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 modelling of rapid solidification
DEFF Research Database (Denmark)
Pryds, Nini; Hattel, Jesper Henri
1997-01-01
A mathematical model of the melt spinning process has been developed based on the control-volume finite-difference method. The model avoids some of the limitations of the previous models, for example including the effect of the wheel in the heat how calculations and the temperature dependence......, for example the recalescence characteristic, was investigated. The results of the model showed that the effect of heating of the wheel is difficult to prevent even for a wheel material of high conductivity. The recalescence effect was found to be influenced by the wheel surface temperature and to decrease...... with increasing thermal conductivity of the wheel. The observed increase in the wheel surface temperature suggests the importance of including the wheel in the numerical calculations, especially for a wheel made of a low-conductive material...
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 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 ...
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...
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).
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 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 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 Simulations of Thermal Convection in Rapidly Rotating Spherical Shell
Energy Technology Data Exchange (ETDEWEB)
Nenkov, Constantine; Peltier, Richard, E-mail: nenkov@atmosp.physics.utoronto.ca, E-mail: peltier@atmosp.physics.utoronto.ca [Department of Physics, University of Toronto Toronto, Ontario, M5S 1A7 (Canada)
2010-11-01
We present a novel numerical model used to simulate convection in the atmospheres of the Gas Giant planets Jupiter and Saturn. Nonlinear, three-dimensional, time-dependant solutions of the anelastic hydrodynamic equations are presented for a stratified, rotating spherical fluid shell heated from below. This new model is specified in terms of a grid-point based methodology which employs a hierarchy of tessellations of the regular icosahedron onto the sphere through the process of recurrent dyadic refinements of the spherical surface. We describe discretizations of the governing equations in which all calculations are performed in Cartesian coordinates in the local neighborhoods of the almost uniform icosahedral grid, a methodology which avoids the potential mathematical and numerical difficulties associated with the pole problem in spherical geometry. Using this methodology we have built our model in primitive equations formulation, whereas the three-dimensional vector velocity field and temperature are directly advanced in time. We show results of thermal convection in rapidly rotating spherical shell which leads to the formation of well pronounced prograde zonal jets at the equator, results which previous experiments with two-dimensional models in the limit of freely evolving turbulence were not able to achieve.
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.
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.
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.
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...
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.
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.
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.
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 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.
Rapid installation of numerical models in multiple parent codes
Energy Technology Data Exchange (ETDEWEB)
Brannon, R.M.; Wong, M.K.
1996-10-01
A set of``model interface guidelines``, called MIG, is offered as a means to more rapidly install numerical models (such as stress-strain laws) into any parent code (hydrocode, finite element code, etc.) without having to modify the model subroutines. The model developer (who creates the model package in compliance with the guidelines) specifies the model`s input and storage requirements in a standardized way. For portability, database management (such as saving user inputs and field variables) is handled by the parent code. To date, NUG has proved viable in beta installations of several diverse models in vectorized and parallel codes written in different computer languages. A NUG-compliant model can be installed in different codes without modifying the model`s subroutines. By maintaining one model for many codes, MIG facilitates code-to-code comparisons and reduces duplication of effort potentially reducing the cost of installing and sharing models.
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.
Asymptotic and Numerical Methods for Rapidly Rotating Buoyant Flow
Grooms, Ian G.
This thesis documents three investigations carried out in pursuance of a doctoral degree in applied mathematics at the University of Colorado (Boulder). The first investigation concerns the properties of rotating Rayleigh-Benard convection -- thermal convection in a rotating infinite plane layer between two constant-temperature boundaries. It is noted that in certain parameter regimes convective Taylor columns appear which dominate the dynamics, and a semi-analytical model of these is presented. Investigation of the columns and of various other properties of the flow is ongoing. The second investigation concerns the interactions between planetary-scale and mesoscale dynamics in the oceans. Using multiple-scale asymptotics the possible connections between planetary geostrophic and quasigeostrophic dynamics are investigated, and three different systems of coupled equations are derived. Possible use of these equations in conjunction with the method of superparameterization, and extension of the asymptotic methods to the interactions between mesoscale and submesoscale dynamics is ongoing. The third investigation concerns the linear stability properties of semi-implicit methods for the numerical integration of ordinary differential equations, focusing in particular on the linear stability of IMEX (Implicit-Explicit) methods and exponential integrators applied to systems of ordinary differential equations arising in the numerical solution of spatially discretized nonlinear partial differential equations containing both dispersive and dissipative linear terms. While these investigations may seem unrelated at first glance, some reflection shows that they are in fact closely linked. The investigation of rotating convection makes use of single-space, multiple-time-scale asymptotics to deal with dynamics strongly constrained by rotation. Although the context of thermal convection in an infinite layer seems somewhat removed from large-scale ocean dynamics, the asymptotic
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.
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 → ∞.
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.
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
Directory of Open Access Journals (Sweden)
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...
Rapid structural analysis of nanomaterials in aqueous solutions
Ryuzaki, Sou; Tsutsui, Makusu; He, Yuhui; Yokota, Kazumichi; Arima, Akihide; Morikawa, Takanori; Taniguchi, Masateru; Kawai, Tomoji
2017-04-01
Rapid structural analysis of nanoscale matter in a liquid environment represents innovative technologies that reveal the identities and functions of biologically important molecules. However, there is currently no method with high spatio-temporal resolution that can scan individual particles in solutions to gain structural information. Here we report the development of a nanopore platform realizing quantitative structural analysis for suspended nanomaterials in solutions with a high z-axis and xy-plane spatial resolution of 35.8 ± 1.1 and 12 nm, respectively. We used a low thickness-to-diameter aspect ratio pore architecture for achieving cross sectional areas of analyte (i.e. tomograms). Combining this with multiphysics simulation methods to translate ionic current data into tomograms, we demonstrated rapid structural analysis of single polystyrene (Pst) beads and single dumbbell-like Pst beads in aqueous solutions.
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.
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.
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
Numerical Comparison of Solutions of Kinetic Model Equations
Directory of Open Access Journals (Sweden)
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
Rapid Sterilization of Escherichia coli by Solution Plasma Process
Andreeva, Nina; Ishizaki, Takahiro; Baroch, Pavel; Saito, Nagahiro
2012-12-01
Solution plasma (SP), which is a discharge in the liquid phase, has the potential for rapid sterilization of water without chemical agents. The discharge showed a strong sterilization performance against Escherichia coli bacteria. The decimal value (D value) of the reduction time for E. coli by this system with an electrode distance of 1.0 mm was estimated to be approximately 1.0 min. Our discharge system in the liquid phase caused no physical damage to the E. coli and only a small increase in the temperature of the aqueous solution. The UV light generated by the discharge was an important factor in the sterilization of E. coli.
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.
Rapid convergence of optimal control in NMR using numerically-constructed toggling frames
Coote, Paul; Anklin, Clemens; Massefski, Walter; Wagner, Gerhard; Arthanari, Haribabu
2017-08-01
We present a numerical method for rapidly solving the Bloch equation for an arbitrary time-varying spin-1/2 Hamiltonian. The method relies on fast, vectorized computations such as summation and quaternion multiplication, rather than slow computations such as matrix exponentiation. A toggling frame is constructed in which the Hamiltonian is time-invariant, and therefore has a simple analytical solution. The key insight is that constructing this frame is faster than solving the system dynamics in the original frame. Rapidly solving the Bloch equations for an arbitrary Hamiltonian is particularly useful in the context of NMR optimal control. Optimal control theory can be used to design pulse shapes for a range of tasks in NMR spectroscopy. However, it requires multiple simulations of the Bloch equations at each stage of the algorithm, and for each relevant set of parameters (e.g. chemical shift frequencies). This is typically time consuming. We demonstrate that by working in an appropriate toggling frame, optimal control pulses can be generated much faster. We present a new alternative to the well-known GRAPE algorithm to continuously update the toggling-frame as the optimal pulse is generated, and demonstrate that this approach is extremely fast. The use and benefit of rapid optimal pulse generation is demonstrated for 19F fragment screening experiments.
Numerical modelling of the binary alloys solidification with solutal undercooling
Directory of Open Access Journals (Sweden)
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)
Numerical simulations of thermal convection in rapidly rotating spherical fluid shells
Energy Technology Data Exchange (ETDEWEB)
Sun, Z.P.
1992-01-01
Numerical simulations of thermal convection in rapidly rotating spherical shells of Boussinesq fluid have been carried out with a nonlinear, three-dimensional, time-dependent spectral-transform code. The basic state is hydrostatic, spherically symmetric, and independent of time. The numerical methods, the numerical stability, and the adequacy of the spatial resolution were examined by a benchmarking study. A sequence of bifurcations from the onset of a steadily propagating convective state, to a periodic state, to a quasi-periodic state and thence a chaotic state has been found. Convective solutions at each stage along the route to chaos have been studied. The emphases are on the three-dimensional and time-dependent convective structures and associated mean zonal flow. The spherical shell is heated from both below and within. The boundaries are isothermal and stress-free. The author has also explored the consequences of imposing a spatially varying temperature anomaly on the upper surface of a spherical shell on thermal convection in the shell. The spherical shell is heated from below and cooled from above. The lower boundary is isothermal and both boundaries are rigid and impermeable. The results show that the patterns and amplitudes of the convective motions and associated mean zonal and meridional flows depend largely on the pattern and amplitude of the imposted thermal anomaly. The purpose of this study is to illustrate the influence of thermal conditions in the lower mantle on motions in the Earth's liquid outer core. The author has carried out numerical simulations at both high Taylor and Rayleigh numbers. The spherical shell is heated from below and cooled from above. The boundaries are isothermal and stress-free. Columnar rolls that are quasi-layered in cylindrical radius and associated banded mean zonal flow are obtained. The quasi-layered convective structure and the banded zonal wind are consequent upon both the high Taylor and Rayleigh numbers.
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.
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.
Wu, Cyuan-Jhang; Singh, Vickramjeet; Sheng, Yu-Jane; Tsao, Heng-Kwong
2017-08-01
Solute separation of aqueous mixtures is mainly dominated by water vaporization. The evaporation rate of an aqueous drop grows with increasing the liquid-gas interfacial area. The spontaneous spreading behavior of a water droplet on a total wetting surface provides huge liquid-gas interfacial area per unit volume; however, it is halted by the self-pinning phenomenon upon addition of nonvolatile solutes. In this work, it is shown that the solute-induced self-pinning can be overcome by gravity, leading to anisotropic spreading much faster than isotropic spreading. The evaporation rate of anisotropic spreading on a zwitterionic sulfobetaine surface is 25 times larger as that on a poly(methyl methacrylate) surface. Dramatic enhancement of evaporation is demonstrated by simultaneous formation of fog atop liquid film. During anisotropic spreading, the solutes are quickly precipitated out within 30 s, showing the rapid solute-water separation. After repeated spreading process for the dye-containing solution, the mean concentration of the collection is doubled, revealing the concentration efficiency as high as 100%. Gravity-enhanced spreading on total wetting surfaces at room temperature is easy to scale-up with less energy consumption, and thus it has great potentials for the applications of solute separation and concentration.
Rapidly decaying solutions of the nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Cazenave, T. (Paris-6 Univ., 75 (France). Lab. d' Analyse Numerique); Weissler, F.B. (ENS, 94 - Cachan (France). Centre de Mathematiques Paris-7 Univ., 94 - Creteil (France). UFR de Sciences)
1992-06-01
We consider global solutions of the nonlinear Schroedinger equation iu{sub t}+{Delta}u={lambda}vertical strokeuvertical stroke{sup {alpha}}u, in R{sup N}, (NLS) where {lambda}{epsilon}R and 0<{alpha}< 4/N-2. In particular, for {alpha}>{alpha}{sub 0}=(2-N+{radical}(N{sup 2}+12N+4))/2N, we show that for every ({phi}{epsilon}H{sup 1}(R{sup N}) such that x{phi}(x){epsilon}L{sup 2}(R{sup N}), the solution of (NLS) with initial value {phi}(x)e{sup i(bvertical} {sup strokexvertical} {sup stroke2/4)} is global and rapidly decaying as t{yields}{infinity} if b is large enough. Furthermore, by applying the pseudo-conformal transformation and studying the resulting nonautonomous nonlinear Schroedinger equation, we obtain both new results and simpler proofs of some known results concerning the scattering theory. In particular, we construct the wave operators for 4/N+2<{alpha}<4/N-2. Also, we establish a low energy scattering theory for the same range of {alpha} and show that, at least for {lambda}<0, the lower bound on {alpha} is optimal. Finally, if {lambda}>0, we prove asymptotic completeness for {alpha}{sub 0}{<=}{alpha}<4/N-2. (orig.).
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.
Microfluidic device for rapid solution exchange to study kinetics of cell physiology
Hu, Howard; Honnatti, Meghana; Gillis, Kevin
2006-11-01
Exchanging the extracellular solution of the cell rapidly (less than 10ms) is an important requirement in study the kinetics of cell physiology. A microfluidic device is developed to exchange the solution around the cells as they flow through a junction at the intersection of two microfluidic channels. The solution exchange time is measured experimentally by fluorescently labeling the cell surface membranes with a styryl dye, FM1-43 or FM 2-10, and then observing the time course of cell fluorescence decay following the rapid drop in the extracellular concentration of the FM dye that occurs as the cell flows past the fluidic junction. A numerical model is developed to guide the experimental design of microfluidic device. In the model, the motion of a single cell through a fluid junction is simulated and the mixing process of the solutions is solved. The model also includes the kinetics of departitioning of FM dyes from the cell membrane. The departitioning time constants for the FM dyes are determined from fitting the measured data of the cell fluorescence decay. This departitioning kinetics is important as FM dyes are commonly used to label cell membranes for the purpose of measuring the release of neurotransmitter from synaptic vesicles via exocytosis and the subsequent reuptake of vesicular membrane by endocytosis.
Numerical Solution of Magnetostatic Field of Maglev System
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
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.
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.
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
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
Directory of Open Access Journals (Sweden)
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).
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.
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...
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 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
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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.
Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil
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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
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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
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Pimenov Vladimir G.
2017-09-01
Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
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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...
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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.
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.
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
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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
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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.
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.
Numerical modeling of rapidly varying flows using HEC-RAS and WSPG models.
Rao, Prasada; Hromadka, Theodore V
2016-01-01
The performance of two popular hydraulic models (HEC-RAS and WSPG) for modeling hydraulic jump in an open channel is investigated. The numerical solutions are compared with a new experimental data set obtained for varying channel bottom slopes and flow rates. Both the models satisfactorily predict the flow depths and location of the jump. The end results indicate that the numerical models output is sensitive to the value of chosen roughness coefficient. For this application, WSPG model is easier to implement with few input variables.
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.
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)
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
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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.
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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
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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.
Rapid Time Response: A solution for Manufacturing Issue
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Norazlin N.
2017-01-01
Full Text Available Respond time in manufacturing give the major impact that able to contribute too many manufacturing issues. Based on two worst case scenario occurred where Toyota in 2009 made a massive vehicles call due to car complexity of 11 major models and over 9 million vehicles. The recalls cost at least $2 billion in cost of repair, lost deals and result in lost 5% of its market share in United State of America, while A380 was reported on missing target in new production and leads to delayed market entry due to their weak product life cycle management (PLM. These cases give a sign to all industries to possess and optimize the facilities for better traceability in shortest time period. In Industry 4.0, the traceability and time respond become the factors for high performance manufacturing and rapid time respond able to expedite the traceability process and strengthen the communication level between man, machine and management. The round trip time (RTT experiment gives variant time respond between two difference operating system for intra and inter-platform signal. If this rapid time respond is adopted in any manufacturing process, the delay in traceability on every issue that lead to losses can be successfully avoided.
Liu, Jianjun; Zhang, Feimin; Pu, Zhaoxia
2017-04-01
Accurate forecasting of the intensity changes of hurricanes is an important yet challenging problem in numerical weather prediction. The rapid intensification of Hurricane Katrina (2005) before its landfall in the southern US is studied with the Advanced Research version of the WRF (Weather Research and Forecasting) model. The sensitivity of numerical simulations to two popular planetary boundary layer (PBL) schemes, the Mellor-Yamada-Janjic (MYJ) and the Yonsei University (YSU) schemes, is investigated. It is found that, compared with the YSU simulation, the simulation with the MYJ scheme produces better track and intensity evolution, better vortex structure, and more accurate landfall time and location. Large discrepancies (e.g., over 10 hPa in simulated minimum sea level pressure) are found between the two simulations during the rapid intensification period. Further diagnosis indicates that stronger surface fluxes and vertical mixing in the PBL from the simulation with the MYJ scheme lead to enhanced air-sea interaction, which helps generate more realistic simulations of the rapid intensification process. Overall, the results from this study suggest that improved representation of surface fluxes and vertical mixing in the PBL is essential for accurate prediction of hurricane intensity changes.
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
Some Comparison of Solutions by Different Numerical Techniques on Mathematical Biology Problem
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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.
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
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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.
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
Directory of Open Access Journals (Sweden)
Tuleja J.
2017-06-01
Full Text Available The paper presents a method of the numerical modelling of micro-stresses in carbonised austenitic cast steel being developed during rapid cooling due to differences in the values of thermal expansion coefficients for this material phases – carbides and austenitic matrix. Micro-stresses are indicated as the main cause of crack initiation in the tooling elements of carburising furnaces being mainly made of austenitic cast steel. A calculation model of carbonised and thermally fatigued austenitic cast steel was developed based on the microstructure images obtained using light microscopy techniques and the phase composition evaluated with the X-ray diffraction method. The values of the stress tensor components and the reduced stress in the complex models of test material structure were determined numerically by the finite element method. The effort analysis was performed and the areas where development of cracks is to be expected were identified, which was experimentally confirmed.
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.
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.
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.
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.
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.
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Elmira Ashpazzadeh
2018-04-01
Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
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
Numerical solutions of stochastic Lotka-Volterra equations via operational matrices
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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.
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.
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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.
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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.
