is the use of the large field enhancement associated with the excitation of localized surface plasmon resonances to reach high nonlinear conversion yields. Among all the nonlinear optical processes, second harmonic generation (SHG), the process whereby two photons at the fundamental frequency are converted into one photon at the second harmonic frequency, is undoubtedly the most studied one due to the relative simplicity of its experimental observation. However, the physical origin of SHG from plasmonic nanostructures hides a lot of subtleties, which are mainly related to its particular behavior upon inversion symmetry. In order to catch all the peculiarities of SHG, it is mandatory to develop dedicated numerical methods able to accurately describe all the underlying physical processes and the influence of the initial assumptions needs to be well-characterized. In this presentation, we discuss and compare different methods (namely full-wave computations based on the surface integral equations method, mode analysis, the Miller's rule, and the effective nonlinear susceptibility method) proposed for the evaluation of the SHG from plasmonic nanoparticles emphasizing their limitations and advantages. In particular, the design of double resonant antennas for efficient nonlinear conversion at the nanoscale is addressed in detail.
Numerical Study of Usage Efficiency of Multistage Filters on Mineral Leaching Process
Inkarbekov, Medet; Kuljabekov, Alibek; Alibayeva, Karlygash; Kaltayev, Aidarkhan
2013-11-01
The numerical study of the usage efficiency of the multistage filters setting technology is carried out on the basis of mathematical simulation. And its application on in-situ mineral leaching process is considered. So long as mineral bearing sandstone in deposit mostly is separated by interbedded layers of sands and clays, it's expedient to use multistage filters setting technology at the mineral extraction. A comparison of the extraction degree at single and multistage filters is implemented. The results of calculations show that the distribution of flow (inflow) on well height is not uniform. In the calculations the well accepted as high-permeability channel, depending on the construction of the filter. Obtained results for a multistage filters setting qualitatively conform to the experimental findings. Wellbore is considered as a surface with a constant reduced pressure in the bottomhole formation zone. But such assumption does not show a qualitative picture of the fluid flow in the bottomhole zone [Brovin K.G., Grabovnikov V.A., 1997]. To construct an accurate mathematical model it's necessary to use Navier-Stokes equation for the interior of a vertical wellbore, and the filtration law for modeling the filtration in the reservoir. Strictly speaking, it would have had to sew two laws on the contact surface of a rock and filter. Such review requires enormous computing, as far as computational grid must be sufficiently thick to cover the interior of the wellbore.
Yon, Steven; Katz, Joseph; Plotkin, Allen
1992-01-01
The practical limit of airfoil thickness ratio for which acceptable engineering results are obtainable with the Dirichlet boundary-condition-based numerical methods is investigated. This is done by studying the effect of thickness on the calculated pressure distribution near the trailing edge and by comparing the aerodynamic coefficients with available exact solutions. The first objective of this study, owing to the wide use of such computational methods, is to demonstrate the numerical symptoms that occur when the body or wing thickness approaches zero and to increase the awareness of potential users of these methods. Additionally, an effort is made to obtain the practical limits of the trailing-edge thickness where such problems will appear in the flow solution, and to propose some possible cures for very thin airfoils or those with cusped trailing edges.
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T.; Oliveira, C.R.E. de [Imperial Coll. of Science, Technology and Medicine, London (United Kingdom). Dept. of Mechanical Engineering
1996-09-01
A maximum principle for the time-dependent first-order Boltzmann equation is established in two independent ways:- by a generalized least squares method and by a method based on the properties of an appropriate bi-linear form. The second derivation suggests a metric for a Hilbert space which provides a geometrical interpretation of the variational principle. This interpretation leads to a Petrov-Galerkin method of Martin for time dependent transport. The maximum principle is used to define a figure of merit for the global error of any numerical solution for time dependent transport. The principle is used also to demonstrate the neutron conservation property of optimized numerical solutions, and the convergence of finite element methods based on the variational principle. (Author).
Manufacturing polymer light emitting diode with high luminance efficiency by solution process
Kim, Miyoung; Jo, SongJin; Yang, Ho Chang; Yoon, Dang Mo; Kwon, Jae-Taek; Lee, Seung-Hyun; Choi, Ju Hwan; Lee, Bum-Joo; Shin, Jin-Koog
2012-06-01
While investigating polymer light emitting diodes (polymer-LEDs) fabricated by solution process, surface roughness influences electro-optical (E-O) characteristics. We expect that E-O characteristics such as luminance and power efficiency related to surface roughness and layer thickness of emitting layer with poly-9-Vinylcarbazole. In this study, we fabricated polymer organic light emitting diodes by solution process which guarantees easy, eco-friendly and low cost manufacturing for flexible display applications. In order to obtain high luminescence efficiency, E-O characteristics of these devices by varying parameters for printing process have been investigated. Therefore, we optimized process condition for polymer-LEDs by adjusting annealing temperatures of emission, thickness of emission layer showing efficiency (10.8 cd/A) at 10 mA/cm2. We also checked wavelength dependent electroluminescence spectrum in order to find the correlation between the variation of efficiency and the thickness of the layer.
Directory of Open Access Journals (Sweden)
Vincenzo Maria De Benedictis
2016-05-01
Full Text Available The Mark–Houwink–Sakurada (MHS equation allows for estimation of rheological properties, if the molecular weight is known along with good understanding of the polymer conformation. The intrinsic viscosity of a polymer solution is related to the polymer molecular weight according to the MHS equation, where the value of the constants is related to the specific solvent and its concentration. However, MHS constants do not account for other characteristics of the polymeric solutions, i.e., Deacetilation Degree (DD when the solute is chitosan. In this paper, the degradation of chitosan in different acidic environments by thermal treatment is addressed. In particular, two different solutions are investigated (used as solvent acetic or hydrochloric acid with different concentrations used for the preparation of chitosan solutions. The samples were treated at different temperatures (4, 30, and 80 °C and time points (3, 6 and 24 h. Rheological, Gel Permeation Chromatography (GPC, Fourier Transform Infrared Spectroscopy (FT-IR, Differential Scanning Calorimetry (DSC and Thermal Gravimetric Analyses (TGA were performed in order to assess the degradation rate of the polymer backbones. Measured values of molecular weight have been integrated in the simulation of the batch degradation of chitosan solutions for evaluating MHS coefficients to be compared with their corresponding experimental values. Evaluating the relationship between the different parameters used in the preparation of chitosan solutions (e.g., temperature, time, acid type and concentration, and their contribution to the degradation of chitosan backbone, it is important to have a mathematical frame that could account for phenomena involved in polymer degradation that go beyond the solvent-solute combination. Therefore, the goal of the present work is to propose an integration of MHS coefficients for chitosan solutions that contemplate a deacetylation degree for chitosan systems or a more
Directory of Open Access Journals (Sweden)
Z. Mosayebi
2014-07-01
Full Text Available In this paper a numerical technique is presented for the solution of fuzzy linear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions(RBFs.We first solve the actual set are equivalent to the fuzzy set, then answer 1-cut into the equation. Also high convergence rates and good accuracy are obtain with the propose method using relativeiy low numbers of data points.
Dryazhenkov, A. A.; Potapov, M. M.
2016-02-01
An algorithm for solving a quadratic minimization problem on an ellipsoidal set in a Hilbert space is proposed. The algorithm is stable to nonuniform perturbations of the operators. A key condition for its application is that we know an estimate for the norm of the exact solution. Applications to boundary control problems for the one-dimensional wave equation are considered. Numerical results are presented.
On the existence of efficient solutions to vector optimization problem of traffic flow on network
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T. A. Bozhanova
2009-09-01
Full Text Available We studied traffic flow models in vector-valued optimization statement where the flow is controlled at the nodes of network. We considered the case when an objective mapping possesses a weakened property of upper semicontinuity and made no assumptions on the interior of the ordering cone. The sufficient conditions for the existence of efficient controls of the traffic problems are derived. The existence of efficient solutions of vector optimization problem for traffic flow on network are also proved.
On the existence of efficient solutions to vector optimization problem of traffic flow on network
T. A. Bozhanova
2009-01-01
We studied traffic flow models in vector-valued optimization statement where the flow is controlled at the nodes of network. We considered the case when an objective mapping possesses a weakened property of upper semicontinuity and made no assumptions on the interior of the ordering cone. The sufficient conditions for the existence of efficient controls of the traffic problems are derived. The existence of efficient solutions of vector optimization problem for traffic flow on network are also...
Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian
2011-01-01
We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.
Dlugach, Janna M.; Mishchenko, Michael I.
2017-01-01
In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.
Goloviznin, V. M.; Kanaev, A. A.
2012-03-01
The CABARET computational algorithm is generalized to one-dimensional scalar quasilinear hyperbolic partial differential equations with allowance for inequality constraints on the solution. This generalization can be used to analyze seepage of liquid radioactive wastes through the unsaturated zone.
Tin melting: Effect of grid size and scheme on the numerical solution
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Vasilios Alexiades
2003-02-01
Full Text Available Benchmark solutions in Computational Fluid Dynamics are necessary for testing and for the verification of newly developed algorithms and codes. For flows involving heat transfer coupled to solid-liquid phase change and convection in the melt, such benchmark solutions do not exist. A set of benchmark problems has recently been proposed for melting of metals and waxes and several researchers responded by providing solutions for the given problems. It was shown in two recent publications that there were large discrepancies in the results obtained by those contributors. In the present, work we focus on one of the four test problems, tin melting at Rayleigh number $Ra=2.5imes 10^{5}$. Solutions obtained for several grids and two discretization schemes are presented and compared. Our results are used to explain the origin of the discrepancies in earlier results. Suggestions for future work are also provided.
Solution of AntiSeepage for Mengxi River Based on Numerical Simulation of Unsaturated Seepage
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Youjun Ji
2014-01-01
Full Text Available Lessening the leakage of surface water can reduce the waste of water resources and ground water pollution. To solve the problem that Mengxi River could not store water enduringly, geology investigation, theoretical analysis, experiment research, and numerical simulation analysis were carried out. Firstly, the seepage mathematical model was established based on unsaturated seepage theory; secondly, the experimental equipment for testing hydraulic conductivity of unsaturated soil was developed to obtain the curve of two-phase flow. The numerical simulation of leakage in natural conditions proves the previous inference and leakage mechanism of river. At last, the seepage control capacities of different impervious materials were compared by numerical simulations. According to the engineering actuality, the impervious material was selected. The impervious measure in this paper has been proved to be effectible by hydrogeological research today.
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
Russo, David
2016-05-01
The aim of the present numerical study was to extend the data-driven protocol for the control of soil salinity, to control chloride and nitrate concentrations and mass fluxes below agricultural fields irrigated with treated waste water (TWW). The protocol is based on alternating irrigation water quality between TWW and desalinized water (DSW), guided by solute concentrations at soil depth, zs. Two different schemes, the first requires measurements of soil solution concentrations of chloride and nitrate at zs, while, the second scheme requires only measurements of soil solution EC at zs, were investigated. For this purpose, 3-D numerical simulations of flow and transport were performed for variably saturated, spatially heterogeneous, flow domains located at two different field sites. The sites differ in crop type, irrigation method, and in their lithology; these differences, in turn, considerably affect the performance of the proposed schemes, expressed in terms of their ability to reduce solute concentrations that drained below the root zone. Results of the analyses suggest that the proposed data-driven schemes allow the use of low-quality water for irrigation, while minimizing the consumption of high-quality water to a level, which, for given climate, soil, crop, irrigation method, and water quality, may be determined by the allowable nitrate and chloride concentrations in the groundwater. The results of the present study indicate that with respect to the diminution of groundwater contamination by chloride and nitrate, the more data demanding, first scheme is superior the second scheme.
Goulet, R.; Knikker, R.; Boudard, E.; Stutz, B.; Bonjour, J.
2014-02-01
This paper describes a numerical and experimental analysis of the process of water vapour absorption by a static lithium bromide solution. In the experiment, the temperature evolution of the absorbent solution is measured at different heights. The numerical model solves the set of governing equations for the simultaneous heat and mass transfer inside the absorbent by means of the finite-volume method. An iterative method is used to take into account the strong coupling of heat and mass transfer at the interface and variations of thermophysical properties. A moving grid technique is employed to represent the increase of the solution volume. Model results are compared with our measurements and data reported in the literature. The influence of using constant properties is analysed by comparison with the variable properties and experimental results. It is found that this assumption provides acceptable results in the investigated pool absorption cases despite a strong underestimation of the increase of the solution volume in the course of the absorption process.
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Iakovlev Roman
2017-01-01
Full Text Available The paper presents the results of a study devoted to the problem of improving the energy efficiency of mechanical motion of anthropomorphic robotic systems. Achieving higher energy efficiency is largely due to the implementation of improvements directly in the algorithms that ensure the movement of a robotic system. For this purpose, several existing analytical methods for solving the inverse kinematics problem for robotic walking platforms were analyzed. According to the survey, key areas where modification can improve the energy efficiency of mechanical motion in various RS are identified. The paper discusses the algorithm developed to optimize the solutions of the inverse kinematics problem in terms of energy consumption.
An Efficient Implementation of Non-Linear Limit State Analysis Based on Lower-Bound Solutions
DEFF Research Database (Denmark)
Damkilde, Lars; Schmidt, Lotte Juhl
2005-01-01
Limit State analysis has been used in design for decades e.g. the yield line theory for concrete slabs or slip line solutions in geotechnics. In engineering practice manual methods have been dominating but in recent years the interest in numerical methods has been increasing. In this respect...... it is mandatory to formulate the methods using the well-known finite element concept in order to interface with other types of analysis....
Global communication schemes for the numerical solution of high-dimensional PDEs
DEFF Research Database (Denmark)
Hupp, Philipp; Heene, Mario; Jacob, Riko
2016-01-01
The numerical treatment of high-dimensional partial differential equations is among the most compute-hungry problems and in urgent need for current and future high-performance computing (HPC) systems. It is thus also facing the grand challenges of exascale computing such as the requirement to red...
A mathematical model and numerical solution of interface problems for steady state heat conduction
Directory of Open Access Journals (Sweden)
Z. Muradoglu Seyidmamedov
2006-01-01
(isolation Ωδ tends to zero. For each case, the local truncation errors of the used conservative finite difference scheme are estimated on the nonuniform grid. A fast direct solver has been applied for the interface problems with piecewise constant but discontinuous coefficient k=k(x. The presented numerical results illustrate high accuracy and show applicability of the given approach.
Czech Academy of Sciences Publication Activity Database
Pokorný, Vladislav; Žonda, M.; Kauch, Anna; Janiš, Václav
2017-01-01
Roč. 131, č. 4 (2017), s. 1042-1044 ISSN 0587-4246 R&D Projects: GA ČR GA15-14259S Institutional support: RVO:68378271 Keywords : Anderson model * parquet equations * numerical renormalization group Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.469, year: 2016
A three–step discretization scheme for direct numerical solution of ...
African Journals Online (AJOL)
In this paper, a three-step discretization (numerical) formula is developed for direct integration of second-order initial value problems in ordinary differential equations. The development of the method and analysis of its basic properties adopt Taylor series expansion and Dahlquist stability test methods. The results show that ...
Numerical solution of the transverse resistivity of superconducting cables under AC conditions
Hartmann, R.A.; Hartmann, R.A.; van Beckum, F.P.H.; van de Klundert, L.J.M.; van de Klundert, L.J.M.; Dijkstra, D.
1989-01-01
The authors develop a numerical method for calculating the transverse resistivity of superconducting cables. A superconducting cable consists of a twisted bundle of strands with a nonconducting inner region. If such a cable is placed in an external magnetic field, the induced currents will not
Yang, Gonghua; Wei, Yanlong; Huang, Zhenzhu; Hu, Jiwen; Liu, Guojun; Ou, Ming; Lin, Shudong; Tu, Yuanyuan
2018-02-21
Reported herein is a novel strategy for the rapid and efficient collection of platinum from Karstedt's catalyst solution. By taking advantage of a ligand-exchange reaction between alkynols and the 1,3-divinyltetramethyldisiloxane ligand (M Vi M Vi ) that coordinated with platinum (Pt(0)), the Karstedt's catalyst particles with a size of approximately 2.5 ± 0.7 nm could be reconstructed and assembled into larger particles with a size of 150 ± 35 nm due to the hydrogen bonding between the hydroxyl groups of the alkynol. In addition, because the silicone-soluble M Vi M Vi ligand of the Karstedt's catalyst was replaced by water-soluble alkynol ligands, the resultant large particles were readily dispersed in water, resulting in rapid, efficient, and complete collection of platinum from the Karstedt's catalyst solutions with platinum concentrations in the range from ∼20 000 to 0.05 ppm. Our current strategy not only was used for the rapid and efficient collection of platinum from the Karstedt's catalyst solutions, but it also enabled the precise evaluation of the platinum content in the Karstedt's catalysts, even if this platinum content was extremely low (i.e., 0.05 ppm). Moreover, these platinum specimens that were efficiently collected from the Karstedt's catalyst solutions could be directly used for the evaluation of platinum without the need for pretreatment processes, such as calcination and digestion with hydrofluoric acid, that were traditionally used prior to testing via inductively coupled plasma mass spectrometry in conventional methods.
Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem
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Vladimir A. Emelichev
2002-07-01
Full Text Available We consider a multiple criterion Boolean programming problem with MINMAX partial criteria. The extreme level of independent perturbations of partial criteria parameters such that efficient (Pareto optimal solution preserves optimality was obtained. MSC: 90C29, 90C31
ENERGY EFFICIENT ROUTING IN COGNITIVE RADIO NETWORKS: CHALLENGES AND EXISTING SOLUTIONS
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K. Lakshmana Rao
2015-03-01
Full Text Available Dynamic Spectrum Allocation using Cognitive Radio (CR is a promising solution to the spectrum availability problem in wireless networks. Cognitive Radio, however, opens up certain new issues, mainly at the physical, medium access control and routing layer levels. Several solutions have been proposed to tackle these issues and use dynamic spectrum allocation to improve the performance of wireless networks. The focus of most of these has been to improve the throughput and other Quality of Service (QoS metrics. However, energy spent by a node is also an important matter of concern in most wireless networks e.g. wireless sensor networks. In this paper, we focus on the challenges posed by CR in routing data in an energy efficient manner. We then study some existing solutions to route data energy efficiently in CR networks and suggest some directions for future research.
DEFF Research Database (Denmark)
Lee, Jonghyun; Rolle, Massimo; Kitanidis, Peter K.
2017-01-01
such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger...... parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection...... meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large PÃ©clet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous...
Nonlinear grid error effects on numerical solution of partial differential equations
Dey, S. K.
1980-01-01
Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.
Henle, James M.
This pamphlet consists of 17 brief chapters, each containing a discussion of a numeration system and a set of problems on the use of that system. The numeration systems used include Egyptian fractions, ordinary continued fractions and variants of that method, and systems using positive and negative bases. The book is informal and addressed to…
Numerical solution of Painlev'e equation I by Daftardar-Gejji and Jafari method
Selamat, M. S.; Latif, B.; Aziz, N. A.; Yahya, F.
2017-08-01
In this paper, Painlev'e equation I problem was solved approximately using Daftardar-Gejji and Jafari Method (DJM) with initial conditions. The results obtained through this iterative method, is compared with that obtained by other methods such as Adomian Decomposition Method (ADM), Homotopy Pertubation Method (HPM) and Variational Iteration Method (VIM). The numerical results show that there is no significant difference. It has been found that the results obtained are in fully agreement.
Editorial: Special Issue on Analytical and Approximate Solutions for Numerical Problems
Walailak Journal of Science and Technology
2014-01-01
Though methods and algorithms in numerical analysis are not new, they have become increasingly popular with the development of high speed computing capabilities. Indeed, the ready availability of high speed modern digital computers and easy-to-employ powerful software packages has had a major impact on science, engineering education and practice in the recent past. Researchers in the past had to depend on analytical skills to solve significant engineering problems but, nowadays, researchers h...
Direct numerical solution of Poisson`s equation in cylindrical (r, z) coordinates
Energy Technology Data Exchange (ETDEWEB)
Chao, E.H.; Paul, S.F.; Davidson, R.C. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Fine, K.S. [Univ. of California, San Diego, La Jolla (Canada). Dept. of Physics
1997-07-22
A direct solver method is developed for solving Poisson`s equation numerically for the electrostatic potential {phi}(r,z) in a cylindrical region (r < R{sub wall}, 0 < z < L). The method assumes the charge density {rho}(r,z) and wall potential {phi}(r = R{sub wall}, z) are specified, and {partial_derivative}{phi}/{partial_derivative}z = 0 at the axial boundaries (z = 0, L).
On the numerical solution of the Gross–Pitaevskii equation | Laoye ...
African Journals Online (AJOL)
... Bogoliubov–de Gennes equations for type II superconductivity. The solution is compared with others in the literature and is shown to be easily adapted to the study of an isolated vortex recently discovered in Bose-Einstein Condensation in trapped gases. Journal of the Nigerian Association of Mathematical Physics Vol.
A comparison of numerical methods for the solution of continuous-time DSGE models
DEFF Research Database (Denmark)
Parra-Alvarez, Juan Carlos
This paper evaluates the accuracy of a set of techniques that approximate the solution of continuous-time DSGE models. Using the neoclassical growth model I compare linear-quadratic, perturbation and projection methods. All techniques are applied to the HJB equation and the optimality conditions...
Numerical solution of two-dimensional non-linear partial differential ...
African Journals Online (AJOL)
differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be solved at each time level. To linearize the resulting system of difference equations, Newton ...
An efficient and practical approach to obtain a better optimum solution for structural optimization
Chen, Ting-Yu; Huang, Jyun-Hao
2013-08-01
For many structural optimization problems, it is hard or even impossible to find the global optimum solution owing to unaffordable computational cost. An alternative and practical way of thinking is thus proposed in this research to obtain an optimum design which may not be global but is better than most local optimum solutions that can be found by gradient-based search methods. The way to reach this goal is to find a smaller search space for gradient-based search methods. It is found in this research that data mining can accomplish this goal easily. The activities of classification, association and clustering in data mining are employed to reduce the original design space. For unconstrained optimization problems, the data mining activities are used to find a smaller search region which contains the global or better local solutions. For constrained optimization problems, it is used to find the feasible region or the feasible region with better objective values. Numerical examples show that the optimum solutions found in the reduced design space by sequential quadratic programming (SQP) are indeed much better than those found by SQP in the original design space. The optimum solutions found in a reduced space by SQP sometimes are even better than the solution found using a hybrid global search method with approximate structural analyses.
Li, Gang
2015-01-01
This book presents an important technique to process organic photovoltaic devices. The basics, materials aspects and manufacturing of photovoltaic devices with solution processing are explained. Solution processable organic solar cells - polymer or solution processable small molecules - have the potential to significantly reduce the costs for solar electricity and energy payback time due to the low material costs for the cells, low cost and fast fabrication processes (ambient, roll-to-roll), high material utilization etc. In addition, organic photovoltaics (OPV) also provides attractive properties like flexibility, colorful displays and transparency which could open new market opportunities. The material and device innovations lead to improved efficiency by 8% for organic photovoltaic solar cells, compared to 4% in 2005. Both academic and industry research have significant interest in the development of this technology. This book gives an overview of the booming technology, focusing on the solution process fo...
S. Saha Ray
2014-01-01
A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1)-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the rel...
An efficient approach to numerical study of the coupled-BBM system with B-spline collocation method
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khalid ali
2016-11-01
Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with cubic trigonometric B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.
Numerical solution of system of boundary value problems using B-spline with free parameter
Gupta, Yogesh
2017-01-01
This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.
Influence of karst evolution on solute transport evaluated by process-based numerical modelling
Hubinger, Bernhard; Birk, Steffen
2010-05-01
Karst waters are of major interest in water resources management. Because of their inherent properties karst systems show great vulnerability with regard to contaminants. Karst systems include highly permeable solution conduit networks formed by chemical aggressive water embedded in a fissured matrix. Small initial voids are widened and thus act as preferential passages, where flow is rapid and often turbulent. Water discharging at karst spring originates from different pathways with different residence times. Contaminant transport through conduit pathways is very rapid, whereas flow through the fissured porous matrix is much slower. Thus, on the one hand, pollutants may be rapidly transported and reach high concentrations at the karst spring shortly after their release; on the other hand, the existence of slow flow components may cause the pollution to last for long times. In this work, solute transport properties of karst aquifers are investigated using generic conduit networks of hydraulically connected proto-conduits with initially log-normally distributed apertures in the millimetre range and below. Conduit evolution is modelled by coupling flow, transport, and dissolution processes, whereby single conduits are widened up to the metre range. Thus, different stages of karst evolution can be distinguished. The resulting flow systems provide the basis for modelling advective-dispersive transport of non-reactive solutes through the network of more or less widened (proto-)conduits. The general transport characteristics in karst systems as well as the influence of heterogeneities and structures on solute transport are illustrated for cases of direct injection into the conduit systems at different evolutionary stages. The resulting breakthrough curves typically show several distinct, chronologically shifted peaks with long tailings, which appears to be similar to data from field tracer experiments.
Influence of Lay Plan Solution in Fabric Efficiency and Consume in Cutting Section
Directory of Open Access Journals (Sweden)
Dumishllari Elmira
2016-12-01
Full Text Available One cutting order may require several lies and markers to achieve optimal efficiency and selection of right Lay Plan is one of the major challenges in cutting section, in a way to lead in fabric economy and reduced costs. The main purpose of this paper is to determine the best solution of lay plan and its influence, in the cutting room, starting from the analysis of the lay indicators calculations. We have studied an order with 200 jackets, with specific sizes. Markers are made by Gemini CAD (Gemini Cut Plan and Gemini Nest Expert. From Gemini CAD, we have taken different solutions of lay plans and chose the three best of them (lay plans that have a smaller number of lies, plies etc., and then, for three best solutions are calculated lay indicators. From this calculation, we have determined the best solution of lay plan. The order to study has 5 different fabrics, so the calculations are made for each of them, and in the end are combined, in a way to have conclusions for an order in general. Best solution of lay plans combination, resulted one which had a better weighted efficiency and a low lay consumption.
Numerical solution of the problem of selecting the optimum method of operating oil wells
Energy Technology Data Exchange (ETDEWEB)
Skryago, A.M.; Chirikov, L.I.; Fridman, G.Sh.; Kolokolov, A.A.; Panteleyev, G.V.; Terent' yev, S.A.; Zabudskiy, G.G.
1981-01-01
A mathematical model is studied for selecting the optimum method of operating the wells of an oil field, which is a linear Boolean programming problem. It is shown that this problem is equivalent to the generalized packet problem and a single product variant model of sectoral planning. Numerical calculations on the computer using as the initial problem the modified method of E. Balash, for the generalized packet problem the method of M.F. Kazakovaya, and the single product variant problem of sectoral planning the method of A. Ye. Bakhtin, show the greatest effectiveness for the problem studied of A. Ye. Bakhtin's method.
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.
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...... 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...... of derivatives and function approximation of Radial Basis Function. As a result, the method can be used to directly approximate the derivatives of dependent variables on a scattered set of knots. In this study knots were distributed irregularly in the solution domain using the Halton sequences. The method...
Directory of Open Access Journals (Sweden)
MH Ehrampoush
2014-09-01
Results: The results indicated that the adsorption process is affected by different parameters such as initial pollutant concentrations, adsorbent dose, pH, and contact time and Cadmiumremoval efficiency increases with increasing adsorbent dose and reaction time and decreases with increasing initial concentration of Cadmium. Therefore, it is observed that by raising the initial Cadmium concentration, the adsorption rate increases. The maximum efficiency of adsorptionin pH=7amounted to 89.6%. Conclusion: It is concluded that Zinc Oxide nanoparticles have proper efficiency in removal of Cadmium from aqueous solutions and can be used in the treatment of wastewater that contains ion Cadmium. However, its efficiency is deeply dependent on ion strength and the interaction of other metals in wastewater.
Analytical Solutions Using Integral Formulations and Their Coupling with Numerical Approaches.
Morel-Seytoux, Hubert J
2015-01-01
Analytical and numerical approaches have their own distinct domains of merit and application. Unfortunately there has been a tendency to use either one or the other even when their domains overlap. Yet there is definite advantage in combining the two approaches. Being relatively new this emerging technique of combining the approaches is, at this stage, more of an art than a science. In this article we suggest approaches for the combination through simple examples. We also suggest that the integral formulation of the analytical problems may have some advantages over the differential formulation. The differential formulation limits somewhat the range of linear system descriptions that can be applied to a variety of practical problems. On the other hand the integral approach tends to focus attention to overall integrated behavior and properties of the system rather than on minute details. This is particularly useful in the coupling with a numerical model as in practice it generally deals also with only the integrated behavior of the system. The thesis of this article is illustrated with some simple stream-aquifer flow exchange examples. © 2014, National GroundWater Association.
Wael M. Mohamed; Ahmed F. Ghaleb; Enaam K. Rawy; Hassan A.Z. Hassan; Adel A. Mosharafa
2015-01-01
A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally treated as well. The volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. The present study is a c...