Wu, M; Tinschert, J; Augthun, M; Wagner, I; Schädlich-Stubenrauch, J; Sahm, P R; Spiekermann, H
2001-03-01
This paper describes a method of making titanium dental crowns by means of integrating laser measuring, numerical simulation and rapid prototype (RP) manufacture of wax patterns for the investment casting process. Four real tooth crowns (FDI No. 24, 25, 26, 27) were measured by means of 3D laser scanning. The laser digitized geometry of the crowns was processed and converted into standard CAD models in STL format, which is used by RP systems and numerical simulation software. Commercial software (MAGMASOFT) was used to simulate the casting process and optimize the runner and gating system (sprue) design. RP crowns were 'printed' directly on a ModelMaker II 3D Plotting System. A silicone negative mold (soft tool) was made from the RP crowns, then more than hundreds wax crowns were duplicated. The duplicated crowns were joined to the optimized runner and gating system. By using the investment casting process 20-25 replicas of each crown were made on a centrifugal casting machine. All castings were examined for porosity by X-ray radiographs. By using the integrated scanning, simulation, RP pattern and casting procedure, cast crowns, free of porosity, with excellent functional contour and a smooth surface finish, were obtained from the first casting trial. The coupling of laser digitizing and RP indicates a potential to replace the traditional 'impression taking and waxing' procedure in dental laboratory, with the quality of the cast titanium prostheses also being improved by using the numerically optimized runner and gating system design.
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.
Laboratory-numerical models of rapidly rotating convection in planetary cores
Cheng, J. S.; Stellmach, S.; Ribeiro, A.; Grannan, A.; King, E. M.; Aurnou, J. M.
2015-04-01
We present laboratory and numerical models investigating the behavioural regimes of rapidly rotating convection in high-latitude planetary core-style settings. Our combined laboratory-numerical approach, utilizing simplified geometries, can access more extreme parameters (e.g. Rayleigh numbers Ra ≲ 1013; Nusselt numbers Nu ≲ 103; Ekman numbers E ≳ 3 × 10- 8) than current global-scale dynamo simulations. Using flow visualizations and heat transfer measurements, we study the axialized flows that exist near the onset of rotating convection, as well as the 3-D flows that develop with stronger forcing. With water as the working fluid (Prandtl number Pr ≃ 7), we find a steep scaling trend for rapidly rotating convective heat transfer, Nu ˜ (Ra/RaC)3.6, that is associated with the existence of coherent, axialized columns. This rapidly rotating trend is steeper than the trends found at moderate values of the Ekman number, and continues a trend of ever-steepening scalings as the rotation rate of the system is increased. In contrast, in more strongly forced or lower rotation rate cases, the heat transfer scaling consistently follows a shallower slope equivalent to that of non-rotating convection systems. The steep heat transfer scaling in the columnar convection regime, corroborated by our laboratory flow visualizations, imply that coherent, axial columns have a relatively narrow range of stability. Thus, we hypothesize that coherent convection columns are not stable in planetary core settings, where the Ekman number is estimated to be ˜10-15. As a consequence, convective motions in the core may not be related to the columnar motions found in present-day global-scale models. Instead, we hypothesize that turbulent rotating convection cascades energy upwards from 3-D motions to large-scale quasi-2-D flow structures that are capable of efficiently generating planetary-scale magnetic fields. We argue that the turbulent regimes of rapidly rotating convection are
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.
Numerical Investigation of the Transient Behavior of a Hot Gas Duct under Rapid Depressurization
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JingBao Liu
2016-01-01
Full Text Available A hot gas duct is an indispensable component for the nuclear-process heat applications of the Very-High-Temperature Reactor (VHTR, which has to fulfill three requirements: to withstand high temperature, high pressure, and large pressure transient. In this paper, numerical investigation of pressure transient is performed for a hot gas duct under rapid depressurization. System depressurization imposes an imploding pressure differential on the internal structural elements of a hot gas duct, the structural integrity of which is susceptible to being damaged. Pressure differential and its imposed duration, which are two key factors to evaluate the damage severity of a hot gas duct under depressurization, are examined in regard to depressurization rate and insulation packing tightness. It is revealed that depressurization rate is a decisive parameter for controlling the pressure differential and its duration, whereas insulating-packing tightness has little effect on them.
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.
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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 Modelling of Rayleigh Wave Propagation in Course of Rapid Impulse Compaction
Herbut, Aneta; Rybak, Jarosław
2017-10-01
As the soil improvement technologies are the area of a rapid development, they require designing and implementing novel methods of control and calibration in order to ensure the safety of geotechnical works. At Wroclaw University of Science and Technology (Poland), these new methods are continually developed with the aim to provide the appropriate tools for the preliminary design of work process, as well as for the further ongoing on-site control of geotechnical works (steel sheet piling, pile driving or soil improvement technologies). The studies include preliminary numerical simulations and field tests concerning measurements and continuous histogram recording of shocks and vibrations and its ground-born dynamic impact on engineering structures. The impact of vibrations on reinforced concrete and masonry structures in the close proximity of the construction site may be destroying in both architectural and structural meaning. Those limits are juxtaposed in codes of practice, but always need an individual judgment. The results and observations make it possible to delineate specific modifications to the parameters of technology applied (e.g. hammer drop height). On the basis of numerous case studies of practical applications, already summarized and published, we were able to formulate the guidelines for work on the aforementioned sites. This work presents specific aspects of the active design (calibration of building site numerical model) by means of technology calibration, using the investigation of the impact of vibrations that occur during the Impulse Compaction on adjacent structures. A case study entails the impact of construction works on Rayleigh wave propagation in the zone of 100 m (radius) around the Compactor.
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.
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.
Numerical Solution of Singularly Perturbed Delay Differential Equations with Layer Behavior
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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.
Directory of Open Access Journals (Sweden)
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.
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
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.
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.
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)
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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
Rapid aggregation and assembly in aqueous solution of Aβ (25-35 ...
Indian Academy of Sciences (India)
... Lecture Workshops · Refresher Courses · Symposia. Home; Journals; Journal of Biosciences; Volume 34; Issue 2. Rapid aggregation and assembly in aqueous solution of A (25-35) peptide. Lia Millucci Roberto Raggiaschi Davide Franceschini Georg Terstappen Annalisa Santucci. Articles Volume 34 Issue 2 June 2009 ...
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.
On the numerical solution of the one-dimensional convection-diffusion equation
Directory of Open Access Journals (Sweden)
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.
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.
The numerical solution of thawing process in phase change slab using variable space grid technique
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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.
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.
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 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.
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
Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations
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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.
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.
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 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 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.
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.
Smith, R.; Horgan, B. H. N.; Christensen, P. R.
2016-12-01
Amorphous silicates of ambiguous origin are detected on the Martian surface through orbiter and rover measurements. Secondary amorphous silicates might precipitate from rapidly evaporating weathering solutions under Amazonian ( 3 BYA - present) surface conditions. Yet, such phases are poorly understood and are underrepresented in infrared spectral libraries. Amazonian weathering was simulated by dissolving two basaltic tephra compositions in DI water under two different atmospheres (1: oxidizing and 2: simulated Martian). The resulting weathering solutions were rapidly evaporated into sample cups. Precipitate mineralogy was studied using visible and near-infrared (VNIR) and thermal-infrared (TIR) spectroscopy and x-ray diffraction (XRD). Solution compositions were analyzed using Ion Chromatography (IC) and Inductively Coupled Plasma Mass-Spectroscopy (ICP-MS). All experiments formed hydrated amorphous silicates and nanophase iron-oxides, but precipitates from solutions formed under a simulated Martian atmosphere also contain crystalline carbonate and sulfate minerals. The oxidizing atmosphere precipitates are also S-bearing, based on solution chemistry, but no crystalline sulfates were unambiguously detected. The TIR spectra of all samples exhibit a spectral feature at 460 cm-1 that was previously only known to be present in the spectra of basaltic glass and some terrestrial palagonitized basalt samples, indicating that the precipitates are new to spectral libraries. Ongoing characterization will help determine the composition and structure of the amorphous phases. TIR spectral and XRD instruments on the Spirit and Mars Science Laboratory (MSL) rovers both indicate high abundances of basaltic glass in rock and soil samples, despite chemical evidence for aqueous alteration. Our results suggest that these measurements are consistent with secondary amorphous silicates formed through the rapid evaporation of basalt weathering solutions. Thus, transient water
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
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Gajda Paweł
2016-01-01
Full Text Available Monte Carlo methodology provides reference statistical solution of neutron transport criticality problems of nuclear systems. Estimated reaction rates can be applied as an input to Bateman equations that govern isotopic evolution of reactor materials. Because statistical solution of Boltzmann equation is computationally expensive, it is in practice applied to time steps of limited length. In this paper we show that simple staircase step model leads to underprediction of numerical fuel burnup (Fissions per Initial Metal Atom – FIMA. Theoretical considerations indicates that this error is inversely proportional to the length of the time step and origins from the variation of heating per source neutron. The bias can be diminished by application of predictor-corrector step model. A set of burnup simulations with various step length and coupling schemes has been performed. SERPENT code version 1.17 has been applied to the model of a typical fuel assembly from Pressurized Water Reactor. In reference case FIMA reaches 6.24% that is equivalent to about 60 GWD/tHM of industrial burnup. The discrepancies up to 1% have been observed depending on time step model and theoretical predictions are consistent with numerical results. Conclusions presented in this paper are important for research and development concerning nuclear fuel cycle also in the context of Gen4 systems.
Numerical 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.
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 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 .
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 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.
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...
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...
A nonlinear self-similar solution to barotropic flow over rapidly varying topography
Ibanez, Ruy; Kuehl, Joseph
2016-11-01
Beginning from the Shallow Water Equations (SWE), a nonlinear self-similar analytic solution is derived for barotropic flow over rapidly varying topography. We study conditions relevant to the ocean slope where the flow is dominated by Earth's rotation and topography. Attention is paid to the northern Gulf of Mexico slope with application to pollutant dispersion and the Norwegian Coastal Current which sheds eddies into the Lofoten Basin that are believe to influence deep water formation. The solution is found to extend the topographic β-plume solution (Kuehl 2014, GRL) in two ways: 1) The solution is valid for intensifying jets. 2) The influence of nonlinear advection is included. The SWE are scaled to the case of a topographically controlled jet, then solved by introducing a similarity variable η = Cxy . The nonlinear solution, valid for topographies h =h0 - αxy3 , takes the form of the Lambert W Function for velocity. The linear solution, valid for topographies h =h0 - αxyγ , takes the form of the Error Function for transport. Kuehl's results considered the case - 1 <= γ < 1 which admits expanding jets, while the new result consider the case γ < - 1 which admits intensifying jets.
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.
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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.
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.
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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
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.
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
2007-12-06
high order well-balanced schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006...schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006), pp.69-80. 39. Y. Xu and C.-W
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.
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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.
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.
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
Favrie, N.; Gavrilyuk, S.
2017-07-01
A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.
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.
Directory of Open Access Journals (Sweden)
M. Golzar
2014-01-01
Full Text Available Recently, iron nanoparticles have attracted more attention for groundwater remediation due to its potential to reduce subsurface contaminants such as PCBs, chlorinated solvents, and heavy metals. The magnetic properties of iron nanoparticles cause to attach to each other and form bigger colloid particles of iron nanoparticles with more rapid sedimentation rate in aqueous environment. Using the surfactants such as poly acrylic acid (PAA prevents iron nanoparticles from forming large flocs that may cause sedimentation and so increases transport distance of the nanoparticles. In this study, the transport of iron oxide nanoparticles (Fe3O4 stabilized with PAA in a one-dimensional porous media (column was investigated. The slurries with concentrations of 20,100 and 500 (mg/L were injected into the bottom of the column under hydraulic gradients of 0.125, 0.375, and 0.625. The results obtained from experiments were compared with the results obtained from numerical solution of advection-dispersion equation based on the classical colloid filtration theory (CFT. The experimental and simulated breakthrough curves showed that CFT is able to predict the transport and fate of iron oxide nanoparticles stabilized with PAA (up to concentration 500 ppm in a porous media.
Doxley, Charles A.
2016-01-01
In the current world of applications that use reconfigurable technology implemented on field programmable gate arrays (FPGAs), there is a need for flexible architectures that can grow as the systems evolve. A project has limited resources and a fixed set of requirements that development efforts are tasked to meet. Designers must develop robust solutions that practically meet the current customer demands and also have the ability to grow for future performance. This paper describes the development of a high speed serial data streaming algorithm that allows for transmission of multiple data channels over a single serial link. The technique has the ability to change to meet new applications developed for future design considerations. This approach uses the Xilinx Serial RapidIO LOGICORE Solution to implement a flexible infrastructure to meet the current project requirements with the ability to adapt future system designs.
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)
Starodumov, Ilya [Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, 620000 Ekaterinburg (Russian Federation); Kropotin, Nikolai [AO NPO MKM, Ilfata Zakirova st. 24, 426000 Izhevsk (Russian Federation)
2016-08-10
We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.
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
Kien, Le Anh
2017-09-01
Rapid Expansion of Supercritical Solutions (RESS) is a solvent-free technology to produce small solid particles with very narrow size distribution. RESS process is simple and easy to control in comparison with other methods based on supercritical techniques. In this study, the engineering of nano (or submicron) acetaminophen particles using rapid expansion CO2 supercritical solution (RESS) was investigated. Empirical model with response surface methodology was used to evaluate the effects of processing parameters, i.e. extraction temperature T (313-333 K), extraction pressure P (90-150 bar) and pre-expansion temperature Texp (353-373 K), on the size of precipitated acetaminophen particles. The results show that the smallest particle size, i.e. 52.08 nm can be achieved at 90 bar, 313 K and 353 K (P, T, Texp, respectively). To better understand and develop a mechanistic predictive tool for RESS process, a one dimensional steady flow model was used in this work to describe the subsonic expansion process inside the capillary nozzle and the supersonic expansion process outside expansion nozzle. It was shown that particle characteristics are governed by both operation parameters such as pre-expansion temperature, pre-expansion pressure, and expansion temperature. These parameters affects particle size in the same trend as that was found from experiment data and empirical model.
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.
Evaluate the accuracy of the numerical solution of hydrogeological problems of mass transfer
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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.
DEFF Research Database (Denmark)
Sheyko, A.A.; Finlay, Chris; Marti, P.
We present a set of numerical dynamo models with the convection strength varied by a factor of 30 and the ratio of magnetic to viscous diffusivities by a factor of 20 at rapid rotation rates (E =nu/(2 Omega d^2 ) = 10-6 and 10-7 ) using a heat flux outer BC. This regime has been little explored...... on the structure of the dynamos and how this changes in relation to the selection of control parameters, a comparison with the proposed rotating convection and dynamo scaling laws, energy spectra of steady solutions and inner core rotation rates. Magnetic field on the CMB. E=2.959*10-7, Ra=6591.0, Pm=0.05, Pr=1....
Pisarenko, Aleksey N; Stanford, Benjamin D; Quiñones, Oscar; Pacey, Gilbert E; Gordon, Gilbert; Snyder, Shane A
2010-02-05
A sensitive, rapid, and rugged liquid chromatography with tandem mass spectrometry (LC-MS/MS) method for measuring concentrations of perchlorate, chlorate, and bromate ions in concentrated sodium hypochlorite solutions is presented. The LC-MS/MS method offers a practical quantitation limit (PQL) of 0.05 microg L(-1) for ClO(4)(-), 0.2 microg L(-1) for BrO(3)(-), and 0.7 microg L(-1) for ClO(3)(-) and a sample analysis time of only 10 min. Additionally, an iodometric titration technique was compared with the LC-MS/MS method for measurement of chlorate ion at high concentration. The LC-MS/MS method was the most reproducible for chlorate concentrations below 0.025 M while the iodometric titration method employed was the most reproducible above 0.025 M. By using both methods, concentrations of chlorate can be measured over a wide range, from 0.7 microg L(-1) to 210 g L(-1) in hypochlorite ion solutions. Seven quenching agents were also evaluated for their ability to neutralize hypochlorite ion, thereby stopping formation of perchlorate ion in solution, without adversely impacting the other oxyhalide ions. Malonic acid was chosen as the quenching agent of choice, meeting all evaluation criteria outlined in this manuscript. Copyright 2009 Elsevier B.V. All rights reserved.
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.
Rapid forecasting of tsunami runup heights from 2-D numerical simulations
Directory of Open Access Journals (Sweden)
B. H. Choi
2011-03-01
Full Text Available We propose a method to compute tsunami runup heights that is based on an integration of numerical, 2-D shallow-water modelling and an analytical, 1-D long-wave runup theory. This approach provides a faster forecast of tsunami runup heights than a complicated coastal inundation model. Through simulations of potential tsunami scenarios, this approach can also be applied to long-term tsunami prediction. We tested the model by simulating the historical event in the East (Japan Sea and found that the estimates of runup heights agreed well with the available observations.
Lin, P.; Pratt, D. T.
1987-01-01
A hybrid method has been developed for the numerical prediction of turbulent mixing in a spatially-developing, free shear layer. Most significantly, the computation incorporates the effects of large-scale structures, Schmidt number and Reynolds number on mixing, which have been overlooked in the past. In flow field prediction, large-eddy simulation was conducted by a modified 2-D vortex method with subgrid-scale modeling. The predicted mean velocities, shear layer growth rates, Reynolds stresses, and the RMS of longitudinal velocity fluctuations were found to be in good agreement with experiments, although the lateral velocity fluctuations were overpredicted. In scalar transport, the Monte Carlo method was extended to the simulation of the time-dependent pdf transport equation. For the first time, the mixing frequency in Curl's coalescence/dispersion model was estimated by using Broadwell and Breidenthal's theory of micromixing, which involves Schmidt number, Reynolds number and the local vorticity. Numerical tests were performed for a gaseous case and an aqueous case. Evidence that pure freestream fluids are entrained into the layer by large-scale motions was found in the predicted pdf. Mean concentration profiles were found to be insensitive to Schmidt number, while the unmixedness was higher for higher Schmidt number. Applications were made to mixing layers with isothermal, fast reactions. The predicted difference in product thickness of the two cases was in reasonable quantitative agreement with experimental measurements.
Fostering Scientific and Numerate Practices in Journalism to Support Rapid Public Learning
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Louise Yarnall
2017-01-01
Full Text Available Journalism has the potential––and arguably the mandate––to expand public understanding of societally important phenomena. However, some methods for more effectively educating the public have been persistently underutilized: in particular, embedding informative numerical rates and efficient scientific explanations in news reports. In the current era of disrupting and downsizing the news business, the challenges to using such methods have only increased. To address this problem, this article seeks to (a raise awareness about the psychological reasons that help explain why it is crucial to use such elements in news reports, and (b exhibit some methods for doing so that require modest effort. Building on a review of relevant psychological literatures, principles, and existing reporting methods, we describe findings from a series of cognitive-scientific studies that demonstrate how using key––and relatively minimal––scientific and numerical elements can enhance public learning from news reports. We conclude by also describing curricula and resources designed to help journalists and bloggers use these methods.
Qin, Jianyuan; Xie, Lijuan; Ying, Yibin
2017-06-01
Despite numerous methods for the detection of antibiotic residues, they are usually destructive and require tedious pre-treatment. Terahertz time-domain spectroscopy (THz-TDS) is an emerging technology that has advantages for analyzing chemical and biological compounds since THz waves are very sensitive to the molecular vibrational modes. Here we incorporated attenuated total reflection technique into the THz-TDS and demonstrated that this technology (ATR THz-TDS) allowed to determine the complex refractive indices of tetracycline hydrochloride (TCH) solutions with high accuracy and could be used to predict their concentrations. Our results from the simple linear regression models indicated that the complex refractive index exhibited a monotonic decrease with an increase in the TCH concentration. This study will provide new knowledge about the concentration determination of a liquid sample that couldn't be elucidated with the conventional THz-TDS technologies. Copyright © 2016 Elsevier Ltd. All rights reserved.
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 the rapid solidification of gas-atomized Al-8 wt pct Fe droplets
Energy Technology Data Exchange (ETDEWEB)
Kim, S.G. (Kunsan National Univ. (Korea, Republic of)); Shin, S.H. (Sammi Steel Corp., Changwon (Korea, Republic of). Central Research Inst.); Suzuki, Toshio; Umeda, Takateru (Univ. of Tokyo (Japan). Dept. of Metallurgy)
1994-12-01
A numerical analysis of the microstructural evolution of microcellular and cellular [alpha]-Al phase in gas-atomized Al-8 wt pct Fe droplets was represented. The two-dimensional (2-D) non-Newtonian heat transfer and the dendritic growth theory in the undercooled melt were combined, assuming a point nucleation on the droplet surface and the macroscopically smooth solid-liquid interface enveloping the cell tips. It reproduced the main characteristic features of the reported microstructures quite well and predicted a considerable volume fraction of thermal dendritic growth region in a droplet smaller than 10[mu]m if an initial undercooling was larger than 100 K. The volume fractions of the microcellular region, g[sub A], and the sum of the microcellular and cellular region, g[sub [alpha
Novel micronisation β-carotene using rapid expansion supercritical solution with co-solvent
Kien, Le Anh
2017-09-01
Rapid expansion of supercritical solution (RESS) is the most common approach of pharmaceutical pacticle forming methods using supercritical fluids. The RESS method is a technology producing a small solid product with a very narrow particle size distribution, organic solvent-free particles. This process is also simple and easy to control the operating parameters in comparision with other ways based on supercritical techniques. In this study, β-carotene, a strongly colored red-orange pigment abundant in plants and fruits, has been forming by RESS. In addition, the size and morphology effect of four different RESS parameters including co-solvent, extraction temperature, and extraction pressure and expansion nozzle temperature has surveyed. The particle size distribution has been determined by using laser diffraction experiment. SEM has conducted to analyze the surface structure, DSC and FTIR for thermal and chemical structure analysis.
Micronization of phenylbutazone by rapid expansion of supercritical CO2 solution.
Moribe, Kunikazu; Tsutsumi, Shun-ichiro; Morishita, Shoko; Shinozaki, Hiroshi; Tozuka, Yuichi; Oguchi, Toshio; Yamamoto, Keiji
2005-08-01
Rapid expansion of supercritical solutions (RESS) technique was applied for the preparation of phenylbutazone fine particles. The operating temperature and pressure affected the yield of the drug fine particles, which was evaluated by dissolving the sprayed product of drug into ethanol. Effect of pre- and post-expansion conditions on the particle size distribution of phenylbutazone was investigated and the smallest sample (mean particle size: 1.59 microm) was obtained when the RESS method was operated at a pressure of 26 MPa combined with a temperature of 32 degrees C. Physicochemical properties of the fine particles were investigated by powder X-ray diffraction and differential scanning calorimetry. It was found that the phenylbutazone fine particles obtained were meta-stable beta form under the experimental conditions tested, suggesting polymorphic transformation during the RESS process.
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).
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
Andresa Pescador
2016-04-01
Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
Panou G.
2017-02-01
Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.
A Rapid and Simple TLC-Densitometric Method for Assay of Clobetasol Propionate in Topical Solution.
Dolowy, Malgorzata; Kozik, Violetta; Bak, Andrzej; Jampilek, Josef; Barbusinski, Krzysztof; Thomas, Maciej; Pyka-Pajak, Alina
2017-11-03
A rapid, simple to use and low-cost thin-layer chromatographic procedure in normal phase system with densitometric detection at 246 nm was carefully validated according to the International Conference on Harmonisation (ICH) guidelines for assay of clobetasol propionate in topical solution containing clobetasol propionate in quantity 0.50 mg/mL. The adopted thin-layer chromatographic (TLC)-densitometric procedure could effectively separate clobetasol propionate from its related compound, namely clobetasol. It is linear for clobetasol propionate in the range of 0.188 ÷ 5 µg/spot. The limit of detection (LOD) and limit of quantification (LOQ) value is 0.061 and 0.186 µg/spot, respectively. Accuracy of proposed procedure was evaluated by recovery test. The mean recovery of studied clobetasol propionate ranges from 98.7 to 101.0%. The coefficient of variation (CV, %) obtained during intra-day and inter-day studies, which was less than 2% (0.40 ÷ 1.17%), confirms the precision of described method. The assay value of clobetasol propionate is consistent with the pharmacopoeial requirements. In conclusion, it can be suitable as a simple and economic procedure for routine quality control laboratories of clobetasol propionate in topical solution.
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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.
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.
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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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.
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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)
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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.
Rapid dechlorination of chlorophenols in aqueous solution by [Ni|Cu] microcell
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Yin, Lifeng, E-mail: yinlifeng@gmail.com [State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875 (China); Dai, Yunrong, E-mail: daiyunrong@mail.bnu.edu.cn [State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875 (China); Niu, Junfeng, E-mail: junfengn@bnu.edu.cn [State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875 (China); Bao, Yueping, E-mail: baoyueping@mail.bnu.edu.cn [State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875 (China); Shen, Zhenyao, E-mail: zyshen@bnu.edu.cn [State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875 (China)
2012-03-30
Highlights: Black-Right-Pointing-Pointer Rapid dechlorination of chlorophenols in aqueous solution can be achieved by [Ni|Cu] mixture. Black-Right-Pointing-Pointer The decomposition rates of chlorophenols by [Ni|Cu] were decuple of that by [Fe|Ni], [Fe|Cu], [Zn|Cu], or [Sn|Cu]. Black-Right-Pointing-Pointer Ni{sup 0} acts as an indirect reductant and catalyst in dechlorination reaction. Black-Right-Pointing-Pointer The H* corridor mechanism from Ni to Cu is proposed based on hydrogen spillover. - Abstract: The [Ni|Cu] microcell was prepared by mixing the Ni{sup 0} and Cu{sup 0} particles. The composition and crystal form were characterized by X-ray diffraction (XRD) and scanning electron microscope. The results evidenced the zero-valence metals Ni and Cu were exposed on the surface of particles mixture. The [Ni|Cu] microcell was employed to decompose chlorophenols in aqueous solution by reductive dechlorination. The dechlorination rates of chlorophenols by [Ni|Cu] were >10 times faster than those by [Fe|Cu], [Zn|Cu], [Sn|Cu], and [Fe|Ni] mixtures under the same conditions. [Ni|Cu] is different from other zero valent metals (ZVMs) in that it performed the best at neutral pH. The main products of chlorophenol dechlorination were cyclohexanol and cyclohexanone. The reduction kinetics was between pseudo zero-order and first-order, depending on the pH, concentration, and temperature. These results, combined with electrochemical analysis, suggested that Ni{sup 0} acted as a reductant and catalyst in dechlorination reaction. The H* corridor mechanism from Ni{sup 0} to Cu{sup 0} was also proposed based on hydrogen spillover. The inhibition on the release of Ni{sup 2+} by adding natural organic matters and adjusting pH was investigated.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
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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 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.
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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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.
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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.
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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.
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).
Ullah, Sana; De Matteis, Fabio; Davoli, Ivan
2017-11-01
Transparent conducting oxide films with optimized dopant molar ratio have been prepared with limited pre- and postdeposition annealing duration of 10 min. Multiple aluminum zinc oxide (AZO) layers were spin-coated on ordinary glass substrates. The predeposition consolidation temperature and dopant molar ratio were optimized for electrical conductivity and optical transparency. Next, a group of films were deposited on Corning glass substrates from precursor solutions with the optimized dopant ratio, followed by postdeposition rapid thermal annealing (RTA) at different temperatures and in controlled environments. The lowest resistivity of 10.1 × 10-3 Ω cm was obtained for films receiving RTA at 600°C for 10 min each in vacuum then in N2-5%H2 environment, while resistivity of 20.3 × 10-3 Ω cm was obtained for films subjected to RTA directly in N2-5%H2. Optical measurements revealed average total transmittance of about 85% in the visible region. A direct allowed transition bandgap was determined based on the absorption edge with a value slightly above 3.0 eV, within the typical range for semiconductors. RTA resulted in desorption of oxygen with enhanced carrier concentration and crystallinity, which increased the carrier mobility with decreased bulk resistivity while maintaining the required optical transparency.
Mass Housing Using GFRG Panels: A Sustainable, Rapid and Affordable Solution
Cherian, Philip; Paul, Shinto; Krishna, S. R. Gouri; Menon, Devdas; Meher Prasad, A.
2017-06-01
This work gives an overview of research and development carried out at IIT Madras, using glass fibre reinforced gypsum (GFRG) panels, to provide an innovative solution for rapid and affordable mass housing. The GFRG panels (124 mm thick), made from recycled industrial waste gypsum (from the fertilizer industry), are prefabricated in 3 m × 12 m sizes with cellular cavities inside, which can be filled with reinforced concrete wherever required and can be used as walls as well as floor slabs. The tests carried out (over the past 12 years) establish the performance of GFRG building systems to resist gravity and lateral loads as a load-bearing system (without beams and columns) in multi-storeyed buildings up to 8-10 storeys, with adequate strength, serviceability, durability and ductility. A two-storeyed four-apartment demonstration building has also been successfully constructed in the IIT Madras campus and presently a mass housing scheme (40 apartment units) using this technology is being demonstrated at Nellore. A structural design code has also been approved by the Bureau of Indian Standards, based on the extensive studies carried out on GFRG building systems.
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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
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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.
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.
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.
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.
Bänsch, Eberhard; Reismann, Simone; Lee, Geoffrey
2014-08-01
A numerical solution of the one-dimensional diffusion equation is presented to describe the 5-layer laminate technique for estimating the saturation solubility of a drug in a thin polymer film. The boundary and initial conditions encompass a donor layer, a separating membrane, and an acceptor layer. Alteration of the drug's partition coefficient between donor and separating membrane has little influence on drug accumulation with the acceptor. The diffusivity in the separating membrane should be high to promote a short experimental time to achieve saturation equilibrium in the acceptor layer. The essential parameter to give rapid equilibrium is the thickness of the acceptor polymer film. For values of diffusivity typical for drugs of molecular weight around 500 an acceptor layer thickness of 10 µm-20 µm is required to achieve equilibrium within less than 10 d. These simulations allow the selection of suitable experimental conditions to make the 5-layer laminate technique a viable method for routine use.
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.
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 ...
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.
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
Directory of Open Access Journals (Sweden)
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.
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...
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Xiaonan Zhang
2012-04-01
Full Text Available The particle sizes of pharmaceutical substances are important for their bioavailability. Bioavailability can be improved by reducing the particle size of the drug. In this study, artemisinin was micronized by the rapid expansion of supercritical solutions (RESS. The particle size of the unprocessed white needle-like artemisinin particles was 30 to 1200 µm. The optimum micronization conditions are determined as follows: extraction temperature of 62 °C, extraction pressure of 25 MPa, precipitation temperature 45 °C and nozzle diameter of 1000 μm. Under the optimum conditions, micronized artemisinin with a (mean particle size MPS of 550 nm is obtained. By analysis of variance (ANOVA, extraction temperature and pressure have significant effects on the MPS of the micronized artemisinin. The particle size of micronized artemisinin decreased with increasing extraction temperature and pressure. Moreover, the SEM, LC-MS, FTIR, DSC and XRD allowed the comparison between the crystalline initial state and the micronization particles obtained after the RESS process. The results showed that RESS process has not induced degradation of artemisinin and that processed artemisinin particles have lower crystallinity and melting point. The bulk density of artemisinin was determined before and after RESS process and the obtained results showed that it passes from an initial density of 0.554 to 0.128 g·cm^{−3} after the processing. The decrease in bulk density of the micronized powder can increase the liquidity of drug particles when they are applied for medicinal preparations. These results suggest micronized powder of artemisinin can be of great potential in drug delivery systems.
Rapid adsorption of Pb, Cu and Cd from aqueous solutions by β-cyclodextrin polymers
He, Junyong; Li, Yulian; Wang, Chengming; Zhang, Kaisheng; Lin, Dongyue; Kong, Lingtao; Liu, Jinhuai
2017-12-01
Removing heavy metals from aqueous solutions has drawn more and more attentions these years because of their serious global health challenge to human society. To develop an adsorbent with low-cost and high-efficiency for removal of heavy metals (HMs), β-cyclodextrin (β-CD) polymers crosslinked with rigid aromatic groups were prepared and used for lead (Pb), copper (Cu) and cadmium (Cd) removal for the first time. The negatively charged β-CD polymers with large BET surface area were suitable to be used in HMs adsorption. The adsorption process completed in 5 min was well fit by Freundlich isotherm model and pseudo-second-order model. The intraparticle diffusion model was also appropriate to describe the adsorption of Pb, Cu and Cd on β-CD polymer. The maximum of adsorption capacities at 25 °C for Pb, Cu and Cd were 196.42, 164.43 and 136.43 mg/g when the initial concentration was 200 mg/L. The HMs adsorption process on the surface of β-CD polymer was an endothermic and spontaneous process. Both of the electrostatic interaction and distribution of Pb, Cu and Cd species influenced the adsorption process at different pH values. The order of removal efficiencies in multi-component adsorption for the three metal ions were Pb > Cu > Cd. The adsorption mechanisms were H+ ions on hydroxyl groups exchanged with heavy metal ions and electrostatic interactions. This study indicated that β-CD polymers could be developed into effective adsorbents for rapid removal of heavy metals.
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…
Rim, Jung H.
Accurate and fast determination of the activity of radionuclides in a sample is critical for nuclear forensics and emergency response. Radioanalytical techniques are well established for radionuclides measurement, however, they are slow and labor intensive, requiring extensive radiochemical separations and purification prior to analysis. With these limitations of current methods, there is great interest for a new technique to rapidly process samples. This dissertation describes a new analyte extraction medium called Polymer Ligand Film (PLF) developed to rapidly extract radionuclides. Polymer Ligand Film is a polymer medium with ligands incorporated in its matrix that selectively and rapidly extract analytes from a solution. The main focus of the new technique is to shorten and simplify the procedure necessary to chemically isolate radionuclides for determination by alpha spectrometry or beta counting. Five different ligands were tested for plutonium extraction: bis(2-ethylhexyl) methanediphosphonic acid (H2DEH[MDP]), di(2-ethyl hexyl) phosphoric acid (HDEHP), trialkyl methylammonium chloride (Aliquat-336), 4,4'(5')-di-t-butylcyclohexano 18-crown-6 (DtBuCH18C6), and 2-ethylhexyl 2-ethylhexylphosphonic acid (HEH[EHP]). The ligands that were effective for plutonium extraction further studied for uranium extraction. The plutonium recovery by PLFs has shown dependency on nitric acid concentration and ligand to total mass ratio. H2DEH[MDP] PLFs performed best with 1:10 and 1:20 ratio PLFs. 50.44% and 47.61% of plutonium were extracted on the surface of PLFs with 1M nitric acid for 1:10 and 1:20 PLF, respectively. HDEHP PLF provided the best combination of alpha spectroscopy resolution and plutonium recovery with 1:5 PLF when used with 0.1M nitric acid. The overall analyte recovery was lower than electrodeposited samples, which typically has recovery above 80%. However, PLF is designed to be a rapid field deployable screening technique and consistency is more important
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).
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 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 ...
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...
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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.
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.
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.
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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...
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...
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.
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.
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.
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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
Moore, Tracy M; Callaway, Clifton W; Hostler, David
2008-02-01
Studies have suggested that inducing mild hypothermia improves neurologic outcomes after traumatic brain injury, major stroke, traumatic hemorrhage, and cardiac arrest. Although infusion of cold normal saline solution is a simple and inexpensive method for initiating hypothermia, human cold-defense mechanisms potentially make this route stressful or ineffective. We hypothesize that rapid infusion of 30 mL/kg of cold (4 degrees C, 39.2 degrees F) 0.9% saline solution during 30 minutes to healthy subjects (aged 27 [standard deviation (SD) 4] years) will reduce core body temperature to the therapeutic range of 33 degrees C to 35 degrees C (91.4 degrees F to 95 degrees F). Sixteen subjects were randomly assigned to receive either cold (4 degrees C, 39.2 degrees F) or room temperature (23 degrees C, 73.4 degrees F) normal saline solution. Subjects were not informed of their assignment, but blinding was not possible after initiation of the infusion. Core temperature, skin temperature, and vital signs were recorded every 2 minutes. Subjects indicated global discomfort during the infusion on a 100-mm visual analog scale at 5-minute intervals. Core temperature decreased in both the cold saline solution (1.0 degrees C [SD 0.4 degrees C]/1.8 degrees F [0.7 degrees F]) and room temperature saline solution (0.5 degrees C [SD 0.1 degrees C]/0.9 degrees F [0.2 degrees F]) groups, whereas skin temperature was unchanged. Slopes calculated from the core temperature cooling curves indicate that the majority of cooling occurred during the first half of the infusion. Examination of the core temperature cooling curves revealed a 2-phase temporal pattern in 30-minute cooling curves. The early phase, spanning 0 to 14 minutes, demonstrated rapid cooling in both groups, with a larger effect observed in subjects receiving cold saline solution. In this pilot study of healthy volunteers, rapid administration of cold saline solution to awake normothermic volunteers resulted in 1 degrees C (1
Rapid synthesis of CdSe nanocrystals in aqueous solution at room ...