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Sung Kim
2014-01-01
Full Text Available This paper describes a numerical study on the improvement of suction performance and hydraulic efficiency of a mixed-flow pump by impellers. The design of these impellers was optimized using a commercial CFD (computational fluid dynamics code and DOE (design of experiments. The design variables of meridional plane and vane plane development were defined for impeller design. In DOE, variables of inlet part were selected as main design variables in meridional plane, and incidence angle was selected in vane plane development. The verification of the experiment sets that were generated by 2k factorial was done by numerical analysis. The objective functions were defined as the NPSHre (net positive suction head required, total efficiency, and total head of the impellers. The importance of the geometric design variables was analyzed using 2k factorial designs. The interaction between the NPSHre and total efficiency, according to the meridional plane and incidence angle, was discussed by analyzing the 2k factorial design results. The performance of optimally designed model was verified by experiments and numerical analysis and the reliability of the model was retained by comparison of numerical analysis and comparative analysis with the reference model.
Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method
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Mustafa Inc
2014-01-01
Full Text Available We demonstrate the efficiency of reproducing kernel Hilbert space method on the seventh-order boundary value problems satisfying boundary conditions. These results have been compared with the results that are obtained by variational iteration method (VIM, homotopy perturbation method (HPM, Adomian decomposition method (ADM, variation of parameters method (VPM, and homotopy analysis method (HAM. Obtained results show that our method is very effective.
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M.A. Maqsood
2009-05-01
Full Text Available Zinc (Zn deficiency is a common micronutrient deficiency in arid and semi arid regions of the world. A solution culture study was conducted to categorize twelve wheat genotypes according to their Zn utilization efficiency. The wheat genotypes were grown in a halfstrength Johnson’s modified nutrient solution supplied with adequate (2 µM and deficient (0.2 µM Zn level. There was a significant effect of Zn level and genotypes on biomass production and Zn concentration. Wheat genotype Sehar-06 produced maximum shoot biomass under both adequate and deficient Zn condition and it was minimum in Vatan. Sehar-06 maintained higher Zn contents at deficient Zn level compared to other genotypes. Genotypes categorized according to their Zn utilization efficiency at deficient Zn supply fell into five categories. Sehar-06 and Auqab-2000 were categorized as HDMHE (high dry matter with high Zn utilization efficiency. Most of the genotypes were categorized as MDM-ME (medium dry matter with medium Zn utilization efficiency category. Genotypes with better growth performance and Zn utilization efficiency such as Sehar-06 and Auqab-2000 can be recommended for Zn deficient soils and for breeding purposes.
Sternovsky, Z; Downum, K; Robertson, S
2004-08-01
A kinetic model of the plasma-sheath problem is presented that includes the effects of charge-exchange collisions of the ion. The collisions are modeled as a sink for accelerated ions and as a source of cold ions. Solutions are obtained by numerical integration of Poisson's equation from a point near the plasma midplane to the wall. In the quasineutral region, these solutions agree with earlier analytic work. As the mean free path is decreased, the current density at the wall decreases and the potential profile in the quasineutral region shows a smooth transition from a parabolic profile to a nearly cubic profile determined by the ion mobility. An approximate expression is found for the ion flux to the wall in the collisional limit.
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A. Mushtaq
2016-01-01
Full Text Available Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i the shooting method and (ii the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.
Salama, Amgad
2015-06-01
In this work, the experimenting fields approach is applied to the numerical solution of the Navier-Stokes equation for incompressible viscous flow. In this work, the solution is sought for both the pressure and velocity fields in the same time. Apparently, the correct velocity and pressure fields satisfy the governing equations and the boundary conditions. In this technique a set of predefined fields are introduced to the governing equations and the residues are calculated. The flow according to these fields will not satisfy the governing equations and the boundary conditions. However, the residues are used to construct the matrix of coefficients. Although, in this setup it seems trivial constructing the global matrix of coefficients, in other setups it can be quite involved. This technique separates the solver routine from the physics routines and therefore makes easy the coding and debugging procedures. We compare with few examples that demonstrate the capability of this technique.
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)
Gunzburger, M. D.; Nicolaides, R. A.
1986-01-01
Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.
Bezier Curves Based Numerical Solutions of Delay Systems with Inverse Time
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F. Ghomanjani
2014-01-01
Full Text Available This paper applied, for the first time, the Bernstein’s approximation on delay differential equations and delay systems with inverse delay that models these problems. The direct algorithm is given for solving this problem. The delay function and inverse time function are expanded by the Bézier curves. The Bézier curves are chosen as piecewise polynomials of degree n, and the Bézier curves are determined on any subinterval by n+1 control points. The approximated solution of delay systems containing inverse time is derived. To validate accuracy of the present algorithm, some examples are solved.
Numerical solution of time- and space-fractional coupled Burgers’ equations via homotopy algorithm
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Jagdev Singh
2016-06-01
Full Text Available In this paper, we constitute a homotopy algorithm basically extension of homotopy analysis method with Laplace transform, namely q-homotopy analysis transform method to solve time- and space-fractional coupled Burgers’ equations. The suggested technique produces many more opportunities by appropriate selection of auxiliary parameters ℏ and n(n⩾1 to solve strongly nonlinear differential equations. The proposed technique provides ℏ and n-curves, which describe that the convergence range is not a local point effects and finds elucidated series solution that makes it superior than HAM and other analytical techniques.
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
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Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Highly efficient solutions for smart and bulk power transmission of 'green energy'
Energy Technology Data Exchange (ETDEWEB)
Breuer, Wilfried; Retzmann, Dietmar; Uecker, Karl
2010-09-15
Environmental constraints, loss minimization and CO2 reduction will play an increasingly more important role in future. Security and sustainability of power supply as well as economic efficiency needs application of advanced technologies. Innovative solutions with HVDC (High Voltage Direct Current) and FACTS (Flexible AC Transmission Systems) have the potential to cope with these challenges. They provide the features which are necessary to avoid technical problems in power systems, they increase the transmission capacity and system stability very efficiently and help prevent cascading outages. Furthermore, they are essential for Grid Access of Renewable Energy Sources such as Hydro, Wind and Solar-Energy.
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Yangsen Kang
2015-01-01
Full Text Available We demonstrate a high-throughput, solution-based process for subwavelength surface texturing of a III-V compound solar cell. A zinc oxide (ZnO nanoparticle ink is spray-coated directly on top of a gallium arsenide (GaAs solar cell. The nanostructured ZnO films have demonstrated antireflection and light scattering properties over the visible/near-infrared (NIR spectrum. The results show a broadband spectral enhancement of the solar cell external quantum efficiency (EQE, a 16% enhancement of short circuit current, and a 10% increase in photovoltaic efficiency.
Pierce, S. A.; Ciarleglio, M.; Dulay, M.; Lowry, T. S.; Sharp, J. M.; Barnes, J. W.; Eaton, D. J.; Tidwell, V. C.
2006-12-01
Work in the literature for groundwater allocation emphasizes finding a truly optimal solution, often with the drawback of limiting the reported results to either maximizing net benefit in regional scale models or minimizing pumping costs for localized cases. From a policy perspective, limited insight can be gained from these studies because the results are restricted to a single, efficient solution and they neglect non-market values that may influence a management decision. Conversely, economically derived objective functions tend to exhibit a plateau upon nearing the optimal value. This plateau effect, or non-uniqueness, is actually a positive feature in the behavior of groundwater systems because it demonstrates that multiple management strategies, serving numerous community preferences, may be considered while still achieving similar quantitative results. An optimization problem takes the same set of initial conditions and looks for the most efficient solution while a decision problem looks at a situation and asks for a solution that meets certain user-defined criteria. In other words, the election of an alternative course of action using a decision support system will not always result in selection of the most `optimized' alternative. To broaden the analytical toolset available for science and policy interaction, we have developed a groundwater decision support system (GWDSS) that generates a suite of management alternatives by pairing a combinatorial search algorithm with a numerical groundwater model for consideration by decision makers and stakeholders. Subject to constraints as defined by community concerns, the tabu optimization engine systematically creates hypothetical management scenarios running hundreds, and even thousands, of simulations, and then saving the best performing realizations. Results of the search are then evaluated against stakeholder preference sets using ranking methods to aid in identifying a subset of alternatives for final
Numerical solutions of anharmonic vibration of BaO and SrO molecules
Pramudito, Sidikrubadi; Sanjaya, Nugraha Wanda; Sumaryada, Tony
2016-03-01
The Morse potential is a potential model that is used to describe the anharmonic behavior of molecular vibration between atoms. The BaO and SrO molecules, which are two almost similar diatomic molecules, were investigated in this research. Some of their properties like the value of the dissociation energy, the energy eigenvalues of each energy level, and the profile of the wavefunctions in their correspondence vibrational states were presented in this paper. Calculation of the energy eigenvalues and plotting the wave function's profiles were performed using Numerov method combined with the shooting method. In general we concluded that the Morse potential solved with numerical methods could accurately produce the vibrational properties and the wavefunction behavior of BaO and SrO molecules from the ground state to the higher states close to the dissociation level.
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Haixiong Yu
2014-01-01
Full Text Available We apply a lumped mass finite element to approximate Dirichlet problems for nonsmooth elliptic equations. It is proved that the lumped mass FEM approximation error in energy norm is the same as that of standard piecewise linear finite element approximation. Under the quasi-uniform mesh condition and the maximum angle condition, we show that the operator in the finite element problem is diagonally isotone and off-diagonally antitone. Therefore, some monotone convergent algorithms can be used. As an example, we prove that the nonsmooth Newton-like algorithm is convergent monotonically if Gauss-Seidel iteration is used to solve the Newton's equations iteratively. Some numerical experiments are presented.
Numerical solution of the Black-Scholes equation using cubic spline wavelets
Černá, Dana
2016-12-01
The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.
Numerical solution of the problem of detecting diffractors in a complex acoustic media
Danilin, Alexander N.; Pestov, Leonid N.
2017-11-01
One of the most effective methods for detecting weak scattering objects (diffractors) associated with cracked-cavernous hydrocarbon reservoirs is the CSP (Common Scattering Point) method [1]. This method is the most effective for weakly inhomogeneous media. The CSP method can be supplemented by a preliminary continuation of the wave field to a certain depth for strongly inhomogeneous medium. In this paper we use Reverse Time Datuming (RTD) procedure for this purpose [2, 3, 4]. The new CSP-RTD method is based on both CSP and RTD methods for determining deep-seated diffractors in complex acoustic medium. The results of numerical studies of CSP-RTD method for a complex acoustic model is presented. The comparison of CSP-RTD method and RTM method is also presented.
Numerical solutions of the momentum equations for the lower overshoot layer
Marik, D.; Petrovay, K.
2001-01-01
The lower overshooting layer, which plays an important role in the dynamo mechanism, is one of the least known regions of the Sun. The most promising way to model this region is the Reynolds-stress method. In this paper we determine the radial distribution of the turbulent kinetic energy k, the mean square relative temperature fluctuation q, the normalized energy flux J, and the energy dissipation rate ɛ. We present solutions in the case of a simple k-ɛ model and in the case of solving all four differential equations using various Δ∇ distributions (temperature stratifications). We use a diffusive approximation for the nonlocal fluxes ("Xiong's closure"), considering the case of both strong and weak nonlocality. The resulting profiles of k and ɛ are found to be approximately linear and the profiles of the turbulent lengths and time scales l and τ are also similar for different cases. The shapes of these profiles thus seem to be robust properties of the solution, with little sensitivity to the particular parameter values and background stratification assumed. In contrast, we find that the penetration depth depends rather sensitively on the slope of the Δ∇ curve and on the strength of nonlocality assumed.
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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.
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.
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J. Vanderborght
1997-01-01
Full Text Available Abstract: Field-scale solute dispersion is determined by water flow heterogeneity which results from spatial variability of soil hydraulic properties and soil moisture state. Measured variabilities of soil hydraulic properties are highly sensitive to the experimental method. Field-scale dispersion derived from leaching experiments in a macroporous loam soil was compared with field-scale dispersion obtained with numerical simulations in heterogeneous random fields. Four types of random fields of hydraulic properties having statistical properties derived from four different types of laboratory measurements were considered. Based on this comparison, the measurement method depicting heterogeneities of hydraulic properties most relevant to field-scale solute transport was identified. For unsaturated flow, the variability of the hydraulic conductivity characteristic measured on a small soil volume was the most relevant parameter. For saturated flow, simulated dispersion underestimated the measured dispersion and it was concluded that heterogeneity of macroscopic hydraulic properties could not represent solute flow heterogeneity under these flow conditions. Field-scale averaged solute concentrations depend both on the detection method and the averaging procedure. Flux-averaged concentrations (relevant to practical applications differ from volume-averaged or resident concentrations (easy to measure, especially when water flow is more heterogeneous. Simulated flux and resident concentrations were subsequently used to test two simple one-dimensional transport models in predicting flux concentrations when they are calibrated on resident concentrations. In the first procedure, solute transport in a heterogeneous soil is represented by a 1-D convection dispersion process. The second procedure was based on the relation between flux and resident concentrations for a stochastic convective process. Better predictions of flux concentrations were obtained using
MacKenzie, Steven J.; Hodgkinson, Jane; Johnson, Mark; Dakin, John P.
1997-01-01
We have measured fluorescence from a waveguide formed by a falling cylindrical stream of liquid. The configuration is suited to taking measurements from liquids with any refractive index, such as aqueous solutions. The parameters which determine the stream stability have been investigated, and the optical collection efficiency has been mathematically modelled. We have produced streams up to 350 mm long with a 2.5 mm diameter, and measured a fluorescence collection enhancemen...
Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers
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Smita Tapaswini
2013-01-01
Full Text Available Present paper proposes a new technique to solve uncertain beam equation using double parametric form of fuzzy numbers. Uncertainties appearing in the initial conditions are taken in terms of triangular fuzzy number. Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. Finally, the same is solved by homotopy perturbation method (HPM to obtain the uncertain responses subject to unit step and impulse loads. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the methodology.