Indian Academy of Sciences (India)
Administrator
NCs dispersed in buffer solution (pH = 4⋅0). FTIR spectra were recorded on a Nexus-470 spectrometer. The morpho- logy measurement was performed using a ... the CdSe solution becomes acidic, free thiols and cad- mium ions will be released from the cadmium thiol com- plexes, the relative coverage rate of the particle ...
A numerical solution for the entrance region of non-newtonian flow in annuli
Directory of Open Access Journals (Sweden)
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
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.
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
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
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.)
Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F
2010-07-01
Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.
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
Numerical Methods For Chemically Reacting Flows
Leveque, R. J.; Yee, H. C.
1990-01-01
Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.
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
Frampton, John P; Lai, David; Lounds, Maxwell; Chung, Kyeongwoon; Kim, Jinsang; Mansfield, John F; Takayama, Shuichi
2015-01-28
A simple method is presented for forming thread-like fibers from highly viscous dextran solutions. Based on the cohesive and adhesive forces between a dextran solution and the substrate to which it is applied, multiple fibers of approximately 10 μm in diameter can be elongated simultaneously. These fibers can be woven into multiple layers to produce fabrics of varying fiber orientations and mechanical properties. Various bioactive agents can be incorporated into the dextran solution prior to fiber formation, including hemostatic and antibiotic agents. Fabrics containing thrombin are capable of coagulating human platelet poor plasma in vitro. Fabrics containing antibiotics are capable of suppressing bacterial growth in a disk diffusion assay. These data suggest that this new material composed entirely of dextran has promise as a drug delivery component in wound dressings. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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
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.
2012-05-16
...The document advises that the interim rule for the Emergency Solutions Grants program, published on December 5, 2011, displayed an incorrect RIN number. This document advises of the correct RIN number, 2506-AC31, as displayed in the heading of this document.
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.
2016-03-31
views expressed in this academic research paper are those of the author and do not reflect the official policy or position of the US government, the...SORDAC) is the Department of Defense (DoD) leader in rapid acquisitions, and its culture and practices should be benchmarked by the other services. This...should be benchmarked by all other services. This essay first examines SORDAC’s acquisition environment and assesses SORDAC’s unique culture. This
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.
Liu, E H; Tan, Y; Loh, N H W; Siau, C
2016-05-01
Anaesthesia machine failure requires rapid solutions to maintain ventilation and anaesthesia. During procedures with poor access to the patient's airway, it may not be possible to use a self-inflating mechanical ventilation device (SIMVD) for emergency ventilation, and alternative solutions are needed. We evaluated five methods for rescue ventilation using a patient simulator. In Method 1, we used the inspiratory and expiratory tubes and the alternative common gas outlet (ACGO) on the anaesthesia machine to produce a Mapleson E system. In Method 2, we used the tubes, ACGO and an open-ended reservoir bag to produce a Mapleson F system, controlling the bag to achieve ventilation. In Method 3, we attached a SIMVD to the inspiratory tube, and controlled occlusion of the expiratory tube. In Method 4, we used the tubes and ACGO in a Mapleson F configuration, replacing the open-ended bag with a SIMVD to facilitate manual ventilation. In Method 5, we attached a SIMVD to the expiratory tube and left the inspiratory tube attached to its mounting. We were able to achieve ventilation, maintain inhalational anaesthesia, and prevent expired gas rebreathing in Methods 1 and 2. In Method 3 ventilation was achieved with minimal rebreathing of expiratory gas, but with no inhalational agent. Methods 4 and 5 led to rebreathing. Our findings indicate that Methods 1 or 2 are the preferred rapid solutions to maintain ventilation and inhalational anaesthesia in the event of anaesthesia machine failure where there is poor airway access.
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.
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.
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).
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.
Stahara, S. S.
1982-01-01
Stahara et al. (1978) have considered the use of an approximation technique which employs two or more nonlinear base solutions determined by the full computational method to predict entire families of related nonlinear solutions. The present investigation provides results for several applications of that method which demonstrate both its accuracy and its utility for engineering applications. Attention is given to the perturbation concept and methods, aspects of coordinate straining, aspects of analytical formulation, and an application to surface properties. In a discussion of the results, single and multiple parameter perturbations are considered along with a combination of the approximation method with optimization procedures. The results show that it is possible to combine in certain cases large savings in computational cost with improved optimization.
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.
Directory of Open Access Journals (Sweden)
Richard Picking
2012-03-01
Full Text Available This paper identifies the need for a secure military social networking site and the underlying research issues linked to the successful development of such sites. The paper further proposes a solution to the most basic issues by identifying and tackling known potential security threats to military personnel and their families. The paper further defines the base platform for this development to facilitate rapid sensemaking to inform critical communications and rapid decision making processes during abrupt governance and eco-system change, and how the plethora of information (termed as Big Data on social networking sites can be analysed and harnessed. Underlying architectural issues, efficiency and complexity are explored and their future development is considered.
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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.)
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.
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Heajeong Cheong
2015-06-01
Full Text Available We fabricated solution-processed indium–gallium–zinc oxide (IGZO thin-film transistors (TFTs by microwave (MW annealing an IGZO precursor film followed by irradiating with vacuum ultraviolet (VUV light. MW annealing allows more rapid heating of the precursor film than conventional annealing processes using a hot plate or electric oven and promotes the crystallization of IGZO. VUV irradiation was used to reduce the duration and temperature of the post-annealing step. Consequently, the IGZO TFTs fabricated through MW annealing for 5 min and VUV irradiation for 1 min exhibited an on/off current ratio of 108 and a field-effect mobility of 0.3 cm2 V−1 s−1. These results indicate that MW annealing and photoirradiation is an effective combination for annealing solution processed IGZO precursor films to prepare the semiconductor layers of TFTs.
Raghunandan, Deshpande; Bedre, Mahesh D; Basavaraja, S; Sawle, Balaji; Manjunath, S Y; Venkataraman, A
2010-08-01
In this paper, we stress upon rapid synthesis of irregular shape gold nanoparticles from a biological base. Treatment of macerated extracellular aqueous dried clove buds (Syzygium aromaticum) solution with the aqueous gold salt solution yielded irregular shaped stable gold nanoparticles in the range of 5-100 nm. The synthesis and morphology of these gold nanoparticles are understood by UV (UV-vis spectroscopy), FESEM (field emission scanning electron microscopy), TEM (transmission electron microscopy) and AFM (atomic force microscopy) techniques. The formation of these bio-adsorbed gold nanoparticles is rapid as the reaction process completes within few minutes. The XRD (X-ray diffraction studies) and EDAX (energy dispersive X-ray analysis) show that the particles are crystalline in nature. This clean-green method of synthesis is performed under ambient conditions. Probable biochemical pathway of the synthesis is studied using FTIR (Fourier transformed infrared spectroscopy). It is observed that the freely water soluble flavonoids of clove buds are responsible for bioreduction. The possible applications viz., catalysis, sensor, diagnostics, biomedical imaging and photo thermal therapy of these functionalized noble metal nanoparticles are envisaged. Copyright 2010 Elsevier B.V. All rights reserved.
Rapid imaging of mycoplasma in solution using Atmospheric Scanning Electron Microscopy (ASEM)
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Sato, Chikara, E-mail: ti-sato@aist.go.jp [Biomedical Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8566 (Japan); Manaka, Sachie [Biomedical Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8566 (Japan); Nakane, Daisuke [Department of Biology, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka 558-8585 (Japan); Nishiyama, Hidetoshi; Suga, Mitsuo [Advanced Technology Division, JEOL Ltd., Akishima, Tokyo 196-8558 (Japan); Nishizaka, Takayuki [Department of Physics, Faculty of Science, Gakushuin University, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-8588 (Japan); Miyata, Makoto [Department of Biology, Graduate School of Science, Osaka City University, Sumiyoshi-ku, Osaka 558-8585 (Japan); Maruyama, Yuusuke [Biomedical Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8566 (Japan)
2012-01-27
Highlights: Black-Right-Pointing-Pointer Mycoplasma mobile was observed in buffer with the Atmospheric Scanning Electron Microscope. Black-Right-Pointing-Pointer Characteristic protein localizations were visualized using immuno-labeling. Black-Right-Pointing-Pointer M. mobile attached to sialic acid on the SiN film surface within minutes. Black-Right-Pointing-Pointer Cells were observed at low concentrations. Black-Right-Pointing-Pointer ASEM should promote study and early-stage diagnosis of mycoplasma. -- Abstract: Mycoplasma is a genus of bacterial pathogen that causes disease in vertebrates. In humans, the species Mycoplasma pneumoniae causes 15% or more of community-acquired pneumonia. Because this bacterium is tiny, corresponding in size to a large virus, diagnosis using optical microscopy is not easy. In current methods, chest X-rays are usually the first action, followed by serology, PCR amplification, and/or culture, but all of these are particularly difficult at an early stage of the disease. Using Mycoplasma mobile as a model species, we directly observed mycoplasma in buffer with the newly developed Atmospheric Scanning Electron Microscope (ASEM). This microscope features an open sample dish with a pressure-resistant thin film window in its base, through which the SEM beam scans samples in solution, from below. Because of its 2-3 {mu}m-deep scanning capability, it can observe the whole internal structure of mycoplasma cells stained with metal solutions. Characteristic protein localizations were visualized using immuno-labeling. Cells were observed at low concentrations, because suspended cells concentrate in the observable zone by attaching to sialic acid on the silicon nitride (SiN) film surface within minutes. These results suggest the applicability of the ASEM for the study of mycoplasmas as well as for early-stage mycoplasma infection diagnosis.
Zhang, Qian; Xiong, Wei; Chen, Yu-Qi; Li, Run-Hua
2011-02-01
A wood slice was used as absorber to transfer liquid sample to solid sample in order to solve the problems existing in directly analyzing aqueous solutions with laser-induced breakdown spectroscopy (LIBS). An optical-electrical dual pulse LIBS (OEDP-LIBS) technique was first used to enhance atomic emission of mercury in laser-induced plasma. The calibration curves of mercury were obtained by typical single pulse LIBS and OEDP-LIBS techniques. The limit of detection (LOD) of mercury in these two techniques reaches 2.4 and 0.3 mg x L(-1), respectively. Under current experimental conditions, the time-integrated a tomic emission of mercury at 253.65 nm was enhanced 50 times and the LOD of mercury was improved by one order, if comparing OEDP-LIBS to single pulse LIBS. The required time for a whole analysis process is less than 5 minutes. As the atomic emission of mercury decays slowly while increasing the delay time between electrical pulse and laser pulse, increasing the electrical pulse width can further enhance the time integrated intensity of mercury emission and improve the detection sensitivity of mercury by OEDP-LIBS technique.
Rapid and molecular selective electrochemical sensing of phthalates in aqueous solution
Zia, Asif I.
2015-05-01
Reported research work presents real time non-invasive detection of phthalates in spiked aqueous samples by employing electrochemical impedance spectroscopy (EIS) technique incorporating a novel interdigital capacitive sensor with multiple sensing thin film gold micro-electrodes fabricated on native silicon dioxide layer grown on semiconducting single crystal silicon wafer. The sensing surface was functionalized by a self-assembled monolayer of 3-aminopropyltrietoxysilane (APTES) with embedded molecular imprinted polymer (MIP) to introduce selectivity for the di(2-ethylhexyl) phthalate (DEHP) molecule. Various concentrations (1-100. ppm) of DEHP in deionized MilliQ water were tested using the functionalized sensing surface to capture the analyte. Frequency response analyzer (FRA) algorithm was used to obtain impedance spectra so as to determine sample conductance and capacitance for evaluation of phthalate concentration in the sample solution. Spectrum analysis algorithm interpreted the experimentally obtained impedance spectra by applying complex nonlinear least square (CNLS) curve fitting in order to obtain electrochemical equivalent circuit and corresponding circuit parameters describing the kinetics of the electrochemical cell. Principal component analysis was applied to deduce the effects of surface immobilized molecular imprinted polymer layer on the evaluated circuit parameters and its electrical response. The results obtained by the testing system were validated using commercially available high performance liquid chromatography diode array detector system.
Gabardo, Christine M; Adams-McGavin, Robert C; Fung, Barnabas C; Mahoney, Eric J; Fang, Qiyin; Soleymani, Leyla
2017-02-13
Three-dimensional electrodes that are controllable over multiple lengthscales are very important for use in bioanalytical systems that integrate solid-phase devices with solution-phase samples. Here we present a fabrication method based on all-solution-processing and thin film wrinkling using smart polymers that is ideal for rapid prototyping of tunable three-dimensional electrodes and is extendable to large volume manufacturing. Although all-solution-processing is an attractive alternative to vapor-based techniques for low-cost manufacturing of electrodes, it often results in films suffering from low conductivity and poor substrate adhesion. These limitations are addressed here by using a smart polymer to create a conformal layer of overlapping wrinkles on the substrate to shorten the current path and embed the conductor onto the polymer layer. The structural evolution of these wrinkled electrodes, deposited by electroless deposition onto a nanoparticle seed layer, is studied at varying deposition times to understand its effects on structural parameters such as porosity, wrinkle wavelength and height. Furthermore, the effect of structural parameters on functional properties such as electro-active surface area and surface-enhanced Raman scattering is investigated. It is found that wrinkling of electroless-deposited thin films can be used to reduce sheet resistance, increase surface area, and enhance the surface-enhanced Raman scattering signal.
Gabardo, Christine M.; Adams-McGavin, Robert C.; Fung, Barnabas C.; Mahoney, Eric J.; Fang, Qiyin; Soleymani, Leyla
2017-02-01
Three-dimensional electrodes that are controllable over multiple lengthscales are very important for use in bioanalytical systems that integrate solid-phase devices with solution-phase samples. Here we present a fabrication method based on all-solution-processing and thin film wrinkling using smart polymers that is ideal for rapid prototyping of tunable three-dimensional electrodes and is extendable to large volume manufacturing. Although all-solution-processing is an attractive alternative to vapor-based techniques for low-cost manufacturing of electrodes, it often results in films suffering from low conductivity and poor substrate adhesion. These limitations are addressed here by using a smart polymer to create a conformal layer of overlapping wrinkles on the substrate to shorten the current path and embed the conductor onto the polymer layer. The structural evolution of these wrinkled electrodes, deposited by electroless deposition onto a nanoparticle seed layer, is studied at varying deposition times to understand its effects on structural parameters such as porosity, wrinkle wavelength and height. Furthermore, the effect of structural parameters on functional properties such as electro-active surface area and surface-enhanced Raman scattering is investigated. It is found that wrinkling of electroless-deposited thin films can be used to reduce sheet resistance, increase surface area, and enhance the surface-enhanced Raman scattering signal.
Directory of Open Access Journals (Sweden)
L. Malgaca
2009-01-01
Full Text Available Piezoelectric smart structures can be modeled using commercial finite element packages. Integration of control actions into the finite element model solutions (ICFES can be done in ANSYS by using parametric design language. Simulation results can be obtained easily in smart structures by this method. In this work, cantilever smart structures consisting of aluminum beams and lead-zirconate-titanate (PZT patches are considered. Two cases are studied numerically and experimentally in parallel. In the first case, a smart structure with a single PZT patch is used for the free vibration control under an initial tip displacement. In the second case, a smart structure with two PZT patches is used for the forced vibration control under harmonic excitation, where one of the PZT patches is used as vibration generating shaker while the other is used as vibration controlling actuator. For the two cases, modal analyses are done using chirp signals; Control OFF and Control ON responses in the time domain are obtained for various controller gains. A non-contact laser displacement sensor and strain gauges are utilized for the feedback signals. It is observed that all the simulation results agree with the experimental results.
Directory of Open Access Journals (Sweden)
Muhammad Awais
Full Text Available Analysis has been done to investigate the heat generation/absorption effects in a steady flow of non-Newtonian nanofluid over a surface which is stretching linearly in its own plane. An upper convected Maxwell model (UCM has been utilized as the non-Newtonian fluid model in view of the fact that it can predict relaxation time phenomenon which the Newtonian model cannot. Behavior of the relaxations phenomenon has been presented in terms of Deborah number. Transport phenomenon with convective cooling process has been analyzed. Brownian motion "Db" and thermophoresis effects "Dt" occur in the transport equations. The momentum, energy and nanoparticle concentration profiles are examined with respect to the involved rheological parameters namely the Deborah number, source/sink parameter, the Brownian motion parameters, thermophoresis parameter and Biot number. Both numerical and analytic solutions are presented and found in nice agreement. Comparison with the published data is also made to ensure the validity. Stream lines for Maxwell and Newtonian fluid models are presented in the analysis.
Energy Technology Data Exchange (ETDEWEB)
Cheng, C.Z.
1988-12-01
A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical ..beta../sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab.
Directory of Open Access Journals (Sweden)
Parovik Roman I.
2016-09-01
Full Text Available The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution.
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.
DeChant, Lawrence J.
1997-01-01
In spite of the rapid advances in both scalar and parallel computational tools, the large number and breadth of variables involved in aerodynamic systems make the use of parabolized or even boundary layer fluid flow models impractical for both preliminary design and inverse design problems. Given this restriction, we have concluded that reduced or approximate models are an important family of tools for design purposes. This study of a combined perturbation/numerical modeling methodology with an application to ejector-mixer nozzles (shown schematically in the following figure) is nearing completion. The work is being funded by a grant from the NASA Lewis Research Center to Texas A&M University. These ejector-mixer nozzle models are designed to be of use to the High Speed Civil Transport Program and may be adopted by both NASA and industry. A computer code incorporating the ejector-mixer models is under development. This code, the Differential Reduced Ejector/Mixer Analysis (DREA), can be run fast enough to be used as a subroutine or to be called by a design optimization routine. Simplified conservation equations--x-momentum, energy, and mass conservation--are used to define the model. Unlike other preliminary design models, DREA requires minimal empirical input and includes vortical mixing and a fully compressible formulation among other features. DREA is being validated by comparing it with results obtained from open literature and proprietary industry data. Preliminary results for a subsonic ejector and a supersonic ejector are shown. In addition, dedicated experiments have been performed at Texas A&M. These experiments use a hydraulic/gas flow analog to provide information about the inviscid mixing interface structure. Final validation and documentation of this work is expected by May of 1997. However, preliminary versions of DREA can be expected in early 1997. In summary, DREA provides a sufficiently detailed and realistic ejector-mixer nozzle model at a
Energy Technology Data Exchange (ETDEWEB)
1994-05-01
The research conducted by Textron Defense Systems (TDS) represents a potential new and innovative concept for dispersed coal liquefaction. The technical approach is generation of ultra-fine catalyst particles from supercritical solutions by rapid expansion of either catalyst only, or mixtures of catalyst and coal material in supersaturated solvents. The process of rapid expansion of supercritical fluid solutions was developed at Battelle`s Pacific Northwest Laboratories for the intended purpose of providing a new analytical technique for characterizing supercritical fluids. The concept forming the basis of this research is that ultra-fine particles can be generated from supercritical solutions by rapid expansion of either catalyst or catalyst/coal-material mixtures in supersaturated solvents, such as carbon dioxide or water. The focal point of this technique is the rapid transfer of low vapor pressure solute (i.e., catalyst), dissolved in the supercritical fluid solvent, to the gas phase as the solution is expanded through an orifice. The expansion process is characterized by highly nonequilibrium conditions which cause the solute to undergo extremely rapid supersaturation with respect to the solvent, leading to nucleation and particle growth resulting in nanometer size catalyst particles. A supercritical expansion system was designed and built by TDS at their Haverhill facility.
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Peige Qin
2017-12-01
Full Text Available In this work, a highly efficient and rapid method for simultaneously removing cationic dyes from aqueous solutions was developed by using monodispersed mesoporous silica nanoparticles (MSNs as the adsorbents. The MSNs were prepared by a facile one-pot method and characterized by scanning electron microscopy, transmission electron microscopy, Fourier-transform infrared spectroscopy, and Brunauer-Emmett-Teller. Experimental results demonstrated that the as-prepared MSNs possessed a large specific surface area (about 585 m2/g, uniform particle size (about 30 nm, large pore volume (1.175 cm3/g, and narrow pore size distribution (1.68 nm. The materials showed highly efficient and rapid adsorption properties for cationic dyes including rhodamine B, methylene blue, methyl violet, malachite green, and basic fuchsin. Under the optimized conditions, the maximum adsorption capacities for the above mentioned cationic dyes were in the range of 14.70 mg/g to 34.23 mg/g, which could be achieved within 2 to 6 min. The probable adsorption mechanism of MSNs for adsorption of cationic dyes is proposed. It could be considered that the adsorption is mainly controlled by electrostatic interactions and hydrogen bonding between the cationic dyes and MSNs. As a low-cost, biocompatible, and environmentally friendly material, MSNs have a potential application in wastewater treatment for removing some environmental cationic contaminants.
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Gonzalez Gonzalez, A.; Rubayo Soneira, J.; Portuondo Campa, E.
2001-07-01
In this work the use of numerical methods in the solution of physics academic problems is discussed, particularly those on classical mechanics. Frequently the solution of academic problems is limited to finding a differential equation which is left unsolved for having no analytical solution. However, by means of numerical methods we can solve these equations and enrich the physical analysis of the problem. This approach also makes the academic process a little closer to modern physical research, where numerical methods have increasingly been used in almost every field. In the present paper we discuss a classical mechanics problem using these methods. We start from both Newton's and Lagrange's formulations and apply different numerical algorithms in the solution of the obtained equations. During last academic semester, recently concluded, we tested the ideas of this work with students of Nuclear Physics career of the Higher Institute of Nuclear Sciences and technologies, at Havana, cuba. The results were encouraging. (Author) 7 refs.
Abrashkevich, Alexander; Puzynin, I. V.
2004-01-01
A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program. Program summaryTitle of program: CANM Catalogue number: ADSN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSN Program available from: CPC Program Library, Queen's University of Belfast, Northern Ireland Licensing provisions: none Computer for which the program is designed and others on which it has been tested: Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PC Installation: Department of Chemistry, University of Toronto, Toronto, Canada Operating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7 Programming language used: FORTRAN 90 Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KB No. of bits in distributed program including test data, etc.: 15283 Distribution format: tar gz format No. of lines in distributed program, including test data, etc.: 1794 Peripherals used: line printer, scratch disc store External subprograms used: DGECO and DGESL [1] Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's method Nature of physical problem: System of nonlinear simultaneous equations F i(x 1,x 2,…,x n)=0,1⩽i⩽n, is numerically solved. It can be written in vector form as F( X)= 0, X∈ Rn, where F : Rn→ Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of
Rao, G Shanker
2006-01-01
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...
Shibata, Masaru
2016-01-01
This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.
Khabaza, I M
1960-01-01
Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in comput
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.
Mail, Noor; Albarakati, Y.; Khan, M. Ahmad; Saeedi, F.; Safadi, N.; Al-Ghamdi, S.; Saoudi, A.
2012-03-01
In this study, we investigate the effect of dental filling materials (DFM) on RapidArcTM treatment plans and delivery in a patient undergoing radiotherapy treatment. The presence of DFM creates uncertainties in CT number and causes long streaking artifacts in the reconstructed images which greatly affect the dose distribution inside the oral cavity. The influence of extensive dental filling artifacts on dose distribution was performed using a geometrically well defined head and neck IMRT verification phantom (PTW, Freiburg, Germany) together with inserts from DFM (Amalgam, 11.3 g/cm3). The phantom was scanned using Siemens SOMATOM Sensation CT simulator (Siemens AG, Germany) under standard head and neck imaging protocol (120 kV, 120 mAs, voxel size 1×1×2 mm3). Three RapidArcTM plans were created in the Varian Eclipse treatment planning System (TPS) to treat oral cavity using the same CT dataset including; 1) raw CT image, 2) streaking artifacts replaced with a mask of 10 HU and 3) 2 cm thick 6000 HU virtual filter (a volume around the teeth in TPS to mimic extra attenuation). The virtual filter thickness optimization was purely based on measured PDD data acquired with DFM and the calculation in Eclipse Planning System using direct beam. The dose delivery and distribution for the three plans was verified using Gafchromic EBT2 (International Specialty Product, Wayne, NJ, USA) film measurements. The artifact mask and virtual filter around the teeth in the planning was found very useful to reduce the discrepancies between the dose plan and delivery. From clinical point of view, these results can be helpful to understand the increase of mucositis in patient having DFM, and further investigation is underway for clinical solution.
Sweeney, Kristin; Roering, Joshua J.
2016-01-01
Volcanic eruptions fundamentally alter landscapes, paving over channels, decimating biota, and emplacing fresh, unweathered material. The fluvial incision of blocky lava flows is a geomorphic puzzle. First, high surface permeability and lack of sediment should preclude geomorphically effective surface runoff and dissection. Furthermore, past work has demonstrated the importance of extreme floods in driving incision via column toppling and plucking in columnar basalt, but it is unclear how incision occurs in systems where surface blocks are readily mobile. We examine rapid fluvial incision of the Collier lava flow, an andesitic Holocene lava flow in the High Cascades of Oregon. Since lava flow emplacement ∼1600 yr ago, White Branch Creek has incised bedrock gorges up to 8 m deep into the coherent core of the lava flow and deposited >0.2 km3 of sediment on the lava flow surface. Field observation points to a bimodal discharge regime in the channel, with evidence for both annual snowmelt runoff and outburst floods from Collier glacier, as well as historical evidence of vigorous glacial meltwater. To determine the range of discharge events capable of incision in White Branch Creek, we used a mechanistic model of fluvial abrasion. We show that the observed incision implies that moderate flows are capable of both initiating channel formation and sustaining incision. Our results have implications for the evolution of volcanic systems worldwide, where glaciation and/or mass wasting may accelerate fluvial processes by providing large amounts of sediment to otherwise porous, sediment-starved landscapes.
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....
Putra, Alfian; Vassileva, Maria; Santo, Ryoko; Tsenkova, Roumina
2017-06-01
Cadmium (Cd) is a common industrial pollutant with long biological half-life, which makes it as a cumulative toxicant. Near-infrared spectroscopy has been successfully used for quick and accurate assessment of Cd content in agricultural materials, but the development of a quick detection method for ground and drinking water samples is equal importance for pollution monitoring. Metals have no absorbance in the NIR spectral range, thus the methods developed so far have focused on detection of metal-organic complexes (move to intro). This study focuses on the use of Aquaphotomics technique to measure Cd in aqueous solutions by analyzing the changes in water spectra that occur due to water-metal interaction. Measurements were performed with Cd (II) in 0.1 M HNO3, in the 680-1090 nm (water second and third overtones) and 1110-1800 nm (water first overtone) spectral regions, and were subjected to partial least-square regression analysis. It was found/determined that A concentration of Cd from 1 mg L-1 to 10 mg L-1 could be predicted by this model with average prediction correlation coefficient of 0.897. The model was tested by perturbations with temperature and other metal presence in the solution. The regression coefficient showed consistent peaks at 728, 752, 770, 780, 1362, 1430,1444, 1472/1474 and 1484 nm under various perturbations, indicating that metal to influence the water spectra. The residual predictive deviation values (RPD) were greater than 2, indicating that the model is appropriate for practical use. The result suggested that this newly proposed approach is capable of detecting metal ion in a much simpler, rapid and reliable way.
A Well-Posed Two Phase Flow Model and its Numerical Solutions for Reactor Thermal-Fluids Analysis
Energy Technology Data Exchange (ETDEWEB)
Kadioglu, Samet Y. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Berry, Ray [Idaho National Lab. (INL), Idaho Falls, ID (United States); Martineau, Richard [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2016-08-01
A 7-equation two-phase flow model and its numerical implementation is presented for reactor thermal-fluids applications. The equation system is well-posed and treats both phases as compressible flows. The numerical discretization of the equation system is based on the finite element formalism. The numerical algorithm is implemented in the next generation RELAP-7 code (Idaho National Laboratory (INL)’s thermal-fluids code) built on top of an other INL’s product, the massively parallel multi-implicit multi-physics object oriented code environment (MOOSE). Some preliminary thermal-fluids computations are presented.
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.
Energy Technology Data Exchange (ETDEWEB)
Balan, C.; Neagoe, A.; Nistoran, D. [Hydraulics and Hydraulic Machinery Department - REOROM Group, University ' ' Politehnica' ' of Bucharest, Splaiul Independentei 313, 79590, Bucharest (Romania); Legat, V. [University of Louvain-la-Neuve - Center for Systems Engineering Applied Mechanics (CESAME), Batiment Euler, Av. Georges Lemaitre 4, 1348, Louvain-la-Neuve (Belgium)
2004-03-01
The present paper is concerned with experimental and numerical investigations of planar complex flows of ''weak'' elastic polymer solutions (whose concentration are below the critical overlap concentration), characterised by small relaxation times ({lambda}<0.1 s) and almost constant shear viscosities for small and medium shear rates. The main aim of the study is to detect to what extent a very small amount of elasticity present in a viscous fluid can influence its behaviour in complex flows, without introducing major modifications of classical rheological tests. The samples are polymer solutions of low PIB molecular weight dissolved in highly viscous Newtonian mineral oil. The analysed motion is steady, and takes place in an open channel around a ''T'' profile. Maximum values of the characteristic parameters for the experiments, the Reynolds and Weissenberg numbers, were 45 and 0.1, respectively. The experiments show a decrease of the wake length downstream the profile for weak elastic solutions in comparison to the Newtonian solvent. Actually, the same wake length as in the Newtonian case was obtained for tested polymer solutions, but at higher Re numbers. Numerical simulations using the Giesekus model predict the same behaviour and are consistent with experiments from both qualitative and quantitative point of views. The results of research conclude that, even in small amounts, the presence of elasticity in pure viscous liquids induces quantitative changes from Newtonian flow in complex dominant elongational flows, at elongational rates for which the sudden thickening of extensional viscosity is remarkable. The study is important, since it should enable better understanding and modelling of viscoelastic flows that involve dilute polymer solutions, or fluids with similar rheology; biofluid mechanics being one area of application of this research. Corroboration of experimental flow visualization with numerical simulation is
CSIR Research Space (South Africa)
Shatalov, M
2012-09-01
Full Text Available Exact solutions of equations of longitudinal vibration of conical and exponential rod are analyzed for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown that the method...
Energy Technology Data Exchange (ETDEWEB)
Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva, E-mail: dani@ime.usp.br, E-mail: joyce@ime.usp.br [Universidade de Sao Paulo (IME/USP), SP (Brazil). Instituto de Matematica e Estatistica; Todo, Alberto Saburo; Rodrigues Junior, Orlando, E-mail: astodo@ipen.br, E-mail: rodrijr@ipen.br [Instituto de Pesquisas Energeticas Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2013-07-01
Biokinetics models for radionuclides applied to dosimetry problems are constantly reviewed by ICRP. The radionuclide trajectory could be represented by compartmental models, assuming constant transfer rates between compartments. A better understanding of physiological or biochemical phenomena, improve the comprehension of radionuclide behavior in the human body and, in general, more complex compartmental models are proposed, increasing the difficulty of obtaining the analytical solution for the system of first order differential equations. Even with constant transfer rates numerical solutions must be carefully implemented because of almost singular characteristic of the matrix of coefficients. In this work we compare numerical methods with different strategies for ICRP-78 models for Thorium-228 and Uranium-234. The impact of uncertainty in the parameters of the equations is also estimated for local and global truncation errors. (author)
Chang, Sin-Chung; To, Wai-Ming
1992-01-01
A new numerical method for solving conservation laws is being developed. It differs substantially from the well established methods, i.e., finite difference, finite volume, finite element, and spectral methods, in both concept and methodology. It is much simpler than a typical high resolution method. No flux limiter or any technique related to characteristics is involved. No artificial viscosity or smoothing is introduced, and no moving mesh is used. Yet this method is capable of generating highly accurate shock tube solutions. The slight numerical overshoot and/or oscillations generated can be removed if a simple averaging formula initially used is replaced by a weighted formula. This modification has little effect on other parts of the solution. Because of its simplicity, generalization of this new method for multi-dimensional problems is straightforward.
Energy Technology Data Exchange (ETDEWEB)
Mail, Noor; Al-Ghamdi, S.; Saoudi, A. [Princess Norah Oncology Center, National Guard Health Affairs, Jeddah 21423, Saudi Arabia and King Abdullah International Medical Research Center, Jeddah 21423 (Saudi Arabia); Albarakati, Y.; Ahmad Khan, M.; Saeedi, F.; Safadi, N. [Princess Norah Oncology Center, National Guard Health Affairs, Jeddah 21423 (Saudi Arabia)
2013-08-15
Purpose: The presence of high-density material in the oral cavity creates dose perturbation in both downstream and upstream directions at the surfaces of dental filling materials (DFM). In this study, the authors have investigated the effect of DFM on head and neck RapidArc treatment plans and delivery. Solutions are proposed to address (1) the issue of downstream dose perturbation, which might cause target under dosage, and (2) to reduce the upstream dose from DFM which may be the primary source of mucositis. In addition, an investigation of the clinical role of a custom-made plastic dental mold/gutter (PDM) in sparing the oral mucosa and tongue reaction is outlined.Methods: The influence of the dental filling artifacts on dose distribution was investigated using a geometrically well-defined head and neck intensity modulated radiation therapy (IMRT) verification phantom (PTW, Freiberg, Germany) with DFM inserts called amalgam, which contained 50% mercury, 25% silver, 14% tin, 8% copper, and 3% other trace metals. Three RapidArc plans were generated in the Varian Eclipse System to treat the oral cavity using the same computer tomography (CT) dataset, including (1) a raw CT image, (2) a streaking artifacts region, which was replaced with a mask of 10 HU, and (3) a 2 cm-thick 6000 HU virtual filter [a volume created in treatment planning system to compensate for beam attenuation, where the thickness of this virtual filter is based on the measured percent depth dose (PDD) data and Eclipse calculation]. The dose delivery for the three plans was verified using Gafchromic-EBT2 film measurements. The custom-made PDM technique to reduce backscatter dose was clinically tested on four head and neck cancer patients (T3, N1, M0) with DFM, two patients with PDM and the other two patients without PDM. The thickness calculation of the PDM toward the mucosa and tongue was purely based on the measured upstream dose. Patients’ with oral mucosal reaction was clinically examined
Goloviznin, V. M.; Kanaev, A. A.
2011-05-01
For the CABARET finite difference scheme, a new approach to the construction of convective flows for the one-dimensional nonlinear transport equation is proposed based on the minimum principle of partial local variations. The new approach ensures the monotonicity of solutions for a wide class of problems of a fairly general form including those involving discontinuous and nonconvex functions. Numerical results illustrating the properties of the proposed method are discussed.
On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation
Wang, Y.
2013-01-01
A numerical method is proposed to compute full-tensor permeability of porous media without artificial simplification. Navier-Stokes (N-S) equation and Darcy\\'s law are combined to design these numerical experiments. This method can successfully detect the permeability values in principle directions of the porous media and the anisotropic degrees. It is found that the same configuration of porous media may possess isotropic features at lower Reynolds numbers while manifesting anisotropic features at higher Reynolds numbers due to the nonlinearity from convection. Anisotropy becomes pronounced especially when convection is dominant. 2013 Yi Wang et al.