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M Malakootian
2015-07-01
Full Text Available Introduction: Carbon nano tubes are products which have the ability to remove some contaminants from aqueous solutions and wastewater. The efficiency of these products depends on different factors such as PH, concentration, contact, mixing time, etc. in this research the efficiency of oxidized multi- walled carbon nanotubes is studied. Methods: The study is Experimental. The multi-walled carbon nanotubes were oxidized and Three PH 4, 7 and 10 and contact times 5, 10 and 40 min, and the concentrations of 50, 100 and 125 mg of carbon nanotubes from aqueous Pb removal efficiency were examined.All of the tests were done according to the standard methods for the examination of water and wastewater book 21th edited..Real samples of drinking water was the village of Ebrahim Abad RazaviSirjan. Data analysis was done using SPSS statistical software version 16 Results: By Simultaneous changes in time and PH was changed the efficiency of lead removal by the oxidized multi- walled carbon nanotubes. The most important factor in increasing the efficiency of removal, using acidic PH (PH =4 is. With a Simultaneous increase in contact time and concentration of nanotubes, the removal efficiency increased. In optimal conditions, 125 mg of nanotube concentration, contact time of 10 minutes and PH=4 removal of lead in synthetic samples and real samples, respectively, 99.1 and 94% were achieved. In total there is little difference between the real conditions and the synthetic conditions of the removal efficiency that this difference arises from the interaction of cations, anions and heavy metals in real samples. Conclusion: Oxidized multi-walled Carbon nanotubes has a high capacity for the removal of lead from aqueous solutions.
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Sie Long Kek
2015-01-01
Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.
Solution-processed small-molecule solar cells: breaking the 10% power conversion efficiency.
Liu, Yongsheng; Chen, Chun-Chao; Hong, Ziruo; Gao, Jing; Yang, Yang Michael; Zhou, Huanping; Dou, Letian; Li, Gang; Yang, Yang
2013-11-28
A two-dimensional conjugated small molecule (SMPV1) was designed and synthesized for high performance solution-processed organic solar cells. This study explores the photovoltaic properties of this molecule as a donor, with a fullerene derivative as an acceptor, using solution processing in single junction and double junction tandem solar cells. The single junction solar cells based on SMPV1 exhibited a certified power conversion efficiency of 8.02% under AM 1.5 G irradiation (100 mW cm(-2)). A homo-tandem solar cell based on SMPV1 was constructed with a novel interlayer (or tunnel junction) consisting of bilayer conjugated polyelectrolyte, demonstrating an unprecedented PCE of 10.1%. These results strongly suggest solution-processed small molecular materials are excellent candidates for organic solar cells.
Efficient Solutions and Cost-Optimal Analysis for Existing School Buildings
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Paolo Maria Congedo
2016-10-01
Full Text Available The recast of the energy performance of buildings directive (EPBD describes a comparative methodological framework to promote energy efficiency and establish minimum energy performance requirements in buildings at the lowest costs. The aim of the cost-optimal methodology is to foster the achievement of nearly zero energy buildings (nZEBs, the new target for all new buildings by 2020, characterized by a high performance with a low energy requirement almost covered by renewable sources. The paper presents the results of the application of the cost-optimal methodology in two existing buildings located in the Mediterranean area. These buildings are a kindergarten and a nursery school that differ in construction period, materials and systems. Several combinations of measures have been applied to derive cost-effective efficient solutions for retrofitting. The cost-optimal level has been identified for each building and the best performing solutions have been selected considering both a financial and a macroeconomic analysis. The results illustrate the suitability of the methodology to assess cost-optimality and energy efficiency in school building refurbishment. The research shows the variants providing the most cost-effective balance between costs and energy saving. The cost-optimal solution reduces primary energy consumption by 85% and gas emissions by 82%–83% in each reference building.
A numerical solution for the entrance region of non-newtonian flow in annuli
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Maia M.C.A.
2003-01-01
Full Text Available Continuity and momentum equations applied to the entrance region of an axial, incompressible, isothermal, laminar and steady flow of a power-law fluid in a concentric annulus, were solved by a finite difference implicit method. The Newtonian case was solved used for validation of the method and then compared to reported results. For the non-Newtonian case a pseudoplastic power-law model was assumed and the equations were transformed to obtain a pseudo-Newtonian system which enabled its solution using the same technique as that used for the Newtonian case. Comparison of the results for entrance length and pressure drop with those available in the literature showed a qualitative similarity, but significant quantitative differences. This can be attributed to the differences in entrance geometries and the definition of asymptotic entrance length.
DEFF Research Database (Denmark)
Kaiser, Franz-Joachim; Bassler, Niels; Tölli, Heikki
2012-01-01
. In this study the effect of the underlying dose distribution on columnar recombination, a quantitative model for initial recombination,is investigated. Material and Methods Jaffe’s theory, formulated in 1913 quantifies initial recombination by elemental processes, providing an analytical (closed) solution. Here...... in the assessment of the saturation current or charge is suggested by the data. Conclusion The established model of columnar recombination reproduces the experimental data well, whereas the extentions using track structure models do not show such an agreement. Additionally, the effect of initial recombination...... on the saturation curve (i.e. Jaffe plot) does not follow a linear behavior as suggested by current dosimetry protocols, therefore higher order corrections (such as the investigated ones) might be necessary....
Light scattering and absorption by space weathered planetary bodies: Novel numerical solution
Markkanen, Johannes; Väisänen, Timo; Penttilä, Antti; Muinonen, Karri
2017-10-01
Airless planetary bodies are exposed to space weathering, i.e., energetic electromagnetic and particle radiation, implantation and sputtering from solar wind particles, and micrometeorite bombardment.Space weathering is known to alter the physical and chemical composition of the surface of an airless body (C. Pieters et al., J. Geophys. Res. Planets, 121, 2016). From the light scattering perspective, one of the key effects is the production of nanophase iron (npFe0) near the exposed surfaces (B. Hapke, J. Geophys. Res., 106, E5, 2001). At visible and ultraviolet wavelengths these particles have a strong electromagnetic response which has a major impact on scattering and absorption features. Thus, to interpret the spectroscopic observations of space-weathered asteroids, the model should treat the contributions of the npFe0 particles rigorously.Our numerical approach is based on the hierarchical geometric optics (GO) and radiative transfer (RT). The modelled asteroid is assumed to consist of densely packed silicate grains with npFe0 inclusions. We employ our recently developed RT method for dense random media (K. Muinonen, et al., Radio Science, submitted, 2017) to compute the contributions of the npFe0 particles embedded in silicate grains. The dense media RT method requires computing interactions of the npFe0 particles in the volume element for which we use the exact fast superposition T-matrix method (J. Markkanen, and A.J. Yuffa, JQSRT 189, 2017). Reflections and refractions on the grain surface and propagation in the grain are addressed by the GO. Finally, the standard RT is applied to compute scattering by the entire asteroid.Our numerical method allows for a quantitative interpretation of the spectroscopic observations of space-weathered asteroids. In addition, it may be an important step towards more rigorous a thermophysical model of asteroids when coupled with the radiative and conductive heat transfer techniques.Acknowledgments. Research supported by
Numerical solution of the asymmetric water impact of a wedge in three degrees of freedom
Ghazizade-Ahsaee, H.; Nikseresht, A. H.
2013-06-01
Impact problems associated with water entry have important applications in various aspects of naval architecture and ocean engineering. Estimation of hydrodynamic impact forces especially during the first instances after the impact is very important and is of interest. Since the estimation of hydrodynamic impact load plays an important role in safe design and also in evaluation of structural weight and costs, it is better to use a reliable and accurate prediction method instead of a simple estimation resulted by analyzing methods. In landing of flying boats, some phenomena such as weather conditions and strong winds can cause asymmetric instead of symmetric descent. In this paper, a numerical simulation of the asymmetric impact of a wedge, as the step of a flying boat, considering dynamic equations in two-phase flow is taken into account. The dynamic motion of the wedge in two-phase flow is solved based on finite volume method with volume of fluid (VOF) scheme considering dynamic equations. Then the effects of different angles of impact and water depth on the velocity change and slamming forces in an asymmetric impact are investigated. The comparison between the simulation results and experimental data verifies the accuracy of the method applied in the present study.
Ab initio theory of superconductivity in a magnetic field. II. Numerical solution
Linscheid, A.; Sanna, A.; Gross, E. K. U.
2015-07-01
We numerically investigate the spin density functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding Paper I [A. Linscheid et al., Phys. Rev. B 92, 024505 (2015), 10.1103/PhysRevB.92.024505]. As a test system, we employ a free-electron gas featuring an exchange splitting, a phononic pairing field, and a Coulomb repulsion. SpinSCDFT results are compared with Sarma, the Bardeen-Cooper-Schrieffer theory, and with an Eliashberg type of approach. We find that the spectrum of the superconducting Kohn-Sham SpinSCDFT system is not in agreement with the true quasiparticle structure. Therefore, starting from the Dyson equation, we derive a scheme that allows to compute the many-body excitations of the superconductor and represents the extension to superconductivity of the G0W0 method in band-structure theory. This superconducting G0W0 method vastly improves the predicted spectra.
Numerical solution of multiband k.p model for tunnelling in type-II heterostructures
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A.E. Botha
2010-01-01
Full Text Available A new and very general method was developed for calculating the charge and spin-resolved electron tunnelling in type-II heterojunctions. Starting from a multiband k.p description of the bulk energy-band structure, a multiband k.p Riccati equation was derived. The reflection and transmission coefficients were obtained for each channel by integrating the Riccati equation over the entire heterostructure. Numerical instability was reduced through this method, in which the multichannel log-derivative of the envelope function matrix, rather than the envelope function itself, was propagated. As an example, a six-band k.p Hamiltonian was used to calculate the current-voltage characteristics of a 10-nm wide InAs/ GaSb/InAs single quantum well device which exhibited negative differential resistance at room temperature. The calculated current as a function of applied (bias voltage was found to be in semiquantitative agreement with the experiment, a result which indicated that inelastic transport mechanisms do not contribute significantly to the valley currents measured in this particular device.
Numerical Solution and it's Analysis during Solar Drying of Green Peas
Godireddy, Arunsandeep; Lingayat, Abhay; Naik, Razat Kumar; Chandramohan, V. P.; Raju, V. Rajesh Kanan
2017-08-01
A mathematical model is developed for solar drying of green peas (Botanical name: Pisum Sativum). The problem is solved assuming the shape of the green peas is spherical. The governing transient mass transfer equation is discretized into finite difference scheme. The time marching is performed by implicit scheme. The governing equations and boundary conditions are non-dimensionalized to get generic results. The product in the chamber is in contact with air which is heated by solar energy, so the boundary conditions of third kind (convective boundary conditions) are considered. By space and time discretization a set of algebraic equations are generated and these algebraic equations are solved by tridiagonal matrix algorithm. A computer code is developed in MATLAB in order to compute the transient moisture content distribution inside the product. Center point, boundary and mean moisture of green peas are estimated at different temperatures and drying time. Present numerical result is compared with experimental result from literature and it was found that there is a good agreement of results. The drying time is predicted for how quickly the mean moisture of green peas is reached to 50, 40, 30, 20 and 10% of its initial moisture corresponding to different temperatures.
León, Ileana R.; Schwämmle, Veit; Jensen, Ole N.; Sprenger, Richard R.
2013-01-01
The majority of mass spectrometry-based protein quantification studies uses peptide-centric analytical methods and thus strongly relies on efficient and unbiased protein digestion protocols for sample preparation. We present a novel objective approach to assess protein digestion efficiency using a combination of qualitative and quantitative liquid chromatography-tandem MS methods and statistical data analysis. In contrast to previous studies we employed both standard qualitative as well as data-independent quantitative workflows to systematically assess trypsin digestion efficiency and bias using mitochondrial protein fractions. We evaluated nine trypsin-based digestion protocols, based on standard in-solution or on spin filter-aided digestion, including new optimized protocols. We investigated various reagents for protein solubilization and denaturation (dodecyl sulfate, deoxycholate, urea), several trypsin digestion conditions (buffer, RapiGest, deoxycholate, urea), and two methods for removal of detergents before analysis of peptides (acid precipitation or phase separation with ethyl acetate). Our data-independent quantitative liquid chromatography-tandem MS workflow quantified over 3700 distinct peptides with 96% completeness between all protocols and replicates, with an average 40% protein sequence coverage and an average of 11 peptides identified per protein. Systematic quantitative and statistical analysis of physicochemical parameters demonstrated that deoxycholate-assisted in-solution digestion combined with phase transfer allows for efficient, unbiased generation and recovery of peptides from all protein classes, including membrane proteins. This deoxycholate-assisted protocol was also optimal for spin filter-aided digestions as compared with existing methods. PMID:23792921
Block-pulse functions approach to numerical solution of Abel’s integral equation
Directory of Open Access Journals (Sweden)
Monireh Nosrati Sahlan
2015-12-01
Full Text Available This study aims to present a computational method for solving Abel’s integral equation of the second kind. The introduced method is based on the use of Block-pulse functions (BPFs via collocation method. Abel’s integral equations as singular Volterra integral equations are hard and heavy in computation, but because of the properties of BPFs, as is reported in examples, this method is more efficient and more accurate than some other methods for solving this class of integral equations. On the other hand, the benefit of this method is low cost of computing operations. The applied method transforms the singular integral equation into triangular linear algebraic system that can be solved easily. An error analysis is worked out and applications are demonstrated through illustrative examples.
Feng, S; Ng, C W W; Leung, A K; Liu, H W
2017-10-01
Microbial aerobic methane oxidation in unsaturated landfill cover involves coupled water, gas and heat reactive transfer. The coupled process is complex and its influence on methane oxidation efficiency is not clear, especially in steep covers where spatial variations of water, gas and heat are significant. In this study, two-dimensional finite element numerical simulations were carried out to evaluate the performance of unsaturated sloping cover. The numerical model was calibrated using a set of flume model test data, and was then subsequently used for parametric study. A new method that considers transient changes of methane concentration during the estimation of the methane oxidation efficiency was proposed and compared against existing methods. It was found that a steeper cover had a lower oxidation efficiency due to enhanced downslope water flow, during which desaturation of soil promoted gas transport and hence landfill gas emission. This effect was magnified as the cover angle and landfill gas generation rate at the bottom of the cover increased. Assuming the steady-state methane concentration in a cover would result in a non-conservative overestimation of oxidation efficiency, especially when a steep cover was subjected to rainfall infiltration. By considering the transient methane concentration, the newly-modified method can give a more accurate oxidation efficiency. Copyright © 2017. Published by Elsevier Ltd.
DEFF Research Database (Denmark)
Leon, Ileana R; Schwämmle, Veit; Jensen, Ole N
2013-01-01
The majority of mass spectrometry-based protein quantification studies uses peptide-centric analytical methods and thus strongly relies on efficient and unbiased protein digestion protocols for sample preparation. We present a novel objective approach to assess protein digestion efficiency using...... a combination of qualitative and quantitative LC-MS/MS methods and statistical data analysis. In contrast to previous studies we employed both standard qualitative as well as data-independent quantitative workflows to systematically assess trypsin digestion efficiency and bias using mitochondrial protein...... protocols and replicates, with an average 40% protein sequence coverage and an average of 11 peptides identified per protein. Systematic quantitative and statistical analysis of physicochemical parameters demonstrated that deoxycholate-assisted in-solution digestion combined with phase transfer allows...