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Medviďová-Lukáčová, M.; Nečasová, Šárka; Novotný, A.; She, Bangwei
2018-01-01
Roč. 16, č. 1 (2018), s. 150-183 ISSN 1540-3459 R&D Projects: GA ČR GA16-03230S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : Navier-Stokes system * finite element numerical method * finite volume numerical method * asymptotic preserving schemes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.865, year: 2016 http://epubs.siam.org/doi/10.1137/16M1094233
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...
CSIR Research Space (South Africa)
Smith, S
2015-11-01
Full Text Available -1 RAPDASA 2015 conference, Roodevallei, Pretoria, 4 - 6 November 2015 PLUG-AND-PLAY PAPER-BASED TOOLKIT FOR RAPID PROTOTYPING OF MICROFLUIDICS AND ELECTRONICS TOWARDS POINT-OF-CARE DIAGNOSTIC SOLUTIONS S. Smith1*, K. Moodley2 & K. Land3 1...
Kapoor, Mamta; Winter, Tate; Lis, Lev; Georg, Gunda I; Siegel, Ronald A
2014-05-01
Current treatments for seizure emergencies, such as status epilepticus, include intravenous or rectal administration of benzodiazepines. While intranasal delivery of these drugs is desirable, the small volume of the nasal cavity and low drug solubility pose significant difficulties. Here, we prepared supersaturated diazepam solutions under physiological conditions and without precipitation, using a prodrug/enzyme system. Avizafone, a peptide prodrug of diazepam, was delivered with--Aspergillus oryzae (A.O.) protease, an enzyme identified from a pool of hydrolytic enzymes in assay buffer, pH 7.4 at 32°C. This enzyme converted avizafone to diazepam at supersaturated concentrations. In vitro permeability studies were performed at various prodrug/enzyme ratios using Madin-Darby canine kidney II-wild type (MDCKII-wt) monolayers, a representative model of the nasal epithelium. Monolayer integrity was examined using TEER measurement and the lucifer yellow permeability assay. Prodrug/drug concentrations were measured using HPLC. Enzyme kinetics with avizafone-protease mixtures revealed K(M) = 1,501 ± 232 μM and V(max) = 1,369 ± 94 μM/s. Prodrug-protease mixtures, when co-delivered apically onto MDCKII-wt monolayers, showed 2-17.6-fold greater diazepam flux (S = 1.3-15.3) compared to near-saturated diazepam (S = 0.7). Data for prodrug conversion upstream (apical side) and drug permeability downstream (basolateral side) fitted reasonably well to a previously developed in vitro two compartment pharmacokinetic model. Avizafone-protease mixtures resulted in supersaturated diazepam in less than 5 min, with the rate and extent of supersaturation determined by the prodrug/enzyme ratio. Together, these results suggest that an intranasal avizafone-protease system may provide a rapid and alternative means of diazepam delivery.
Zhang, Kejiang; Achari, Gopal; Li, Hua
2009-11-03
Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.
DEFF Research Database (Denmark)
Johannesson, Björn; Hosokawa, Yoshifumi; Yamada, Kazuo
2009-01-01
A method to analyse and calculate concentration profiles of different types of ions in the pore solution of porous materials such as concrete subjected to external wetting and drying is described. The equations in use have a solid theoretical meaning and are derived from a porous media technique,...... of the model should be judged from the assumptions made when developing the balance laws and the constitutive equations and the assumptions made in obtaining a working numerical calculation scheme....... on the ionic diffusion resistance in the pore solution of the porous material. The Gauss’ law is included in the model in order to be able to calculate the electrical potential which develops due to small deviations from total charge neutrality among the ionic species in the pore solution. The correctness...
Albacete, J L; Milhano, J G; Salgado, C A; Wiedemann, Urs Achim
2005-01-01
We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum $Q_s$ on the nuclear size $A$ and results in an exponential dependence on rapidity $Y$, $Q^2_s(Y) = Q^2_s(Y_0) \\exp{[ \\bar\\alpha_s d (Y-Y_0) ]}$. For the running coupling case, we re-derive analytical estimates for the $A$- and $Y$-dependences of the saturation scale and test them numerically. The $A$-dependence of $Q_s$ vanishes $\\propto 1/ \\sqrt{Y}$ for large $A$ and $Y$. The $Y$-dependence is reduced to $Q_s^2(Y) \\propto \\exp{(\\Delta^\\prime\\sqrt{Y+X})}$ where we find numerically $\\Delta^\\prime\\simeq 3.2$, approximately 12% smaller than analytical estimates. In contrast to previous analytical work, we find a marked difference between the anomalous dimension $1-\\gamma$ governing the large transverse momentum behaviour of the gluon distribution for fixed coupling ($\\gamma \\simeq 0.65$) and for running coupling ($\\gam...
Zhuravlev, A. K.; Anokhin, A. O.; Irkhin, V. Yu.
2018-02-01
Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s-d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.
Swanson, Ryan David
The advection-dispersion equation (ADE) fails to describe non-Fickian solute transport breakthrough curves (BTCs) in saturated porous media in both laboratory and field experiments, necessitating the use of other models. The dual-domain mass transfer (DDMT) model partitions the total porosity into mobile and less-mobile domains with an exchange of mass between the two domains, and this model can reproduce better fits to BTCs in many systems than ADE-based models. However, direct experimental estimation of DDMT model parameters remains elusive and model parameters are often calculated a posteriori by an optimization procedure. Here, we investigate the use of geophysical tools (direct-current resistivity, nuclear magnetic resonance, and complex conductivity) to estimate these model parameters directly. We use two different samples of the zeolite clinoptilolite, a material shown to demonstrate solute mass transfer due to a significant internal porosity, and provide the first evidence that direct-current electrical methods can track solute movement into and out of a less-mobile pore space in controlled laboratory experiments. We quantify the effects of assuming single-rate DDMT for multirate mass transfer systems. We analyze pore structures using material characterization methods (mercury porosimetry, scanning electron microscopy, and X-ray computer tomography), and compare these observations to geophysical measurements. Nuclear magnetic resonance in conjunction with direct-current resistivity measurements can constrain mobile and less-mobile porosities, but complex conductivity may have little value in relation to mass transfer despite the hypothesis that mass transfer and complex conductivity lengths scales are related. Finally, we conduct a geoelectrical monitored tracer test at the Macrodispersion Experiment (MADE) site in Columbus, MS. We relate hydraulic and electrical conductivity measurements to generate a 3D hydraulic conductivity field, and compare to
Directory of Open Access Journals (Sweden)
Maria de Hoyos Guajardo, Ph.D. Candidate, M.Sc., B.Eng.
2004-11-01
Full Text Available The theory that is presented below aims to conceptualise how a group of undergraduate students tackle non-routine mathematical problems during a problem-solving course. The aim of the course is to allow students to experience mathematics as a creative process and to reflect on their own experience. During the course, students are required to produce a written ‘rubric’ of their work, i.e., to document their thoughts as they occur as well as their emotionsduring the process. These ‘rubrics’ were used as the main source of data.Students’ problem-solving processes can be explained as a three-stage process that has been called ‘solutioning’. This process is presented in the six sections below. The first three refer to a common area of concern that can be called‘generating knowledge’. In this way, generating knowledge also includes issues related to ‘key ideas’ and ‘gaining understanding’. The third and the fourth sections refer to ‘generating’ and ‘validating a solution’, respectively. Finally, once solutions are generated and validated, students usually try to improve them further before presenting them as final results. Thus, the last section deals with‘improving a solution’. Although not all students go through all of the stages, it may be said that ‘solutioning’ considers students’ main concerns as they tackle non-routine mathematical problems.
Ahmadian, A.; Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.
2017-12-01
The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed.
Energy Technology Data Exchange (ETDEWEB)
Samaras, T; Christ, A; Kuster, N [Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki (Greece); Foundation for Research on Information Technologies in Society (IT' IS Foundation), Swiss Federal Institute of Technology (ETH), CH-8004 Zurich (Switzerland)
2006-06-07
In this work, we highlight two issues that have to be taken into consideration for accurate thermal modelling with the finite-difference time-domain (FDTD) method, namely the tissue interfaces and the staircasing effect. The former appears less critical in the overall accuracy of the results, whereas the latter may have an influence on the worst-case approach used in numerical dosimetry of non-ionizing radiation. (note)
Goloviznin, V. M.; Karabasov, S. A.; Kozubskaya, T. K.; Maksimov, N. V.
2009-12-01
A generalization of the CABARET finite difference scheme is proposed for linearized one-dimensional Euler equations based on the characteristic decomposition into local Riemann invariants. The new method is compared with several central finite difference schemes that are widely used in computational aeroacoustics. Numerical results for the propagation of an acoustic wave in a homogeneous field and the refraction of this wave through a contact discontinuity obtained on a strongly nonuniform grid are presented.
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Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.
2015-12-01
We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.
Directory of Open Access Journals (Sweden)
M.J. Uddin
2016-09-01
Full Text Available The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate for methanol are higher (lower than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate factor of Newtonian fluid is higher (lower than the dilatant fluid.
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Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.
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.
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M. Ilić
2008-01-01
Full Text Available This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE (−∇2α/2φ=g(x,y with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(Ab≈β0Vmf(Tme1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.
Paster, Amir; Bolster, Diogo; Benson, David A.
2014-04-01
We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion-reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies.
Brezinski, C
2012-01-01
Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<
Akulenko, L. D.; Gavrikov, A. A.; Nesterov, S. V.
2017-09-01
A numerical-analytical iterative method is proposed for solving generalized self-adjoint regular vector Sturm-Liouville problems with Dirichlet boundary conditions. The method is based on eigenvalue (spectral) correction. The matrix coefficients of the equations are assumed to be nonlinear functions of the spectral parameter. For a relatively close initial approximation, the method is shown to have second-order convergence with respect to a small parameter. Test examples are considered, and the model problem of transverse vibrations of a hinged rod with a variable cross section is solved taking into account its rotational inertia.
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Finan, C.H. III
1980-12-01
Resistive magnetohydrodynamics (MHD) is described by a set of eight coupled, nonlinear, three-dimensional, time-dependent, partial differential equations. A computer code, IMP (Implicit MHD Program), has been developed to solve these equations numerically by the method of finite differences on an Eulerian mesh. In this model, the equations are expressed in orthogonal curvilinear coordinates, making the code applicable to a variety of coordinate systems. The Douglas-Gunn algorithm for Alternating-Direction Implicit (ADI) temporal advancement is used to avoid the limitations in timestep size imposed by explicit methods. The equations are solved simultaneously to avoid syncronization errors.
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López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es
2017-03-15
Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.
Mukaiyama, Yuji; Iizuka, Masaya; Vorob'ev, Andrey; Kalaev, Vladimir
2017-10-01
In the present work, a combined 2D-3D numerical simulation was performed to study the effect of shape change in the graphite crucible on the heat transfer, flow pattern, mass transport, and electromagnetic field during top seeded solution growth of SiC considering the dissolution of carbon during crystal growth. The graphite crucible shapes at each growth process time were predicted using 2D axisymmetric steady global heat and mass transfer simulations. The crucible geometries obtained for each time step, including the predicted crucible shapes, were used for 3D unsteady simulations. The investigation revealed a significant effect of the shape change of the crucible on the temperature, Lorentz force distribution induced by the radiofrequency heating system, flow pattern, carbon concentration in the solution, and growth rate of SiC.
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Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-08-15
Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.
Campbell, W.
1981-01-01
A theoretical evaluation of the stability of an explicit finite difference solution of the transient temperature field in a composite medium is presented. The grid points of the field are assumed uniformly spaced, and media interfaces are either vertical or horizontal and pass through grid points. In addition, perfect contact between different media (infinite interfacial conductance) is assumed. A finite difference form of the conduction equation is not valid at media interfaces; therefore, heat balance forms are derived. These equations were subjected to stability analysis, and a computer graphics code was developed that permitted determination of a maximum time step for a given grid spacing.
Projected discrete ordinates methods for numerical transport problems
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Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Ha, Sanghyun; Park, Junshin; You, Donghyun
2018-01-01
Utility of the computational power of Graphics Processing Units (GPUs) is elaborated for solutions of incompressible Navier-Stokes equations which are integrated using a semi-implicit fractional-step method. The Alternating Direction Implicit (ADI) and the Fourier-transform-based direct solution methods used in the semi-implicit fractional-step method take advantage of multiple tridiagonal matrices whose inversion is known as the major bottleneck for acceleration on a typical multi-core machine. A novel implementation of the semi-implicit fractional-step method designed for GPU acceleration of the incompressible Navier-Stokes equations is presented. Aspects of the programing model of Compute Unified Device Architecture (CUDA), which are critical to the bandwidth-bound nature of the present method are discussed in detail. A data layout for efficient use of CUDA libraries is proposed for acceleration of tridiagonal matrix inversion and fast Fourier transform. OpenMP is employed for concurrent collection of turbulence statistics on a CPU while the Navier-Stokes equations are computed on a GPU. Performance of the present method using CUDA is assessed by comparing the speed of solving three tridiagonal matrices using ADI with the speed of solving one heptadiagonal matrix using a conjugate gradient method. An overall speedup of 20 times is achieved using a Tesla K40 GPU in comparison with a single-core Xeon E5-2660 v3 CPU in simulations of turbulent boundary-layer flow over a flat plate conducted on over 134 million grids. Enhanced performance of 48 times speedup is reached for the same problem using a Tesla P100 GPU.
Directory of Open Access Journals (Sweden)
2015-12-01
Full Text Available Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.
Nguyen, Dinh-Liem; Klibanov, Michael V.; Nguyen, Loc H.; Kolesov, Aleksandr E.; Fiddy, Michael A.; Liu, Hui
2017-09-01
We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. The challenges for the inverse problem under the consideration are not only from its high nonlinearity and severe ill-posedness but also from the facts that the amount of the measured data is minimal and that these raw data are contaminated by a significant amount of noise, due to a non-ideal experimental setup. This setup is motivated by our target application in detecting and identifying explosives. We show in this paper how the raw data can be preprocessed and successfully inverted using our inversion method. More precisely, we are able to reconstruct the dielectric constants and the locations of the scattering objects with a good accuracy, without using any advanced a priori knowledge of their physical and geometrical properties.
Atkins, H. L.; Helenbrook, B. T.
2005-01-01
This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.
An Experimenting Field Approach for the Numerical Solution of Multiphase Flow in Porous Media
Salama, Amgad
2015-07-14
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.
Lamar, John E.; Abdol-Hamid, Khaled S.
2009-01-01
In support of the Cranked Arrow Wing Aerodynamic Project International (CAWAPI) with its goal of improving the Technology Readiness Level of flow solvers by comparing results with measured F-16XL-1 flight data, NASA Langley employed the TetrUSS unstructured grid solver, USM3D, to obtain solutions for all seven flight conditions of interest. A newly available solver version that incorporates a number of turbulence models, including the two-equation linear and non-linear k- , was used in this study. As a first test, a choice was made to utilize only a single grid resolution with the solver for the simulation of the different flight conditions. Comparisons are presented with three turbulence models in USM3D, flight data for surface pressure, boundary-layer profiles, and skin-friction distribution, as well as limited predictions from other solvers. A result of these comparisons is that the USM3D solver can be used in an engineering environment to predict vortex-flow physics on a complex configuration at flight Reynolds numbers with a two-equation linear k- turbulence model.
Directory of Open Access Journals (Sweden)
M.G. Pantelyat
2016-09-01
Full Text Available Purpose. To develop an effective approach for the numerical solution of transient thermo-contact problems and present a typical example of its utilization regarding devices working on the principle of thermoelasticity produced by induction heating and specific technological processes intended for assembly and disassembly of systems containing shrink fits. Methodology. A finite element technique for solution of 2D multiphysics (electromagnetic, thermal and structural problems is developed, taking into account temperature dependences of material properties and continuous variations of the contact surfaces. Modeling of the contact interaction between two parts is based on the concept of a special contact finite element having no thickness. The functional for the temperature problem is supplemented with components corresponding to the thermal conductivity of this contact layer. The heat generated due to mutual sliding of both parts can also be taken into account, but the heat capacity (specific heat of the contact layer is neglected. Using a special 1D 4-node finite elements a system of equations for the description of the thermo-contact problem is obtained. Originality. Relatively simple analytical formulae for calculation of the contact thermal resistances occurring in specific parts of electrical machines are known. The paper offers an alternative approach for the numerical solution of transient thermo-contact problems based on the concept of a special 1D contact finite element having no thickness. Results. The presented technique is applied for the computer simulation of assembly and disassembly of a shrink fit using induction heating. Conclusions regarding the choice of technological modes are made. Comparative computations for drills made from hard alloy and alloyed tool steel are carried out.
Zhang, Juan; Han, Qiaofeng; Zhu, Junwu; Wang, Xin
2016-09-01
The unique nanosheet-based flower-like BiOCl1-xBrx (x=0-1) hierarchical solid solutions have been prepared by the reaction of Bi2O3 and KCl/KBr in mixed solution of glacial acetic acid (HAc) and H2O in dozens of minutes under ambient conditions. During the preparation process, the intermediate bismuth oxide acetate (CH3COOBiO) plays a key role in the formation of BiOCl1-xBrx solid solutions in such a short time. The as-prepared hierarchical BiOCl1-xBrx solid solutions possess high specific surface areas and modified band structures, which exhibit enhanced photocatalytic activity for Rhodamine B (RhB) degradation in comparison with pure BiOCl and BiOBr under visible light irradiation, with the activity reaching the maximum at x=0.5. The photodegradation efficiency of the BiOCl0.5Br0.5 solid solution is twice and 12times higher than P25 TiO2 under UV and visible light irradiation, respectively. Copyright © 2016 Elsevier Inc. All rights reserved.
Rong, Li; Nielsen, Peter V; Zhang, Guoqiang
2010-04-01
This paper reports the results of an investigation, based on fundamental fluid dynamics and mass transfer theory, carried out to obtain a general understanding of ammonia mass transfer from an emission surface. The effects of airflow and aqueous ammonium solution temperature on ammonia mass transfer are investigated by using computational fluid dynamics (CFD) modeling and by a mechanism modeling using dissociation constant and Henry's constant models based on the parameters measured in the experiments performed in a wind tunnel. The validated CFD model by experimental data is used to investigate the surface concentration distribution and mass transfer coefficient at different temperatures and velocities for which the Reynolds number is from 1.36 x 10(4) to 5.43 x 10(4) (based on wind tunnel length). The surface concentration increases as velocity decreases and varies greatly along the airflow direction on the emission surface. The average mass transfer coefficient increases with higher velocity and turbulence intensity. However, the mass transfer coefficient estimated by CFD simulation is consistently larger than the calculated one by the method using dissociation constant and Henry's constant models. In addition, the results show that the liquid-air temperature difference has little impact on the simulated mass transfer coefficient by CFD modeling, whereas the mass transfer coefficient increases with higher liquid temperature using the other method under the conditions that the liquid temperature is lower than the air temperature. Although there are differences of mass transfer coefficients between these two methods, the mass transfer coefficients determined by these two methods are significantly related.
Liolios, K.; Tsihrintzis, V.; Angelidis, P.; Georgiev, K.; Georgiev, I.
2016-10-01
Current developments on modeling of groundwater flow and contaminant transport and removal in the porous media of Horizontal Subsurface Flow Constructed Wetlands (HSF CWs) are first reviewed in a short way. The two usual environmental engineering approaches, the black-box and the process-based one, are briefly presented. Next, recent research results obtained by using these two approaches are briefly discussed as application examples, where emphasis is given to the evaluation of the optimal design and operation parameters concerning HSF CWs. For the black-box approach, the use of Artificial Neural Networks is discussed for the formulation of models, which predict the removal performance of HSF CWs. A novel mathematical prove is presented, which concerns the dependence of the first-order removal coefficient on the Temperature and the Hydraulic Residence Time. For the process-based approach, an application example is first discussed which concerns procedures to evaluate the optimal range of values for the removal coefficient, dependent on either the Temperature or the Hydraulic Residence Time. This evaluation is based on simulating available experimental results of pilot-scale units operated in Democritus University of Thrace, Xanthi, Greece. Further, in a second example, a novel enlargement of the system of Partial Differential Equations is presented, in order to include geothermal effects. Finally, in a third example, the case of parameters uncertainty concerning biodegradation procedures is considered and the use of upper and a novel approach is presented, which concerns the upper and the lower solution bound for the practical draft design of HSF CWs.
Ranjan, Srikant
2005-11-01
Fatigue-induced failures in aircraft gas turbine and rocket engine turbopump blades and vanes are a pervasive problem. Turbine blades and vanes represent perhaps the most demanding structural applications due to the combination of high operating temperature, corrosive environment, high monotonic and cyclic stresses, long expected component lifetimes and the enormous consequence of structural failure. Single crystal nickel-base superalloy turbine blades are being utilized in rocket engine turbopumps and jet engines because of their superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities over polycrystalline alloys. These materials have orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. Computation of stress intensity factors (SIFs) and the ability to model fatigue crack growth rate at single crystal cracks subject to mixed-mode loading conditions are important parts of developing a mechanistically based life prediction for these complex alloys. A general numerical procedure has been developed to calculate SIFs for a crack in a general anisotropic linear elastic material subject to mixed-mode loading conditions, using three-dimensional finite element analysis (FEA). The procedure does not require an a priori assumption of plane stress or plane strain conditions. The SIFs KI, KII, and KIII are shown to be a complex function of the coupled 3D crack tip displacement field. A comprehensive study of variation of SIFs as a function of crystallographic orientation, crack length, and mode-mixity ratios is presented, based on the 3D elastic orthotropic finite element modeling of tensile and Brazilian Disc (BD) specimens in specific crystal orientations. Variation of SIF through the thickness of the specimens is also analyzed. The resolved shear stress intensity coefficient or effective SIF, Krss, can be computed as a function of crack tip SIFs and the
For most species, evolutionary adaptation is not expected to be sufficiently rapid to buffer the effects of human-mediated environmental changes. Yet large persistent populations of small bodied fish residing in some of the most contaminated estuaries of the US have provided some...
Whitehead, Andrew; Clark, Bryan W.; Reid, Noah M.; Hahn, Mark E.; Nacci, Diane
2017-01-01
Abstract For most species, evolutionary adaptation is not expected to be sufficiently rapid to buffer the effects of human‐mediated environmental changes, including environmental pollution. Here we review how key features of populations, the characteristics of environmental pollution, and the genetic architecture underlying adaptive traits, may interact to shape the likelihood of evolutionary rescue from pollution. Large populations of Atlantic killifish (Fundulus heteroclitus) persist in som...
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.
Ruthven, Mackenzie; Ko, Kristin Robin; Agarwal, Rishima; Frampton, John P
2017-05-30
Aqueous two-phase systems have emerged as valuable tools for microscale analysis of cell growth and many other biotechnology applications. The most critical step in developing an aqueous two-phase system for a specific application is identifying the critical concentrations at which the polymer solutions phase-separate. Current techniques for determining these critical concentrations rely on laborious methods, highly specialized assays or computational methods that make this step difficult for non-specialists. To overcome these limitations, we present a simplified assay that uses only readily accessible laboratory instruments and consumables (e.g., multichannel micropipettes, 96-well plates and a simple compound microscope) to determine the critical concentrations of aqueous two-phase system-forming polymers. We demonstrate that formulations selected from phase diagrams that describe these critical concentrations can be applied for solution micropatterning of cells.
Coutts, Janelle L.; Lunn, Griffin M.; Koss, Lawrence L.; Hummerick, Mary E.; Spencer, Lachelle E.; Johnsey, Marissa N.; Richards, Jeffrey T.; Ellis, Ronald; Birmele, Michele N.; Wheeler, Raymond M.
2014-01-01
Bioreactor research is mostly limited to continuous stirred-tank reactors (CSTRs) which are not an option for microgravity (g) applications due to the lack of a gravity gradient to drive aeration as described by the Archimedes principle. Bioreactors and filtration systems for treating wastewater in g could avoid the need for harsh pretreatment chemicals and improve overall water recovery. Solution: Membrane Aerated Bioreactors (MABRs) for g applications, including possible use for wastewater treatment systems for the International Space Station (ISS).
Directory of Open Access Journals (Sweden)
Hric Vladimír
2015-01-01
Full Text Available We present an engineering approach to mathematical modeling and numerical solution of 2D inviscid transonic flow of wet steam in a steam turbine cascade channel of penultimate stage at rotor tip section in full Eulerian framework. Our flow model consists of the Euler system for the mixture (dry steam + homogeneously dispersed water droplets and transport equations for moments of droplet number distribution function known as method of moments. Thermodynamic properties of vapor steam are provided by set of IAPWS equations. For equation of state for vapor phase valid both in superheated and wet (meta-stable region we adopted recently developed equation in CFD formulation for low pressures provi1ded by Hrubý et al. [9], [8], [10]. For extraction of vapor parameters from the mixture ones we implemented simple relations in polynomial form describing thermodynamic properties of saturated liquid state. Nucleation model is resorting to modified classical nucleation theory. Linear droplet growth model is implemented for calculation of liquid sources. Numerical method is simple: cell-centered finite volume approach, 1st-order AUSM+ scheme for spatial derivatives, symmetrical fractional step method for separation of convection and condensation part, explicit 2-stage 2nd-order Runge-Kutta method for time integration. Geometry of blade profile and experimental results are provided by Bakhtar’s work [22], [23]. Results were obtained for one subsonic inlet/subsonic outlet regime and gave quite reasonable accordance with experiment.
Hric, Vladimír; Halama, Jan
2015-05-01
We present an engineering approach to mathematical modeling and numerical solution of 2D inviscid transonic flow of wet steam in a steam turbine cascade channel of penultimate stage at rotor tip section in full Eulerian framework. Our flow model consists of the Euler system for the mixture (dry steam + homogeneously dispersed water droplets) and transport equations for moments of droplet number distribution function known as method of moments. Thermodynamic properties of vapor steam are provided by set of IAPWS equations. For equation of state for vapor phase valid both in superheated and wet (meta-stable) region we adopted recently developed equation in CFD formulation for low pressures provi1ded by Hrubý et al. [9], [8], [10]. For extraction of vapor parameters from the mixture ones we implemented simple relations in polynomial form describing thermodynamic properties of saturated liquid state. Nucleation model is resorting to modified classical nucleation theory. Linear droplet growth model is implemented for calculation of liquid sources. Numerical method is simple: cell-centered finite volume approach, 1st-order AUSM+ scheme for spatial derivatives, symmetrical fractional step method for separation of convection and condensation part, explicit 2-stage 2nd-order Runge-Kutta method for time integration. Geometry of blade profile and experimental results are provided by Bakhtar's work [22], [23]. Results were obtained for one subsonic inlet/subsonic outlet regime and gave quite reasonable accordance with experiment.
Novak, A.; Honzik, P.; Bruneau, M.
2017-08-01
Miniaturized vibrating MEMS devices, active (receivers or emitters) or passive devices, and their use for either new applications (hearing, meta-materials, consumer devices,…) or metrological purposes under non-standard conditions, are involved today in several acoustic domains. More in-depth characterisation than the classical ones available until now are needed. In this context, the paper presents analytical and numerical approaches for describing the behaviour of three kinds of planar micro-beams of rectangular shape (suspended rigid or clamped elastic planar beam) loaded by a backing cavity or a fluid-gap, surrounded by very thin slits, and excited by an incident acoustic field. The analytical approach accounts for the coupling between the vibrating structure and the acoustic field in the backing cavity, the thermal and viscous diffusion processes in the boundary layers in the slits and the cavity, the modal behaviour for the vibrating structure, and the non-uniformity of the acoustic field in the backing cavity which is modelled in using an integral formulation with a suitable Green's function. Benchmark solutions are proposed in terms of beam motion (from which the sensitivity, input impedance, and pressure transfer function can be calculated). A numerical implementation (FEM) is handled against which the analytical results are tested.
Energy Technology Data Exchange (ETDEWEB)
Molinero Huguet, J.
2001-07-01
This work deals with numerical modeling of groundwater flow, solute transport and chemical reactions through fractured media. These models have been developed within the framework of research activities founded by ENRESA , the Spanish Company for Nuclear Waste Management. This project is the result of a collaborative agreement between ENRESA and his equivalent Swedish Company (SKB) through the research project Task Force 5 of the Aspo Underground Laboratory. One of the objectives of this project is to assess quantitatively th hydrogeological and hydrochemical impact produced by the construction of a Deep Geological Repository in fractured granites. This is important because the new conditions altered construction impact will constitute the initial conditions for the repository closure stage. A second goo l of this work deals with testing the ability of current numerical tools to cope simultaneously with the complex hydrogeological and hydrochemical settlings, which are expected to take place in actual nuclear waste underground repositories constructed in crystalline fractured bed racks. This study has been undertaken through the performance of numerical models, which have subsequently been applied to simulate the hydrogeological and hydrochemical behavior of a granite massif, at a kilo metrical scale, during construction of the Aspo Hard Rock Underground Laboratory (Sweden). The Aspo Hard Rock Laboratory is a prototype, full-scale underground facility launched and operated by SKB. The main aim of the laboratory is to provide an opportunity for research, development and demonstration in a realistic rock environment down to the depth planned for the future deep repository. The framework of this underground facility provides a unique opportunity to attempt the objectives of the present dissertation. (Author)
Xie, Xiande; Hu, Yuanan; Cheng, Hefa
2016-02-01
Although banned in some developed countries, p-arsanilic acid (p-ASA) is still used widely as a feed additive for swine production in many countries. With little uptake and transformation in animal bodies, nearly all the p-ASA administered to animals is excreted chemically unchanged in animal wastes, which can subsequently release the more toxic inorganic arsenic species upon degradation in the environment. For safe disposal of the animal wastes laden with p-ASA, we proposed a method of leaching the highly water-soluble p-ASA out of the manure first, followed by treatment of the leachate using the Fenton process to achieve fast oxidation of p-ASA and removal of the inorganic arsenic species released (predominantly arsenate) from solution simultaneously. The effects of solution pH, dosages of H2O2 and Fe(2+), and the presence of dissolved organic matter (DOM) on the treatment efficiency were systematically investigated. Under the optimum treatment conditions (0.53 mmol L(-1) Fe(2+), 2.12 mmol L(-1) H2O2, and initial pH of 3.0), p-ASA (10 mg-As L(-1)) could be completely oxidized to As(V) within 30 min in pure water and 4 natural water samples, and at the final pH of 4.0, the residual arsenic levels in solution phase were as low as 1.1 and 20.1-43.4 μg L(-1) in the two types of water matrixes, respectively. The presence of humic acid significantly retarded the oxidation of p-ASA by scavenging HO, and inhibited the As(V) removal through competitive adsorption on ferric hydroxide. Due to the high contents of DOM in the swine manure leachate samples (TOC at ∼500 mg L(-1)), much higher dosages of Fe(2+) (10.0 mmol L(-1)) and H2O2 (40.0 mmol L(-1)) and a longer treatment time (120 min) were required to achieve near complete oxidation of p-ASA (98.0%), while maintaining the levels of residual arsenic in the solution at factory farms. Copyright © 2015 Elsevier Ltd. All rights reserved.
Zhang, Xiaotao; Hao, Yinan; Wang, Ximing; Chen, Zhangjing
2017-08-28
A low-cost activated carbon (XSBLAC) prepared from XanthocerasSorbifoliaBungehull via chemical activation was investigated to determine its adsorption and desorption properties for zinc(II) ions from aqueous solutions. XSBLAC was characterized based on its N₂-adsorption/desorption isotherm, EDX, XRD, SEM and FTIR results. An adsorption study was conducted in a series of experiments to optimize the process variables for zinc(II) removal using XSBLAC. Modeling the adsorption kinetics indicated good agreement between the experimental data and the pseudo-second-order kinetic model. The Langmuir equilibrium isotherm fit the experimental data reasonably well. The calculated enthalpy (ΔH⁰), entropy (ΔS⁰) and Gibbs free energy (ΔG⁰) values revealed the endothermic and spontaneous nature of the adsorption process. HNO₃ displayed the best desorption performance. The adsorption mechanism was investigated in detail through FTIR and SEM/EDX spectroscopic analyses. The results suggested that XSBLAC is a potential biosorbent for removing zinc(II) from aqueous solutions.
Rapid degradation of aniline in aqueous solution by ozone in the presence of zero-valent zinc.
Zhang, Jing; Wu, Yao; Qin, Chao; Liu, Liping; Lan, Yeqing
2015-12-01
The effects of Zn(0) dosage from 0.1 to 1.3gL(-1), pH from 2 to 12 and temperature from 288 to 318K on the degradation of aniline in aqueous solution by ozone in the presence of Zn(0) were investigated through batch experiments. The results demonstrated that Zn(0) had a significantly synergistic role in the degradation of aniline by ozone. A complete decomposition of the initial aniline (10mgL(-1)) was achieved by ozone together with Zn(0) within 25min, and meanwhile nearly 70% of the total organic carbon in the solution was removed. The decomposition efficiency of aniline markedly increased with an increase of Zn(0) dosage. However, temperature exerted a slight impact on the degradation of aniline and the optimum removal efficiency of aniline was realized at 298K. Aniline was efficiently degraded at all the tested pHs except for 12. Free radicals were investigated by electron paramagnetic resonance technique and free radical scavengers. H2O2 concentration generated during the reactions was analyzed using a photometric method. Based on the results obtained in this study, it is proposed that O2(-) instead of OH is the dominant active species responsible for the degradation of aniline. It is concluded that ozone combined with Zn(0) is an effective and promising approach to the degradation of organic pollutants. Copyright © 2015 Elsevier Ltd. All rights reserved.
Lunn, Griffin; Wheeler, Raymond; Hummerick, Mary; Birmele, Michele; Richards, Jeffrey; Coutts, Janelle; Koss, Lawrence; Spencer, Lashelle.; Johnsey, Marissa; Ellis, Ronald
Bioreactor research, even today, is mostly limited to continuous stirred-tank reactors (CSTRs). These are not an option for microgravity applications due to the lack of a gravity gradient to drive aeration as described by the Archimedes principle. This has led to testing of Hollow Fiber Membrane Bioreactors (HFMBs) for microgravity applications, including possible use for wastewater treatment systems for the International Space Station (ISS). Bioreactors and filtration systems for treating wastewater could avoid the need for harsh pretreatment chemicals and improve overall water recovery. However, the construction of these reactors is difficult and commercial off-the-shelf (COTS) versions do not exist in small sizes. We have used 1-L modular HFMBs in the past, but the need to perform rapid testing has led us to consider even smaller systems. To address this, we designed and built 125-mL, rectangular reactors, which we have called the Fiber Attachment Module Experiment (FAME) system. A polycarbonate rack of four square modules was developed with each module containing removable hollow fibers. Each FAME reactor is self-contained and can be easily plumbed with peristaltic and syringe pumps for continuous recycling of fluids and feeding, as well as fitted with sensors for monitoring pH, dissolved oxygen, and gas measurements similar to their larger counterparts. The first application tested in the FAME racks allowed analysis of over a dozen fiber surface treatments and three inoculation sources to achieve rapid reactor startup and biofilm attachment (based on carbon oxidation and nitrification of wastewater). With these miniature FAME reactors, data for this multi-factorial test were collected in duplicate over a six-month period; this greatly compressed time period required for gathering data needed to study and improve bioreactor performance.