Using the Efficient Frontier to Obtain the Best Solution for the Storage Location Assignment Problem
Directory of Open Access Journals (Sweden)
Marcele Elisa Fontana
2014-01-01
Full Text Available The main variables that influence the efficiency of a warehouse are the use of space and the order picking distance. In the literature, there are proposals to add the costs with space and order picking in order to evaluate each alternative for storage location assignment. However, there were problems with the adoption of this methodology, including difficulties in determining the costs and tradeoffs between them. These difficulties can result in solutions that are suboptimal. Based on these facts, this paper proposes a class-based storage process and storage location assignment by a cube-per-order index (COI that analyzes the space required and the total order picking distance by Pareto-optimal calculations. The efficient frontier possibilities allow the reduction of the set of alternatives, and the DM can analyze only the alternatives on efficient frontier.
Directory of Open Access Journals (Sweden)
Turp Sinan Mehmet
2017-12-01
Full Text Available This study investigates the estimated adsorption efficiency of artificial Nickel (II ions with perlite in an aqueous solution using artificial neural networks, based on 140 experimental data sets. Prediction using artificial neural networks is performed by enhancing the adsorption efficiency with the use of Nickel (II ions, with the initial concentrations ranging from 0.1 mg/L to 10 mg/L, the adsorbent dosage ranging from 0.1 mg to 2 mg, and the varying time of effect ranging from 5 to 30 mins. This study presents an artificial neural network that predicts the adsorption efficiency of Nickel (II ions with perlite. The best algorithm is determined as a quasi-Newton back-propagation algorithm. The performance of the artificial neural network is determined by coefficient determination (R2, and its architecture is 3-12-1. The prediction shows that there is an outstanding relationship between the experimental data and the predicted values.
Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko
2017-09-01
Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.
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Basuki Widodo
2012-02-01
Full Text Available Corrosion process is a natural case that happened at the various metals, where the corrosion process in electrochemical can be explained by using galvanic cell. The iron corrosion process is based on the acidity degree (pH of a condensation, iron concentration and condensation temperature of electrolyte. Those are applied at electrochemistry cell. The iron corrosion process at this electrochemical cell also able to generate electrical potential and electric current during the process takes place. This paper considers how to build a mathematical model of iron corrosion, electrical potential and electric current. The mathematical model further is solved using the finite element method. This iron corrosion model is built based on the iron concentration, condensation temperature, and iteration time applied. In the electric current density model, the current based on electric current that is happened at cathode and anode pole and the iteration time applied. Whereas on the potential electric model, it is based on the beginning of electric potential and the iteration time applied. The numerical results show that the part of iron metal, that is gristle caused by corrosion, is the part of metal that has function as anode and it has some influences, such as time depth difference, iron concentration and condensation temperature on the iron corrosion process and the sum of reduced mass during corrosion process. Moreover, difference influence of time and beginning electric potential has an effect on the electric potential, which emerges during corrosion process at the electrochemical cell. Whereas, at the electrical current is also influenced by difference of depth time and condensation temperature applied.Keywords: Iron Corrosion, Concentration of iron, Electrochemical Cell and Finite Element Method
An Experimenting Field Approach for the Numerical Solution of Multiphase Flow in Porous Media.
Salama, Amgad; Sun, Shuyu; Bao, Kai
2016-03-01
In this work, we apply the experimenting pressure field technique to the problem of the flow of two or more immiscible phases in porous media. In this technique, a set of predefined pressure fields are introduced to the governing partial differential equations. This implies that the velocity vector field and the divergence at each cell of the solution mesh can be determined. However, since none of these fields is the true pressure field entailed by the boundary conditions and/or the source terms, the divergence at each cell will not be the correct one. Rather the residue which is the difference between the true divergence and the calculated one is obtained. These fields are designed such that these residuals are used to construct the matrix of coefficients of the pressure equation and the right-hand side. The experimenting pressure fields are generated in the solver routine and are fed to the different routines, which may be called physics routines, which return to the solver the elements of the matrix of coefficients. Therefore, this methodology separates the solver routines from the physics routines and therefore results in simpler, easy to construct, maintain, and update algorithms. © 2015, National Ground Water Association.
Some strange numerical solutions of the non-stationary Navier-Stokes equations in pipes
Energy Technology Data Exchange (ETDEWEB)
Rummler, B.
2001-07-01
A general class of boundary-pressure-driven flows of incompressible Newtonian fluids in three-dimensional pipes with known steady laminar realizations is investigated. Considering the laminar velocity as a 3D-vector-function of the cross-section-circle arguments, we fix the scale for the velocity by the L{sub 2}-norm of the laminar velocity. The usual new variables are introduced to get dimension-free Navier-Stokes equations. The characteristic physical and geometrical quantities are subsumed in the energetic Reynolds number Re and a parameter {psi}, which involves the energetic ratio and the directions of the boundary-driven part and the pressure-driven part of the laminar flow. The solution of non-stationary dimension-free Navier-Stokes equations is sought in the form u=u{sub L}+u, where u{sub L} is the scaled laminar velocity and periodical conditions in center-line-direction are prescribed for u. An autonomous system (S) of ordinary differential equations for the time-dependent coefficients of the spatial Stokes eigenfunction is got by application of the Galerkin-method to the dimension-free Navier-Stokes equations for u. The finite-dimensional approximations u{sub N({lambda}}{sub )} of u are defined in the usual way. (orig.)
Efficient algorithms for finding optimal binary features in numeric and nominal labeled data
Mampaey, Michael; Nijssen, Siegfried; Feelders, Adrianus; Konijn, Rob; Knobbe, Arno
2013-01-01
An important subproblem in supervised tasks such as decision tree induction and subgroup discovery is finding an interesting binary feature (such as a node split or a subgroup refinement) based on a numeric or nominal attribute, with respect to some discrete or continuous target variable. Often one
Miyabe, Kanji; Guiochon, Georges
2011-01-01
It is probably impossible to prepare high-performance liquid chromatography (HPLC) columns that have a completely homogeneous packing structure. Many reports in the literature show that the radial distributions of the mobile phase flow velocity and the local column efficiency are not flat, even in columns considered as good. A degree of radial heterogeneity seems to be a common property of all HPLC columns and an important source of peak tailing, which prevents the derivation of accurate information on chromatographic behavior from a straightforward analysis of elution peak profiles. This work reports on a numerical method developed to derive from recorded peak profiles the column efficiency at the column center, the degree of column radial heterogeneity, and the polynomial function that best represents the radial distributions of the flow velocity and the column efficiency. This numerical method was applied to two concrete examples of tailing peak profiles previously described. It was demonstrated that this numerical method is effective to estimate important parameters characterizing the radial heterogeneity of chromatographic columns.
Efficiency enhancement in solution processed organic and organic-inorganic perovskite solar cells
Xiao, Zhengguo
Solution processed thin film photovoltaic devices are one of the most promising renewable energy sources. Organic solar cells have been intensively studied due to their advantages of light-weight, flexibility and low-cost materials and manufacturing. The organic-inorganic hybrid perovskite materials have recently shown great potential application in solar cells. The PCE increased dramatically from 3.8% in 2009 to a certified efficiency of 20.1% in 2014. In this dissertation, we focus on the efficiency enhancement for solution processed organic and organic-inorganic solar cells. In Chapter 2, I demonstrated that the crystallinity of the ferroelectric polymer P(VDF-TrFE) at the organic active layer/ electrode interface plays a critical role in the efficiency enhancement of organic solar cells. Then, The ferroelectric P(VDF-TrFE) nanocrystals was synthesized and successfully applied in the low band gap polymers. A high efficiency of 6.8% was achieved in the PCDTBT:PCBM system. Another small polar molecule, TPACA, was also applied to increase the efficiency of organic solar cells. In Chapter 3, I developed a universal approach of solvent fluxing to fabricate graded bulk heterojunction (BHJ) polymer:fullerene films to increase the device efficiency. The solvent fluxing process can extract part of the fullerene inside the BHJ film to the top surface to form graded BHJ. The PCE of the devices after solvent fluxing is increased by 15%--50% compared with the control devices without solvent fluxing. In Chapter 5, a two-step spin coating approach was developed to fabricate the continuous and compact organolead trihalide perovskite (OTP) films. The average PCE of methylammonium lead iodide (MAPbI3) perovskite devices reached 14.5% and 85% of the devices had efficiency above 14%. In Chapter 6, I discovered that the solvent annealing can be used to increase the grain size and crystallinity of the perovskite films. The highest device efficiency reached 15.6%, and device
An optimized efficient dual junction InGaN/CIGS solar cell: A numerical simulation
Farhadi, Bita; Naseri, Mosayeb
2016-08-01
The photovoltaic performance of an efficient double junction InGaN/CIGS solar cell including a CdS antireflector top cover layer is studied using Silvaco ATLAS software. In this study, to gain a desired structure, the different design parameters, including the CIGS various band gaps, the doping concentration and the thickness of CdS layer are optimized. The simulation indicates that under current matching condition, an optimum efficiency of 40.42% is achieved.
Naganthran, Kohilavani; Nazar, Roslinda
2017-08-01
In this study, the influence of the first order chemical reaction towards the magnetohydrodynamics (MHD) stagnation-point boundary layer flow past a permeable stretching/shrinking surface (sheet) is considered numerically. The governing boundary layer equations are transformed into a system of ordinary differential equations from the system of partial differential equations by using a proper similarity transformation so that it can be solved numerically by the "bvp4c" function in Matlab software. The main numerical solutions are presented graphically and discussed in the relevance of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is done to determine which solution is stable and valid physically. The results of the stability analysis show that the first solution (upper branch) is physically stable and realizable while the second solution (lower branch) is impracticable.
Numerical solution of the start-up of well drilling fluid flows
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Gabriel Merhy de; Negrao, Cezar Otaviano Ribeiro; Franco, Admilson Teixeira [UTFPR - Federal University of Technology - Parana - Curitiba, PR (Brazil)], e-mails: gabrielm@utfpr.edu.br, negrao@utfpr.edu.br, admilson@utfpr.edu.br; Martins, Andre Leibsohn; Gandelman, Roni Abensur [TEP/CENPES - PETROBRAS S/A, Rio de Janeiro, RJ (Brazil)], e-mails: aleibsohn@petrobras.com.br, roniag@petrobras.com.br
2010-07-01
The drilling fluid is designed to build up a gel-like structure, when at rest, in order to avoid cuttings to drop at the bore bottom and therefore to prevent the bit obstruction. As consequence, high pressures, which can be larger than the formation pressure and can damage the well, are needed to break up the gel when circulation resumes. Due to its thixotropic effect, the gel viscosity remains high for a while after the circulation restarts. The gelation may have significant importance, specially, in deep waters where high pressures and low temperatures take place. The current work presents a compressible transient flow model of the start-up flow of drilling fluids, in order to predict borehole pressures. The model comprises one-dimensional conservation equations of mass and momentum and one state equation for the calculation of the fluid density as a function of the pressure. The considered geometry is a concentric annular pipe of length L. Its internal diameter is D1 and external one, D2. For a circular pipe, the internal diameter is made equal to zero. The main difference from previous model was the type of boundary condition: Constant flow rate at the pipe inlet rather than the constant pressure. Both Newtonian and non-Newtonian Bingham fluid flows are considered. The governing equations are discretized by the Finite Volume Method using the fully implicit formulation and the first-order upwind scheme. The resulting non-linear algebraic equations are iteratively solved. The model results were corroborated with an analytical solution for Newtonian flows. Case studies are conducted to evaluate the effect of fluid flow properties, well geometry and flow rate on borehole pressures. For Bingham fluid flow one can observe that large pressures (compared with Newtonian fluid flow) are observed when constant flow rate are input as boundary condition. Pressure peaks caused by the acoustic wave propagation can be more intense in low compressible fluid flow, low viscosity
FAST LABEL: Easy and efficient solution of joint multi-label and estimation problems
Sundaramoorthi, Ganesh
2014-06-01
We derive an easy-to-implement and efficient algorithm for solving multi-label image partitioning problems in the form of the problem addressed by Region Competition. These problems jointly determine a parameter for each of the regions in the partition. Given an estimate of the parameters, a fast approximate solution to the multi-label sub-problem is derived by a global update that uses smoothing and thresholding. The method is empirically validated to be robust to fine details of the image that plague local solutions. Further, in comparison to global methods for the multi-label problem, the method is more efficient and it is easy for a non-specialist to implement. We give sample Matlab code for the multi-label Chan-Vese problem in this paper! Experimental comparison to the state-of-the-art in multi-label solutions to Region Competition shows that our method achieves equal or better accuracy, with the main advantage being speed and ease of implementation.
Energy Technology Data Exchange (ETDEWEB)
Talik, N.A.; Yeoh, K.H.; Ng, C.Y.B [Low Dimensional Research Center, Department of Physics, University Malaya, 50603 Kuala Lumpur (Malaysia); ItraMAS Corporation. Sdn. Bhd., 542A-B Mukim 1, Lorong Perusahaan Baru 2, Kawasan Perindustrian, Perai 13600, Penang (Malaysia); Yap, B.K. [Center of Microelectronic and Nanotechnology Engineering (CeMNE), College of Engineering, Universiti Tenaga Nasional, Jln. Uniten-Ikram, 4300 Kajang, Selangor (Malaysia); Woon, K.L., E-mail: ph7klw76@um.edu.my [Low Dimensional Research Center, Department of Physics, University Malaya, 50603 Kuala Lumpur (Malaysia)
2014-10-15
A novel solution processable charge generating layer (CGL) that consists of 1,4,5,8,9,11-hexaazatriphenylene hexacarbonitrile (HATCN{sub 6})/Poly(N-vinylcarbazole) (PVK): 1,1-bis-(4-bis(4-tolyl)-aminophenyl) cyclohexene (TAPC) for a tandem green phosphorescent organic light emitting diode (PHOLED) is demonstrated. The use of orthogonal solvent to dissolve HATCN{sub 6} and PVK:TAPC is the key to overcome the interface erosion problem for the solution processed CGL. The current efficiency of the 2 wt% TAPC mixed with PVK is the highest at 24.2 cd/A, which is more than three-folds higher than that of the single device at 1000 cd/m{sup 2}. - Highlights: • A solution processable tandem OLED is built using a novel charge generating layer. • HATCN{sub 6} and PVK:TAPC are shown to be effective charge generating layers. • The turn on voltages for tandem devices are almost similar to single unit. • 2 wt% TAPC blended with PVK exhibits three-folds increase in efficiency.
New efficient optimizing techniques for Kalman filters and numerical weather prediction models
Famelis, Ioannis; Galanis, George; Liakatas, Aristotelis
2016-06-01
The need for accurate local environmental predictions and simulations beyond the classical meteorological forecasts are increasing the last years due to the great number of applications that are directly or not affected: renewable energy resource assessment, natural hazards early warning systems, global warming and questions on the climate change can be listed among them. Within this framework the utilization of numerical weather and wave prediction systems in conjunction with advanced statistical techniques that support the elimination of the model bias and the reduction of the error variability may successfully address the above issues. In the present work, new optimization methods are studied and tested in selected areas of Greece where the use of renewable energy sources is of critical. The added value of the proposed work is due to the solid mathematical background adopted making use of Information Geometry and Statistical techniques, new versions of Kalman filters and state of the art numerical analysis tools.
Directory of Open Access Journals (Sweden)
Mohammad hasan Ehrampoosh
2017-05-01
Full Text Available Background: Humic acids (HAs have adverse effects on the environment; therefore, they should be removed from the water and wastewater. The aim of this study was to evaluate the efficiency of the electron beam irradiation for removal of humic acid from aqueous solutions. Methods: Humic acid was purchased from Sigma-Aldrich Company. After preparation of stock solution in alkaline condition, different concentrations of humic acid (10, 25 and 50 mg were prepared. Study has done at pH= 8 and in different dose rates of 1, 3, 6, 9 and 15 kGy. Then initial absorption of samples was measured at 254 nm using UV-Visible spectrophotometer before and after the irradiation. Excel and SPSS Ver. 18 were used for analyzing the data and drawing graphs. Results: The results of this study showed that by increasing adsorbed dose from 1 to 15 kGy, the efficiency of HA removal increased and by increasing humic acid concentration from 10 to 50 mg/L, the removal efficiency of humic acid decreased. The results of the kinetic study showed that irradiation of humic acid followed pseudo second-order reaction. Conclusion: It can be concluded that electron beam irradiation can be a useful technology for the treatment of environmental samples contaminated by humic acid.
Farinelli, R.; Ceccobello, C.; Romano, P.; Titarchuk, L.
2012-02-01
Context. Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative equation according to the expected physical conditions of the systems under study. Aims: We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods: We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system τ using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results: We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth τ produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions: The algorithm has been implemented in the xspec package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (≳ 1012 G). This latter case is expected to be typical of accreting systems such as X
Zeebe, Richard E.
2017-11-01
I report results from accurate numerical integrations of solar system orbits over the past 100 Myr with the integrator package HNBody. The simulations used different integrator algorithms, step sizes, and initial conditions, and included effects from general relativity, different models of the Moon, the Sun’s quadrupole moment, and up to 16 asteroids. I also probed the potential effect of a hypothetical Planet 9, using one set of possible orbital elements. The most expensive integration (Bulirsch-Stoer) required 4 months of wall-clock time with a maximum relative energy error ≲ 3× {10}-13. The difference in Earth’s eccentricity ({{Δ }}{e}{ E }) was used to track the difference between two solutions, considered to diverge at time τ when max | {{Δ }}{e}{ E }| irreversibly crossed ˜10% of mean {e}{ E } ({{˜ }}0.028× 0.1). The results indicate that finding a unique orbital solution is limited by initial conditions from current ephemerides and asteroid perturbations to ˜54 Myr. Bizarrely, the 4-month Bulirsch-Stoer integration and a symplectic integration that required only 5 hr of wall-clock time (12-day time step, with the Moon as a simple quadrupole perturbation), agree to ˜63 Myr. Internally, such symplectic integrations are remarkably consistent even for large time steps, suggesting that the relationship between time step and τ is not a robust indicator of the absolute accuracy of symplectic integrations. The effect of a hypothetical Planet 9 on {{Δ }}{e}{ E } becomes discernible at ˜65 Myr. Using τ as a criterion, the current state-of-the-art solutions all differ from previously published results beyond ˜50 Myr. I also conducted an eigenmode analysis, which provides some insight into the chaotic nature of the inner solar system. The current study provides new orbital solutions for applications in geological studies. .
Fairnelli, R.; Ceccobello, C.; Romano, P.; Titarchuk, L.
2011-01-01
Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative transfer equation according to the expected physical conditions of the systems under study. Aims. We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system pi using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth pi produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions. The algorithm has been implemented in the XPEC package for X-ray fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (approx > 10(exp 12) G). This latter case is expected to be of typical accreting systems such as X
Bao, Weizhu
2013-01-01
We propose a simple, efficient, and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with or without longrange dipole-dipole interaction (DDI). We begin with the three-dimensional (3D) Gross-Pitaevskii equation (GPE) with an angular momentum rotation term and/or long-range DDI, state the twodimensional (2D) GPE obtained from the 3D GPE via dimension reduction under anisotropic external potential, and review some dynamical laws related to the 2D and 3D GPEs. By introducing a rotating Lagrangian coordinate system, the original GPEs are reformulated to GPEs without the angular momentum rotation, which is replaced by a time-dependent potential in the new coordinate system. We then cast the conserved quantities and dynamical laws in the new rotating Lagrangian coordinates. Based on the new formulation of the GPE for rotating BECs in the rotating Lagrangian coordinates, a time-splitting spectral method is presented for computing the dynamics of rotating BECs. The new numerical method is explicit, simple to implement, unconditionally stable, and very efficient in computation. It is spectral-order accurate in space and second-order accurate in time and conserves the mass on the discrete level. We compare our method with some representative methods in the literature to demonstrate its efficiency and accuracy. In addition, the numerical method is applied to test the dynamical laws of rotating BECs such as the dynamics of condensate width, angular momentum expectation, and center of mass, and to investigate numerically the dynamics and interaction of quantized vortex lattices in rotating BECs without or with the long-range DDI.Copyright © by SIAM.
Development of a numerical simulation tool for efficient and robust prediction of ship resistance
Directory of Open Access Journals (Sweden)
Geon-Hong Kim
2017-09-01
Full Text Available In this paper, a two-phase flow solver HiFoam® has been developed based on the OpenFOAM® to predict resistance of a ship in calm water. The VOF method of OpenFOAM® was reviewed and a simple flux limiter was introduced to enhance the robustness of the solver. The procedure for predicting ship motion was modified by introducing Quasi-Steady Fluid-Body Interaction (QS-FBI with least square regression to improve the efficiency. Other minor factors were considered as well in terms of the efficiency and robustness. The HiFoam was applied to KCS and JBC simulations to validate its efficiency and accuracy by comparing the results to experimental data and STAR-CCM+. The HiFoam® was also applied to various ships and it showed good agreements to the experimental data.
Adsorption Efficiency of Iron Modified Carbons for Removal of Pb(II Ions from Aqueous Solution
Directory of Open Access Journals (Sweden)
Mohammad Hossein Salmani
2016-06-01
Full Text Available Abstract Introduction: The Lead causes severe damage to several systems of the body, especially to bony tissues. Until now, several low-cost biosorbents have been studied for removal of heavy metal ions from aqueous solutions. In the present study, carbonized pomegranate peels modified with Fe2+ and Fe3+ ions and then it was investigated for removal of Pb(II ions from aqueous solution. Materials and methods: the washed granola of pomegranate peel was separately socked with FeCl3 and FeCl2 solutions for 24 h. Then, the granules were carbonized at 400 ºC for 3 h in a programmable furnace in the atmosphere of nitrogen. The adsorption experiments were carried out for two types of iron-modified carbons by batch adsorption using one variable at a time procedures. Results: The optimum conditions were found as contact time 90 min, initial concentration 50 mg/l, and adsorbent dose, 1.00 g/100 ml solution. Maximum removal efficiency was calculated as 84% and 89% for Fe3+ and Fe2+ impregnated pomegranate peel carbons respectively. Conclusion: The iron treatment pomegranate peel carbons modified their surfaces for adsorption of heavy metals. The results showed that chemical modification of the low-cost adsorbents originating from agricultural waste has stood out for metal removal capabilities.
Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Cordua, Knud Skou; Mosegaard, Klaus
2012-01-01
Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample solutions to non-linear inverse problems. In principle, these methods allow incorporation of prior information of arbitrary complexity. If an analytical closed form description of the prior....... We propose an algorithm, called sequential Gibbs sampling, allowing the Metropolis algorithm to efficiently incorporate complex priors into the solution of an inverse problem, also for the case where no closed form description of the prior exists. First, we lay out the theoretical background...... for applying the sequential Gibbs sampler and illustrate how it works. Through two case studies, we demonstrate the application of the method to a linear image restoration problem and to a non-linear cross-borehole inversion problem. We demonstrate how prior information can reduce the complexity of an inverse...
Solution-processable graphene oxide as an efficient hole transport layer in polymer solar cells.
Li, Shao-Sian; Tu, Kun-Hua; Lin, Chih-Cheng; Chen, Chun-Wei; Chhowalla, Manish
2010-06-22
The utilization of graphene oxide (GO) thin films as the hole transport and electron blocking layer in organic photovoltaics (OPVs) is demonstrated. The incorporation of GO deposited from neutral solutions between the photoactive poly(3-hexylthiophene) (P3HT):phenyl-C61-butyric acid methyl ester (PCBM) layer and the transparent and conducting indium tin oxide (ITO) leads to a decrease in recombination of electrons and holes and leakage currents. This results in a dramatic increase in the OPV efficiencies to values that are comparable to devices fabricated with PEDOT:PSS as the hole transport layer. Our results indicate that GO could be a simple solution-processable alternative to PEDOT:PSS as the effective hole transport and electron blocking layer in OPV and light-emitting diode devices.
Numerical modelling of high efficiency InAs/GaAs intermediate band solar cell
Imran, Ali; Jiang, Jianliang; Eric, Debora; Yousaf, Muhammad
2018-01-01
Quantum Dots (QDs) intermediate band solar cells (IBSC) are the most attractive candidates for the next generation of photovoltaic applications. In this paper, theoretical model of InAs/GaAs device has been proposed, where we have calculated the effect of variation in the thickness of intrinsic and IB layer on the efficiency of the solar cell using detailed balance theory. IB energies has been optimized for different IB layers thickness. Maximum efficiency 46.6% is calculated for IB material under maximum optical concentration.
Directory of Open Access Journals (Sweden)
Wael M. Mohamed
2015-12-01
Full Text Available A numerical solution is presented for a one-dimensional, nonlinear boundary-value problem of thermoelasticity with variable volume force and heat supply in a slab. One surface of the body is subjected to a given periodic displacement and Robin thermal condition, while the other is kept fixed and at zero temperature. Other conditions may be equally treated as well. The volume force and bulk heating simulate the effect of a beam of hot particles infiltrating the medium. The present study is a continuation of previous work by the same authors for the half-space [1]. The presented Figures display the process of propagation and reflection of the coupled nonlinear thermoelastic waves in the slab. They also show the effects of volume force and heat supply on the distributions of the mechanical displacements and temperature inside the medium. The propagation of beats provides evidence for sufficiently large time values.
Sun, Shuyu
2012-06-02
A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.
Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.
1983-01-01
In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.
Zhidkov, E P; Solovieva, T M
2001-01-01
The spectral problems with the eigenvalue-depending operator usually appear when the relative variants of the Schroedinger equation are considered in the impulse space. The eigenvalues and eigenfunctions calculation error caused by the numerical solving of such equations is the sum of the error entering the approximation of a continuous equation by the discrete equations systems with the help of the Bubnov-Galerkine method and the iterative method one. It is shown that the iterative method error is one-two order smaller than the problem of the discretisation one. Hence, the eigenvalues and eigenfunctions calculation accuracy of the spectral problem with the eigenvalue-depending operator is not worse than the linear spectral problem solution accuracy.
Salama, Amgad
2012-06-17
The flow of two immiscible fluids in porous media is ubiquitous particularly in petroleum exploration and extraction. The displacement of one fluid by another immiscible with it represents a very important aspect in what is called enhanced oil recovery. Another example is related to the long-term sequestration of carbon dioxide, CO2 , in deep geologic formations. In this technique, supercritical CO2 is introduced into deep saline aquifer where it displaces the hosting fluid. Furthermore, very important classes of contaminants that are very slightly soluble in water and represent a huge concern if they get introduced to groundwater could basically be assumed immiscible. These are called light non-aqueous phase liquids (LNAPL) and dense non-aqueous phase liquids (DNAPL). All these applications necessitate that efficient algorithms be developed for the numerical solution of these problems. In this work we introduce the use of shifting matrices to numerically solving the problem of two-phase immiscible flows in the subsurface. We implement the cell-center finite difference method which discretizes the governing set of partial differential equations in conservative manner. Unlike traditional solution methodologies, which are based on performing the discretization on a generic cell and solve for all the cells within a loop, in this technique, the cell center information for all the cells are obtained all at once without loops using matrix oriented operations. This technique is significantly faster than the traditional looping algorithms, particularly for larger systems when coding using languages that require repeating interpretation each time a loop is called like Mat Lab, Python and the like. We apply this technique to the transport of LNAPL and DNAPL into a rectangular domain.
Pedretti, Daniele; Masetti, Marco; Beretta, Giovanni Pietro
2017-10-01
The expected long-term efficiency of vertical cutoff walls coupled to pump-and-treat technologies to contain solute plumes in highly heterogeneous aquifers was analyzed. A well-characterized case study in Italy, with a hydrogeological database of 471 results from hydraulic tests performed on the aquifer and the surrounding 2-km-long cement-bentonite (CB) walls, was used to build a conceptual model and assess a representative remediation site adopting coupled technologies. In the studied area, the aquifer hydraulic conductivity Ka [m/d] is log-normally distributed with mean E (Ya) = 0.32 , variance σYa2 = 6.36 (Ya = lnKa) and spatial correlation well described by an exponential isotropic variogram with integral scale less than 1/12 the domain size. The hardened CB wall's hydraulic conductivity, Kw [m/d], displayed strong scaling effects and a lognormal distribution with mean E (Yw) = - 3.43 and σYw2 = 0.53 (Yw =log10Kw). No spatial correlation of Kw was detected. Using this information, conservative transport was simulated across a CB wall in spatially correlated 1-D random Ya fields within a numerical Monte Carlo framework. Multiple scenarios representing different Kw values were tested. A continuous solute source with known concentration and deterministic drains' discharge rates were assumed. The efficiency of the confining system was measured by the probability of exceedance of concentration over a threshold (C∗) at a control section 10 years after the initial solute release. It was found that the stronger the aquifer heterogeneity, the higher the expected efficiency of the confinement system and the lower the likelihood of aquifer pollution. This behavior can be explained because, for the analyzed aquifer conditions, a lower Ka generates more pronounced drawdown in the water table in the proximity of the drain and consequently a higher advective flux towards the confined area, which counteracts diffusive fluxes across the walls. Thus, a higher σYa2 results
Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.
2018-01-01
The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.
Bechtold, T.; Hohlfeld, D.; Rudnyi, E.B.; Günther, M.
2010-01-01
In this paper we present a novel highly efficient approach to determine material properties from measurement results. We apply our method to thermal properties of thin-film multilayers with three different materials, amorphous silicon, silicon nitride and silicon oxide. The individual material
Efficient Hybrid-Spectral Model for Fully Nonlinear Numerical Wave Tank
DEFF Research Database (Denmark)
Christiansen, Torben; Bingham, Harry B.; Engsig-Karup, Allan Peter
2013-01-01
method in the vertical for the discretization of the Laplace equation in the fluid domain, which yields a sparse and spectrally accurate Dirichletto-Neumann operator. The Laplace problem is solved with an efficient Defect Correction method preconditioned with a spectral discretization of the linearised...
Energy Technology Data Exchange (ETDEWEB)
Balducelli, C.; Vicoli, G.
1992-12-31
This paper describes the application of computerized operator support systems in a primary aluminium production plant in the phases of operative training and on-line supervisory and diagnosis. The phases in which there is a great demand for this types of system are initially pointed out by describing all the possible benefits. After a brief description of numerical modeling approaches useful in the development of training simulators, attention is devoted to the symbolic modeling methodologies designed to emulate operator cognitive behaviour aimed at early fault detection in electrolitic cell operation.
Solutions for Energy Efficient and Sustainable Heating of Ventilation Air: A Review
Directory of Open Access Journals (Sweden)
A. Žandeckis
2015-10-01
Full Text Available A high energy efficiency and sustainability standards defined by modern society and legislation requires solutions in the form of complex integrated systems. The scope of this work is to provide a review on technologies and methods for the heating of ventilation air as a key aspect for high energy and environmental performance of buildings located in a cold climate. The results of this work are more relevant in the buildings where space heating consumes a significant part of the energy balance of a building, and air exchange is arranged in an organized manner. A proper design and control strategy, heat recovery, the use of renewable energy sources, and waste heat are the main aspects which must be considered for efficient and sustainable ventilation. This work focuses on these aspects. Air conditioning is not in the scope of this study.
Kou, Jisheng
2015-08-01
Surface tension significantly impacts subsurface flow and transport, and it is the main cause of capillary effect, a major immiscible two-phase flow mechanism for systems with a strong wettability preference. In this paper, we consider the numerical simulation of the surface tension of multi-component mixtures with the gradient theory of fluid interfaces. Major numerical challenges include that the system of the Euler-Lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite. We construct a linear transformation to reduce the Euler-Lagrange equations, and naturally introduce a path function, which is proven to be a monotonic function of the spatial coordinate variable. By using the linear transformation and the path function, we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions. Moreover, the computation of the surface tension is also simplified. The proposed methods do not need to solve the differential equation system, and they are easy to be implemented in practical applications. Numerical examples are tested to verify the efficiency of the proposed methods. © 2014 Elsevier B.V.
Analytical And Numerical Approaches For Diffraction Efficiency In Low-curvature Curved Crystals
Bellucci, V.; Camattari, R.; Guidi, V.; Neri, I.
2011-09-01
Crystals with curved diffraction planes (CDPC) are an emerging technology in X-ray optics. CDPC allow manipulating the trajectories of high-energy photons with efficiency near the unity in a broad energy range. An elective application of CDPC is the construction of hard X-ray lenses. Up to now, the impossibility to focalize hard X-rays left the observation of the sky in this energy range to direct-view instruments, featuring low sensitivity and resolution. In fact, only the spectra of few and strongest sources is known above 70 keV. Mosaic crystals have already been implemented for the construction of focusing optics, but they show low reproducibility in the fabrication, and diffraction efficiency is physically limited to 50% at most. The theory of diffraction in curved crystals was developed in the past half century in the frame of the dynamical theory of diffraction, with particular contribution by C. Malgrange If the curvature is quite strong, is possible to find a simple expression to quantitatively determine the fraction of diffracted photons. To date, it exists no analytical theory that quantitatively calculates the diffraction efficiency for crystals of low curvature. Indeed, the applications of CDPC sometimes requires a curvature radius in this range. For this reason, we developed a model, which is able to produce realistic previsions of the diffraction efficiency of a thick crystal in Laue geometry for any curvature radius. The model agrees with the results of the dynamical theory when this latter is applicable. It also leads to the same results of the flat crystal case when the curvature radius is very large, and gives a realistic and quantitative description of diffraction efficiency when these two cases are not applicable.
Radhakrishnan, Krishnan
1994-01-01
LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 1 of a series of three reference publications that describe LENS, provide a detailed guide to its usage, and present many example problems. Part 1 derives the governing equations and describes the numerical solution procedures for the types of problems that can be solved. The accuracy and efficiency of LSENS are examined by means of various test problems, and comparisons with other methods and codes are presented. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.
Directory of Open Access Journals (Sweden)
MH Ehrampoush
2014-05-01
Methods:This experimental study was performed in laboratory scale and was performed on 243 synthetic samples in a batch system. In this study the effect of parameters such as contact time (5,15,30,60,120,min and 24 h, pH (5,7,9, fluoride concentration (100, 250, 500, 750,1000 µg/l and absorbent dosages (0.5,1,2/5,5g/l was evaluated. Finally biosorption kinetic and equilibrium isotherms of adsorbent was investigated. Results: The removal efficiency of inactive Saccharomyces cerevisiae was 89.49% at pH 5, adsorbent dose of 1g/L and initial metal concentration of 100 mg/L. Maximum uptake was observed after the Contact time of 60 minutes. In addition absorption isotherm followed pseudo-second order model with a maximum R2 = 0.999. Conclusion:The results of study showed that biosorption efficiency decreases with increase in pH of solution. Optimum pH of biosorption was 5. The Removal efficiency of arsenic enhanced with increase in mass of Saccharomyces cerevisiae up to 1 g/L, but The Removal efficiency decreased with increase in initial concentration of arsenic. Maximum absorption was observed in 15 minutes.
Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case
Energy Technology Data Exchange (ETDEWEB)
Fernández-Nieto, Enrique D., E-mail: edofer@us.es [Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura, Avda, Reina Mercedes, s/n, 41012 Sevilla (Spain); Gallardo, José M., E-mail: jmgallardo@uma.es [Departamento de Análisis Matemático, Universidad de Málaga, F. Ciencias, Campus Teatinos S/N (Spain); Vigneaux, Paul, E-mail: Paul.Vigneaux@math.cnrs.fr [Unitée de Mathématiques Pures et Appliquées, Ecole Normale Supérieure de Lyon, 46 allée d' Italie, 69364 Lyon Cedex 07 (France)
2014-05-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.
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.
Pouran, Behdad; Arbabi, Vahid; Weinans, Harrie; Zadpoor, Amir A
2016-11-01
Transport of solutes helps to regulate normal physiology and proper function of cartilage in diarthrodial joints. Multiple studies have shown the effects of characteristic parameters such as concentration of proteoglycans and collagens and the orientation of collagen fibrils on the diffusion process. However, not much quantitative information and accurate models are available to help understand how the characteristics of the fluid surrounding articular cartilage influence the diffusion process. In this study, we used a combination of micro-computed tomography experiments and biphasic-solute finite element models to study the effects of three parameters of the overlying bath on the diffusion of neutral solutes across cartilage zones. Those parameters include bath size, degree of stirring of the bath, and the size and concentration of the stagnant layer that forms at the interface of cartilage and bath. Parametric studies determined the minimum of the finite bath size for which the diffusion behavior reduces to that of an infinite bath. Stirring of the bath proved to remarkably influence neutral solute transport across cartilage zones. The well-stirred condition was achieved only when the ratio of the diffusivity of bath to that of cartilage was greater than ≈1000. While the thickness of the stagnant layer at the cartilage-bath interface did not significantly influence the diffusion behavior, increase in its concentration substantially elevated solute concentration in cartilage. Sufficient stirring attenuated the effects of the stagnant layer. Our findings could be used for efficient design of experimental protocols aimed at understanding the transport of molecules across articular cartilage. Copyright © 2016 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Bassi, F. [Universita degli Studi di Ancona (Italy); Rebay, S. [Universita degli Studi di Brescia (Italy)
1997-03-01
This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. We extend a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier-Stokes equations by treating the viscous terms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. As a consequence the method is ideally suited to compute high-order accurate solution of the Navier-Stokes equations on unstructured grids. The performance of the proposed method is illustrated by computing the compressible viscous flow on a flat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements. 23 refs., 24 figs., 3 tabs.
Hajipour, Mojtaba; Jajarmi, Amin
2018-02-01
Using the Pontryagin's maximum principle for a time-delayed optimal control problem results in a system of coupled two-point boundary-value problems (BVPs) involving both time-advance and time-delay arguments. The analytical solution of this advance-delay two-point BVP is extremely difficult, if not impossible. This paper provides a discrete general form of the numerical solution for the derived advance-delay system by applying a finite difference θ-method. This method is also implemented for the infinite-time horizon time-delayed optimal control problems by using a piecewise version of the θ-method. A matrix formulation and the error analysis of the suggested technique are provided. The new scheme is accurate, fast and very effective for the optimal control of linear and nonlinear time-delay systems. Various types of finite- and infinite-time horizon problems are included to demonstrate the accuracy, validity and applicability of the new technique.
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.
Energy Technology Data Exchange (ETDEWEB)
Spoerl, Andreas
2008-06-05
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.)
Energy Technology Data Exchange (ETDEWEB)
Azadeh, A.; Amalnick, M.S.; Ghaderi, S.F.; Asadzadeh, S.M. [Department of Industrial Engineering, Faculty of Engineering, Center of Excellence for Intelligent Experimental Mechanics, Research Institute of Energy Management and Planning, P.O. Box 14178-43111, University of Tehran (Iran); Department of Engineering Optimization Research, Faculty of Engineering, Center of Excellence for Intelligent Experimental Mechanics, Research Institute of Energy Management and Planning, P.O. Box 14178-43111, University of Tehran (Iran)
2007-07-15
This paper introduces an integrated approach based on data envelopment analysis (DEA), principal component analysis (PCA) and numerical taxonomy (NT) for total energy efficiency assessment and optimization in energy intensive manufacturing sectors. Total energy efficiency assessment and optimization of the proposed approach considers structural indicators in addition conventional consumption and manufacturing sector output indicators. The validity of the DEA model is verified and validated by PCA and NT through Spearman correlation experiment. Moreover, the proposed approach uses the measure-specific super-efficiency DEA model for sensitivity analysis to determine the critical energy carriers. Four energy intensive manufacturing sectors are discussed in this paper: iron and steel, pulp and paper, petroleum refining and cement manufacturing sectors. To show superiority and applicability, the proposed approach has been applied to refinery sub-sectors of some OECD (Organization for Economic Cooperation and Development) countries. This study has several unique features which are: (1) a total approach which considers structural indicators in addition to conventional energy efficiency indicators; (2) a verification and validation mechanism for DEA by PCA and NT and (3) utilization of DEA for total energy efficiency assessment and consumption optimization of energy intensive manufacturing sectors. (author)
Ortleb, Sigrun; Seidel, Christian
2017-07-01
In this second symposium at the limits of experimental and numerical methods, recent research is presented on practically relevant problems. Presentations discuss experimental investigation as well as numerical methods with a strong focus on application. In addition, problems are identified which require a hybrid experimental-numerical approach. Topics include fast explicit diffusion applied to a geothermal energy storage tank, noise in experimental measurements of electrical quantities, thermal fluid structure interaction, tensegrity structures, experimental and numerical methods for Chladni figures, optimized construction of hydroelectric power stations, experimental and numerical limits in the investigation of rain-wind induced vibrations as well as the application of exponential integrators in a domain-based IMEX setting.
Efficient and stable solution-processed planar perovskite solar cells via contact passivation
Tan, Hairen
2017-02-03
Planar perovskite solar cells (PSCs) made entirely via solution processing at low temperatures (<150°C) offer promise for simple manufacturing, compatibility with flexible substrates, and perovskite-based tandem devices. However, these PSCs require an electron-selective layer that performs well with similar processing. We report a contact-passivation strategy using chlorine-capped TiO2 colloidal nanocrystal film that mitigates interfacial recombination and improves interface binding in low-temperature planar solar cells. We fabricated solar cells with certified efficiencies of 20.1 and 19.5% for active areas of 0.049 and 1.1 square centimeters, respectively, achieved via low-temperature solution processing. Solar cells with efficiency greater than 20% retained 90% (97% after dark recovery) of their initial performance after 500 hours of continuous room-temperature operation at their maximum power point under 1-sun illumination (where 1 sun is defined as the standard illumination at AM1.5, or 1 kilowatt/square meter).
Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case
Fernández-Nieto, Enrique D.; Gallardo, José M.; Vigneaux, Paul
2018-01-01
This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such schemes in 2D as the follow up of the companion paper treating the 1D case. Numerical tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham-Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix-Mont-Blanc to show the usability of these schemes on real topographies from digital elevation models (DEM).
Energy Technology Data Exchange (ETDEWEB)
Sun, Liang [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); University of Chinese Academy of Sciences, Beijing 100049 (China); Shen, Wenfei [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); Institute of Hybrid Materials, Laboratory of New Fiber Materials and Modern Textile—The Growing Base for State Key Laboratory, Qingdao University, Qingdao 266071 (China); Chen, Weichao [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); Bao, Xichang, E-mail: baoxc@qibebt.ac.cn [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China); Wang, Ning; Dou, Xiaowei; Han, Liangliang; Wen, Shuguang [CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess Technology, Chinese Academy of Sciences, Qingdao 266101 (China)
2014-12-31
Titanium oxide (TiO{sub X}) is an effective electron transport layer (ETL) in polymer solar cells (PSCs). We report efficient inverted PSCs with a simple solution-processed amorphous TiO{sub X} (s-TiO{sub X}) film as an ETL. The s-TiO{sub X} film with high light transmittance was prepared by spin-coating titanium (IV) isopropoxide isopropanol solution on indium tin oxide coated glass in inert and then placed in air under room temperature for 60 min. The introduction of s-TiO{sub X} ETL greatly improved the short circuit current density of the devices. PSCs based on poly(3-hexylthiophene):[6,6]-phenyl-C61-butyric acid methyl ester and poly(4,8-bis-alkyloxy-benzo[1,2-b:4,5-b′]dithiophene-alt-alkylcarbonyl -thieno[3,4-b]thiophene):[6,6]-phenyl- C71-butyric acid methyl ester using s-TiO{sub X} film as ETL shows high power conversion efficiency of 4.29% and 6.7% under the illumination of AM 1.5G, 100 mW/cm{sup 2}, which shows enhancements compared to the conventional PSCs with poly(styrenesulfonate)-doped poly(ethylenedioxythiophene) as anode buffer layer. In addition, the device exhibits good stability in a humid ambient atmosphere without capsulation. The results indicate that the annealing-free, simple solution processed s-TiO{sub X} film is an efficient ETL for high-performance PSCs. - Highlights: • High quality s-TiO{sub X} films were prepared by a simple, solution method without thermal treatment. • The s-TiO{sub X} films with high transmittance are very smooth. • The organic photovoltaic performance with s-TiO{sub X} film improved greatly and exhibited good stability. • The annealing-free, simple prepared s-TiO{sub X} film will be much compatible with flexible substrates.
Ferlemann, Paul G.
2000-01-01
A solution methodology has been developed to efficiently model multi-specie, chemically frozen, thermally perfect gas mixtures. The method relies on the ability to generate a single (composite) set of thermodynamic and transport coefficients prior to beginning a CFD solution. While not fundamentally a new concept, many applied CFD users are not aware of this capability nor have a mechanism to easily and confidently generate new coefficients. A database of individual specie property coefficients has been created for 48 species. The seven coefficient form of the thermodynamic functions is currently used rather then the ten coefficient form due to the similarity of the calculated properties, low temperature behavior and reduced CPU requirements. Sutherland laminar viscosity and thermal conductivity coefficients were computed in a consistent manner from available reference curves. A computer program has been written to provide CFD users with a convenient method to generate composite specie coefficients for any mixture. Mach 7 forebody/inlet calculations demonstrated nearly equivalent results and significant CPU time savings compared to a multi-specie solution approach. Results from high-speed combustor analysis also illustrate the ability to model inert test gas contaminants without additional computational expense.
Synthesis of magnetic biocomposite for efficient adsorption of azo dye from aqueous solution.
Sivashankar, R; Sathya, A B; Krishnakumar, Uma; Sivasubramanian, V
2015-11-01
A novel magnetic biocomposite was synthesized using metal chlorides and aquatic macrophytes by co-precipitation method. The resulting product, magnetic biocomposite was characterized by Fourier transform infrared spectra (FTIR), X-ray diffraction (XRD), Energy-dispersive X-ray spectroscopy (EDX) and Scanning electron microscope (SEM). The adsorption performance of the magnetic biocomposite was tested with removal of Metanil Yellow dye from aqueous solution. The effect of influencing parameters such as initial dye concentration, solution pH and agitation were investigated. The equilibrium isotherm was well described by the Langmuir model with the with maximum adsorption capacity of 90.91mg/g. Adsorption kinetics experiments were carried out and the data were well fitted by a pseudo-second-order equation. The results revealed that the magnetic biocomposite could efficiently adsorb the azo dyes from aqueous solution, and the spent adsorbents could be recovered completely by magnetic separation process. Therefore, the prepared magnetic biocomposite could thus be used as promising adsorbent for the removal of azo dyes from polluted water. Copyright © 2015 Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Mehrling, T.J., E-mail: timon.mehrling@desy.de [Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg (Germany); Robson, R.E. [Centre for Quantum Dynamics, School of Natural Sciences, Griffith University, Brisbane (Australia); Erbe, J-H.; Osterhoff, J. [Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg (Germany)
2016-09-01
This paper introduces a semi-analytic numerical approach (SANA) for the rapid computation of the transverse emittance of beams with finite energy spread in plasma wakefield accelerators in the blowout regime. The SANA method is used to model the beam emittance evolution when injected into and extracted from realistic plasma profiles. Results are compared to particle-in-cell simulations, establishing the accuracy and efficiency of the procedure. In addition, it is demonstrated that the tapering of vacuum-to-plasma and plasma-to-vacuum transitions is a viable method for the mitigation of emittance growth of beams during their injection and extraction from and into plasma cells.
Directory of Open Access Journals (Sweden)
Muhammad Mujtaba Shaikh
2016-10-01
Full Text Available In this paper, a simple and efficient numerical method is proposed for computing the number of complex zeros of a real polynomial lying inside the unit disk. The proposed protocol uses the Boubaker polynomial expansion scheme (BPES to build sequence of polynomials based on the concept of Sturm sequences. The method is used in a direct way without using any restrictions in reference to other existing methods. The protocol is applied to some example polynomials of different orders and utility of the algorithm is noticed.
Jagadamma, Lethy Krishnan
2016-09-09
Solution-manufacturing of organic solar cells with best-in-class power conversion efficiency (PCE) will require all layers to be solution-coated without compromising solar cell performance. To date, the hole transporting layer (HTL) deposited on top of the organic bulk heterojunction layer in the inverted architecture is most commonly an ultrathin (<10 nm) metal oxide layer prepared by vacuum-deposition. Here, we show that an alcohol-based nanocrystalline MoOx suspension with carefully controlled nanocrystal (NC) size can yield state of the art reflective and semitransparent solar cells. Using NCs smaller than the target HTL thickness (∼10 nm) can yield compact, pinhole-free films which result in highly efficient polymer:fullerene bulk heterojunction (BHJ) solar cells with PCE=9.5%. The solution processed HTL is shown to achieve performance parity with vacuum-evaporated HTLs for several polymer:fullerene combinations and is even shown to work as hole injection layer in polymer light emitting diodes (PLED). We also demonstrate that larger MoOx NCs (30–50 nm) successfully composite MoOx with Ag nanowires (NW) to form a highly conducting, transparent top anode with exceptional contact properties. This yields state-of-the-art semitransparent polymer: fullerene solar cells with PCE of 6.5% and overall transmission >30%. The remarkable performance of reflective and semitransparent OPVs is due to the uncommonly high fill factors achieved using a carefully designed strategy for implementation of MoOx nanocrystals as HTL materials. © 2016 Elsevier Ltd
Numerical assessment of efficiency and control stability of an HTS synchronous motor
Energy Technology Data Exchange (ETDEWEB)
Xian Wei; Yuan Weijia; Coombs, T A, E-mail: wx210@cam.ac.u [Electronic, Power and Energy Conversion Group, Engineering Department, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3 0FA (United Kingdom)
2010-06-01
A high temperature superconducting (HTS) permanent magnet synchronous motor (PMSM) is designed and developed in Cambridge University. It is expected to become cost competitive with the conventional PMSM owing to its high efficiency, high power density, high torque density, etc. The structure and parameters of HTS PMSM are detailed. Both AC losses by transport current and applied filed in stator armature winding of HTS PMSM are also analyzed. Computed and simulated results of the characteristics of the HTS PMSM and conventional PMSM are compared. The improvement on stability of direct torque control (DTC) on the HTS PMSM is estimated, and proved by simulation on Matlab/Simulink.
An efficient solution of real-time data processing for multi-GNSS network
Gong, Xiaopeng; Gu, Shengfeng; Lou, Yidong; Zheng, Fu; Ge, Maorong; Liu, Jingnan
2017-12-01
Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix-matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively.
EFFICIENCY OF HYPERTONIC SOLUTION INHALATION IN CHILDREN WITH BRONCHITIS AND BRONCHIOLITIS
Directory of Open Access Journals (Sweden)
O. I. Simonova
2014-01-01
Full Text Available Background: Chronic bronchitis and bronchiolitis in children with congenital malformation are often characterized by the severe course of disease. The efficiency of treatment of those conditions can be increased through addition of sodium chloride (NaCl, hypertonic saline which takes a hydrostatic and osmotic effect on mucous membrane of the bronchial tree in broncholytic therapy. Aim: To evaluate the efficiency of 3% NaCl hypertonic solution inhalation in children with chronic bronchitis/bronchiolitis in the setting of bronchi congenital malformation (Kartagener's syndrome and primary ciliary dyskinesia. Patients and methods: The participantsof this study were 28 children in the age of 4–17.5 years with chronic bronchitis/bronchiolitis in the setting of Kartagener's syndrome and primary ciliary dyskinesia in the first days o facute exacerbation of the disease (15 patients in treatment group and 13 patients in control group. In the therapy scheme of treatment group the 3 NaCl hypertonic solution in administered dose of 2 ml was applied 2 times/day during 14 days besides other treatment methods. Results: In patients with chronic bronchiolitis 3% NaCl hypertonic saline inhalation in administered dose of 2 ml twice a day had improved the clinical presentation of disease; by the 14th day of studythe FEV-1 value improved from 70.0 ± 2.1 to 82 ± 3.2% (p = 0.024. The side effects in form of cough aggravation were registered in 13% cases. Among additional criteria of efficiency the improvement of MОС-75 from 52.1 ± 5.2 to 71.2 ± 1.4% (p = 0.011 was also marked in patients. The adverse experience, such as shivering, hypoexcitability and sleep disturbance, were registered in 7% of cases. Conclusion: Inhalation of 3% NaCl hypertonic saline allows the fast arresting of wheezing and eliminates the mycostasis in children with chronic bronchitis/bronchiolitis.
High Efficiency Inverted Planar Perovskite Solar Cells with Solution-Processed NiOx Hole Contact.
Yin, Xuewen; Yao, Zhibo; Luo, Qiang; Dai, Xuezeng; Zhou, Yu; Zhang, Ye; Zhou, Yangying; Luo, Songping; Li, Jianbao; Wang, Ning; Lin, Hong
2017-01-25
NiOx is a promising hole-transporting material for perovskite solar cells due to its high hole mobility, good stability, and easy processability. In this work, we employed a simple solution-processed NiOx film as the hole-transporting layer in perovskite solar cells. When the thickness of the perovskite layer increased from 270 to 380 nm, the light absorption and photogenerated carrier density were enhanced and the transporting distance of electron and hole would also increase at the same time, resulting in a large charge transfer resistance and a long hole-extracted process in the device, characterized by the UV-vis, photoluminescence, and electrochemical impedance spectroscopy spectra. Combining both of these factors, an optimal thickness of 334.2 nm was prepared with the perovskite precursor concentration of 1.35 M. Moreover, the optimal device fabrication conditions were further achieved by optimizing the thickness of NiOx hole-transporting layer and PCBM electron selective layer. As a result, the best power conversion efficiency of 15.71% was obtained with a Jsc of 20.51 mA·cm-2, a Voc of 988 mV, and a FF of 77.51% with almost no hysteresis. A stable efficiency of 15.10% was caught at the maximum power point. This work provides a promising route to achieve higher efficiency perovskite solar cells based on NiO or other inorganic hole-transporting materials.
Varnhagen, Scott; Same, Adam; Remillard, Jesse; Park, Jae Wan
2011-03-01
Series plug-in hybrid electric vehicles of varying engine configuration and battery capacity are modeled using Advanced Vehicle Simulator (ADVISOR). The performance of these vehicles is analyzed on the bases of energy consumption and greenhouse gas emissions on the tank-to-wheel and well-to-wheel paths. Both city and highway driving conditions are considered during the simulation. When simulated on the well-to-wheel path, it is shown that the range extender with a Wankel rotary engine consumes less energy and emits fewer greenhouse gases compared to the other systems with reciprocating engines during many driving cycles. The rotary engine has a higher power-to-weight ratio and lower noise, vibration and harshness compared to conventional reciprocating engines, although performs less efficiently. The benefits of a Wankel engine make it an attractive option for use as a range extender in a plug-in hybrid electric vehicle.
Thompson, J. F.; Mcwhorter, J. C.; Siddiqi, S. A.; Shanks, S. P.
1973-01-01
Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.
Friedrich, Oliver; Eifler, Tim
2018-01-01
Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multiprobe) analyses of the large-scale structure of the Universe. Analytically computed covariances are noise-free and hence straightforward to invert; however, the model approximations might be insufficient for the statistical precision of future cosmological data. Estimating covariances from numerical simulations improves on these approximations, but the sample covariance estimator is inherently noisy, which introduces uncertainties in the error bars on cosmological parameters and also additional scatter in their best-fitting values. For future surveys, reducing both effects to an acceptable level requires an unfeasibly large number of simulations. In this paper we describe a way to expand the precision matrix around a covariance model and show how to estimate the leading order terms of this expansion from simulations. This is especially powerful if the covariance matrix is the sum of two contributions, C = A+B, where A is well understood analytically and can be turned off in simulations (e.g. shape noise for cosmic shear) to yield a direct estimate of B. We test our method in mock experiments resembling tomographic weak lensing data vectors from the Dark Energy Survey (DES) and the Large Synoptic Survey Telescope (LSST). For DES we find that 400 N-body simulations are sufficient to achieve negligible statistical uncertainties on parameter constraints. For LSST this is achieved with 2400 simulations. The standard covariance estimator would require >105 simulations to reach a similar precision. We extend our analysis to a DES multiprobe case finding a similar performance.
Citro, V.; Luchini, P.; Giannetti, F.; Auteri, F.
2017-09-01
The study of the stability of a dynamical system described by a set of partial differential equations (PDEs) requires the computation of unstable states as the control parameter exceeds its critical threshold. Unfortunately, the discretization of the governing equations, especially for fluid dynamic applications, often leads to very large discrete systems. As a consequence, matrix based methods, like for example the Newton-Raphson algorithm coupled with a direct inversion of the Jacobian matrix, lead to computational costs too large in terms of both memory and execution time. We present a novel iterative algorithm, inspired by Krylov-subspace methods, which is able to compute unstable steady states and/or accelerate the convergence to stable configurations. Our new algorithm is based on the minimization of the residual norm at each iteration step with a projection basis updated at each iteration rather than at periodic restarts like in the classical GMRES method. The algorithm is able to stabilize any dynamical system without increasing the computational time of the original numerical procedure used to solve the governing equations. Moreover, it can be easily inserted into a pre-existing relaxation (integration) procedure with a call to a single black-box subroutine. The procedure is discussed for problems of different sizes, ranging from a small two-dimensional system to a large three-dimensional problem involving the Navier-Stokes equations. We show that the proposed algorithm is able to improve the convergence of existing iterative schemes. In particular, the procedure is applied to the subcritical flow inside a lid-driven cavity. We also discuss the application of Boostconv to compute the unstable steady flow past a fixed circular cylinder (2D) and boundary-layer flow over a hemispherical roughness element (3D) for supercritical values of the Reynolds number. We show that Boostconv can be used effectively with any spatial discretization, be it a finite