Zhang, Xiaotao; Wang, Ximing; Chen, Zhangjing
2017-09-22
A sulfhydryl-lignocellulose/montmorillonite (SLT) nanocomposite was prepared using a chemical intercalation reaction. The SLT nanocomposite was characterized by Fourier Transform Infrared Spectroscopy (FTIR), X-Ray Diffraction (XRD), Scanning Electron Microscope (SEM), and Transmission Electron Microscopy (TEM), the results demonstrated that an intercalated-exfoliated nanostructure was formed in the SLT nanocomposite. Batch experiments were conducted to optimize parameters such as SLT nanocomposite dosage, the initial concentration of Ni(II), solution pH, temperature, and time. The results indicated that the attractive adsorption capacity reached 1134.08 mg/g with 0.05 g of SLT at an initial concentration of Ni(II) of 700 mg/L, solution pH of 5.5, adsorption temperature of 50 °C, and adsorption time of 40 min, meanwhile, the Ni(II) adsorption capacity significantly decreased with the increase in ionic strength. The pseudo-second order kinetic model could describe the whole adsorption process well, and the isotherm adsorption equilibrium conformed to the Freundlich model. The adsorption mechanism of SLT was also discussed by means of FTIR and Energy-Dispersive X-Ray (EDX). Dramatically, the introduction of sulfhydryl achieves the increased activated functional groups content of SLT nanocomposite, leading to remarkably higher adsorption amount on Ni(II). The desorption capacity of SLT was dependent on parameters such as HNO3 concentration, desorption temperature, and ultrasonic desorption time. The satisfactory desorption capacity and desorption efficiency of 458.21 mg/g and 40.40% were obtained at an HNO3 concentration, desorption temperature, and ultrasonic desorption time of 0.4 mol/L, 40 °C, and 30 min, respectively. The regeneration studies showed that the adsorption capacity of SLT was consistent for four cycles without any appreciable loss and confirmed that the SLT was reusable. Owing to such outstanding features, the novel SLT nanocomposite proved the
Energy Technology Data Exchange (ETDEWEB)
Oktaviani, Nur Alia [University of Groningen, Groningen Biomolecular Sciences and Biotechnology Institute (Netherlands); Risør, Michael W. [University of Aarhus, Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry (Denmark); Lee, Young-Ho [Osaka University, Institute for Protein Research (Japan); Megens, Rik P. [University of Groningen, Stratingh Institute for Chemistry (Netherlands); Jong, Djurre H. de; Otten, Renee; Scheek, Ruud M. [University of Groningen, Groningen Biomolecular Sciences and Biotechnology Institute (Netherlands); Enghild, Jan J. [University of Aarhus, Interdisciplinary Nanoscience Center (iNANO) and Department of Molecular Biology and Genetics (Denmark); Nielsen, Niels Chr. [University of Aarhus, Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry (Denmark); Ikegami, Takahisa [Yokohama City University, Graduate School of Medical Life Science (Japan); Mulder, Frans A. A., E-mail: fmulder@chem.au.dk [University of Groningen, Groningen Biomolecular Sciences and Biotechnology Institute (Netherlands)
2015-06-15
Co-solute paramagnetic relaxation enhancement (PRE) is an attractive way to speed up data acquisition in NMR spectroscopy by shortening the T{sub 1} relaxation time of the nucleus of interest and thus the necessary recycle delay. Here, we present the rationale to utilize high-spin iron(III) as the optimal transition metal for this purpose and characterize the properties of its neutral chelate form Fe(DO3A) as a suitable PRE agent. Fe(DO3A) effectively reduces the T{sub 1} values across the entire sequence of the intrinsically disordered protein α-synuclein with negligible impact on line width. The agent is better suited than currently used alternatives, shows no specific interaction with the polypeptide chain and, due to its high relaxivity, is effective at low concentrations and in ‘proton-less’ NMR experiments. By using Fe(DO3A) we were able to complete the backbone resonance assignment of a highly fibrillogenic peptide from α{sub 1}-antitrypsin by acquiring the necessary suite of multidimensional NMR datasets in 3 h.
Qiao, Liang; Chen, Xin; Zhang, Ye; Zhang, Jingna; Wu, Yi; Li, Ying; Mo, Xuemei; Chen, Wei; Xie, Bing; Qiu, Mingguo
2017-01-01
This study aimed to propose a pure web-based solution to serve users to access large-scale 3D medical volume anywhere with good user experience and complete details. A novel solution of the Master-Slave interaction mode was proposed, which absorbed advantages of remote volume rendering and surface rendering. On server side, we designed a message-responding mechanism to listen to interactive requests from clients (Slave model) and to guide Master volume rendering. On client side, we used HTML5 to normalize user-interactive behaviors on Slave model and enhance the accuracy of behavior request and user-friendly experience. The results showed that more than four independent tasks (each with a data size of 249.4 MB) could be simultaneously carried out with a 100-KBps client bandwidth (extreme test); the first loading time was <12 s, and the response time of each behavior request for final high quality image remained at approximately 1 s, while the peak value of bandwidth was <50-KBps. Meanwhile, the FPS value for each client was ≥40. This solution could serve the users by rapidly accessing the application via one URL hyperlink without special software and hardware requirement in a diversified network environment and could be easily integrated into other telemedical systems seamlessly.
Directory of Open Access Journals (Sweden)
Liang Qiao
2017-01-01
Full Text Available This study aimed to propose a pure web-based solution to serve users to access large-scale 3D medical volume anywhere with good user experience and complete details. A novel solution of the Master-Slave interaction mode was proposed, which absorbed advantages of remote volume rendering and surface rendering. On server side, we designed a message-responding mechanism to listen to interactive requests from clients (Slave model and to guide Master volume rendering. On client side, we used HTML5 to normalize user-interactive behaviors on Slave model and enhance the accuracy of behavior request and user-friendly experience. The results showed that more than four independent tasks (each with a data size of 249.4 MB could be simultaneously carried out with a 100-KBps client bandwidth (extreme test; the first loading time was <12 s, and the response time of each behavior request for final high quality image remained at approximately 1 s, while the peak value of bandwidth was <50-KBps. Meanwhile, the FPS value for each client was ≥40. This solution could serve the users by rapidly accessing the application via one URL hyperlink without special software and hardware requirement in a diversified network environment and could be easily integrated into other telemedical systems seamlessly.
Chavez, Gustavo Ivan
2017-07-10
This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.
Din, Alif
2017-09-01
The potential structures around a moderate negative biased electron-emitting cylindrical probe in low-density isotropic plasma are calculated in the collisionless sheath region. The formalisms, equations, and solutions for the entire electron emitting range (i.e., subcritical, critical, and supercritical) from the cylindrical emitter and collector surface are discussed. The plasma-electron and emitted-electron are assumed to have half Maxwellian velocity distributions at their respective sheath entering boundaries with cold plasma ions. Poisson's equation is solved numerically in the sheath region for the subcritical, critical, and supercritical emissions. The I-V characteristics for these three cases are presented in tabular form. The results show that we need very high emitted-electron current to solve Poisson's equation for the critical and spercritical emissions. Thus, the floating potential is far away in these scenarios. Also, the number density of emitted-and plasma-electron are comparable at the sheath edge so we cannot neglect the density of former in comparison with latter at the sheath edge.
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.
Díaz, J I; Hidalgo, A; Tello, L
2014-10-08
We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge-Kutta total variation diminishing for time integration.
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Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
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Xie, Wei; Lei, Wei-Hua; Wang, Ding-Xiong, E-mail: leiwh@hust.edu.cn [School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2016-12-20
A stellar-mass black hole (BH) surrounded by a neutrino-dominated accretion flow (NDAF) has been discussed in a number of works as the central engine of gamma-ray bursts (GRBs). It is widely believed that NDAF cannot liberate enough energy for bright GRBs. However, these works have been based on the assumption of a “no torque” boundary condition, which is invalid when the disk is magnetized. In this paper, we present both numerical and analytical solutions for NDAFs with non-zero boundary stresses and reexamine their properties. We find that an NDAF with such a boundary torque can be powerful enough to account for those bright short GRBs, energetic long GRBs, and ultra-long GRBs. The disk becomes viscously unstable, which makes it possible to interpret the variability of GRB prompt emission and the steep decay phase in the early X-ray afterglow. Finally, we study the gravitational waves radiated from a processing BH-NDAF. We find that the effects of the boundary torque on the strength of the gravitational waves can be ignored.
Díaz, J. I.; Hidalgo, A.; Tello, L.
2014-01-01
We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration. PMID:25294969
Wada, Atsushi; Kono, Mari; Kawauchi, Sawako; Takagi, Yuri; Morikawa, Takashi; Funakoshi, Kunihiro
2012-01-01
Background For precise diagnosis of urinary tract infections (UTI), and selection of the appropriate prescriptions for their treatment, we explored a simple and rapid method of discriminating gram-positive and gram-negative bacteria in liquid samples. Methodology/Principal Findings We employed the NaOH-sodium dodecyl sulfate (SDS) solution conventionally used for plasmid extraction from Escherichia coli and the automated urine particle analyzer UF-1000i (Sysmex Corporation) for our novel method. The NaOH-SDS solution was used to determine differences in the cell wall structures between gram-positive and gram-negative bacteria, since the tolerance to such chemicals reflects the thickness and structural differences of bacterial cell walls. The UF-1000i instrument was used as a quantitative bacterial counter. We found that gram-negative bacteria, including E. coli, in liquid culture could easily be lysed by direct addition of equal volumes of NaOH-SDS solution. In contrast, Enterococcus faecalis, which is a gram-positive bacterium, could not be completely lysed by the solution. We then optimized the reaction time of the NaOH-SDS treatment at room temperature by using 3 gram-positive and 4 gram-negative bacterial strains and determined that the optimum reaction time was 5 min. Finally, in order to evaluate the generalizability of this method, we treated 8 gram-positive strains and 8 gram-negative strains, or 4 gram-positive and 4 gram-negative strains incubated in voluntary urine from healthy volunteers in the same way and demonstrated that all the gram-positive bacteria were discriminated quantitatively from gram negative bacteria using this method. Conclusions/Significance Using our new method, we could easily discriminate gram-positive and gram-negative bacteria in liquid culture media within 10 min. This simple and rapid method may be useful for determining the treatment course of patients with UTIs, especially for those without a prior history of UTIs. The method
Directory of Open Access Journals (Sweden)
Atsushi Wada
Full Text Available BACKGROUND: For precise diagnosis of urinary tract infections (UTI, and selection of the appropriate prescriptions for their treatment, we explored a simple and rapid method of discriminating gram-positive and gram-negative bacteria in liquid samples. METHODOLOGY/PRINCIPAL FINDINGS: We employed the NaOH-sodium dodecyl sulfate (SDS solution conventionally used for plasmid extraction from Escherichia coli and the automated urine particle analyzer UF-1000i (Sysmex Corporation for our novel method. The NaOH-SDS solution was used to determine differences in the cell wall structures between gram-positive and gram-negative bacteria, since the tolerance to such chemicals reflects the thickness and structural differences of bacterial cell walls. The UF-1000i instrument was used as a quantitative bacterial counter. We found that gram-negative bacteria, including E. coli, in liquid culture could easily be lysed by direct addition of equal volumes of NaOH-SDS solution. In contrast, Enterococcus faecalis, which is a gram-positive bacterium, could not be completely lysed by the solution. We then optimized the reaction time of the NaOH-SDS treatment at room temperature by using 3 gram-positive and 4 gram-negative bacterial strains and determined that the optimum reaction time was 5 min. Finally, in order to evaluate the generalizability of this method, we treated 8 gram-positive strains and 8 gram-negative strains, or 4 gram-positive and 4 gram-negative strains incubated in voluntary urine from healthy volunteers in the same way and demonstrated that all the gram-positive bacteria were discriminated quantitatively from gram negative bacteria using this method. CONCLUSIONS/SIGNIFICANCE: Using our new method, we could easily discriminate gram-positive and gram-negative bacteria in liquid culture media within 10 min. This simple and rapid method may be useful for determining the treatment course of patients with UTIs, especially for those without a prior history
Wakigawa, Kengo; Gohda, Akinaga; Fukushima, Sunao; Mori, Takeshi; Niidome, Takuro; Katayama, Yoshiki
2013-01-15
We developed a rapid and selective method for determination of free chlorine in aqueous solution by gas chromatography/mass spectrometry for the first time. Free chlorine was converted to styrene chlorohydrin using electrophilic addition to styrene in sodium acetate buffer solution (pH 5). The chlorine derivative obtained was extracted with chloroform, and then analyzed by GC/MS. The calibration curve showed good linearity from 0.2-100 μg/mL (as available chlorine). The detection limit was 0.1 μg/mL, and the intra- and interday accuracy were measured at concentrations of 10, 50, and 75 μg/mL to be -1.3 to 6.9% (intraday) and 3.8-8.0% (interday) as % Bias. The precision was between 1.4 and 4.5% as % RSD. These results indicate that this method is a superior technique for the identification of free chlorine. This method was successfully applied to quantification in commercial samples and in samples of a criminal case. Copyright © 2012 Elsevier B.V. All rights reserved.
Sawada, Masataka; Nishimoto, Soshi; Okada, Tetsuji
2017-01-01
In high-level radioactive waste disposal repositories, there are long-term complex thermal, hydraulic, and mechanical (T-H-M) phenomena that involve the generation of heat from the waste, the infiltration of ground water, and swelling of the bentonite buffer. The ability to model such coupled phenomena is of particular importance to the repository design and assessments of its safety. We have developed a T-H-M-coupled analysis program that evaluates the long-term behavior around the repository (called "near-field"). We have also conducted centrifugal model tests that model the long-term T-H-M-coupled behavior in the near-field. In this study, we conduct H-M-coupled numerical simulations of the centrifugal near-field model tests. We compare numerical results with each other and with results obtained from the centrifugal model tests. From the comparison, we deduce that: (1) in the numerical simulation, water infiltration in the rock mass was in agreement with the experimental observation. (2) The constant-stress boundary condition in the centrifugal model tests may cause a larger expansion of the rock mass than in the in situ condition, but the mechanical boundary condition did not affect the buffer behavior in the deposition hole. (3) The numerical simulation broadly reproduced the measured bentonite pressure and the overpack displacement, but did not reproduce the decreasing trend of the bentonite pressure after 100 equivalent years. This indicates the effect of the time-dependent characteristics of the surrounding rock mass. Further investigations are needed to determine the effect of initial heterogeneity in the deposition hole and the time-dependent behavior of the surrounding rock mass.
Rapidly Deployable Mobile Security Solution
2016-03-01
receivers or direct API lockout. Manage wireless network interfaces (Wi- Fi, Bluetooth, etc.) Our application directly restricts access to WiFi and...application by Google or (2) approach Google for further expansion of their Device Policy Manager class and administrator API for inclusion of all 8 features...Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork
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.
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Muk; Hwang, Soo Min [School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon (Korea, Republic of); Hwang, Soon Yong [Nano-Optical Property Laboratory and Department of Physics, Kyung Hee University, Seoul (Korea, Republic of); Kim, Tae Woong; Lee, Sang Hyub; Park, Geun Chul; Choi, Ju Yun [School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon (Korea, Republic of); Yoon, Jae Jin [KLA-Tencor Corporation, 1 Technology Drive, Milpitas, CA 95035 (United States); Kim, Tae Jung; Kim, Young Dong [Nano-Optical Property Laboratory and Department of Physics, Kyung Hee University, Seoul (Korea, Republic of); Kim, Hyoungsub [School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon (Korea, Republic of); Lim, Jun Hyung, E-mail: lanosjh@gmail.com [School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon (Korea, Republic of); Joo, Jinho, E-mail: jinho@skku.edu [School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon (Korea, Republic of)
2014-05-01
Ti-silicate/Si films were synthesized using a solution deposition route, and the effects of a rapid thermal process (RTP) on the microstructure, chemical bonding state, and interfacial layer (IL) properties were investigated and correlated to the permittivity of the films. The precursor solution was prepared from Ti(IV)-isopropoxide and tetraethylorthosilicate, spin-coated on HF-treated Si substrates, dried, pyrolyzed (400 °C), and subjected to the RTP at 700 °C–1000 °C. The Ti-silicate film consisted of Ti-rich and Si-rich silicates after the pyrolysis and phase segregation became significant as the RTP temperature increase. The silicates segregated into TiO{sub 2}-like nanocrystals and Si-richer silicate at up to 850 °C, and the TiO{sub 2}-like nanocrystals grew remarkably while the Si-richer silicate was converted into nearly pure SiO{sub 2} at 1000 °C. In addition, the Ti content in the Ti-silicate layer decreased due to Ti out-diffusion to the IL and substrate. Based on HRTEM, FT-IR, XPS, and SIMS analyses, we suggest a model of phase segregation with Ti diffusion and demonstrate that the Ti diffusion can be a critical issue in applications of Ti-silicate/Si systems, in addition to other well-known phenomena, including phase segregation, TiO{sub 2} precipitation, or interface properties. - Highlights: • Role of RTP on microstructure and properties of Ti-silicate film was investigated. • Phase segregation and Ti diffusion varied with the RTP. • Effects of the Ti diffusion on the dielectric properties were firstly investigated. • The Ti diffusion seemed to be one of the critical issues in the film applications. • New phase segregation model with Ti diffusion was suggested.
Ahmad, Waqas; Kim, Soohyun; Kim, Dongkyun
2017-04-01
Land subsidence and crustal deformation associated with groundwater abstraction is a gradually instigating phenomenon. The exploitation of Interferometric Synthetic Aperture Radar (InSAR) for land subsidence velocity and the Gravity Recovery and Climate Experiment (GRACE) for change in groundwater storage have great potential besides other applications to address this problem. In this paper we used an integrated approach to combine InSAR and GRACE solutions to show that land subsidence velocity in a rapidly urbanizing and groundwater dependent basin in Pakistan is largely attributed to over exploitation of groundwater aquifer. We analyzed a total of 28 Sentinel-1 based interferograms generated for the period October 2014 to November 2016 to quantify the level of land subsidence in the study area. To increase the accuracy of our interferometry results we then applied a filter of Amplitude Dispersion Index (ADI) to confine the spatial extent of land subsidence to persistently scattering pixels. For the GRACE experiment we take the average of change in Total Water Storage (TWS) solutions provided by the Center for Space Research (CSR), the German Research Centre for Geosciences (GFZ), and the Jet Propulsion Laboratory (JPL) and validate this mean TWS for the study area using a network of observed time series groundwater levels. The validation result of GRACE TWS field shows that although the GRACE foot print is spatially larger than the extent of the study area but significant change in water storage can contribute to the overall trend of declining water storage. Finally we compared our results of InSAR land subsidence velocities and GRACE TWS change field. A strong dependence of the land subsidence on the temporal change in TWS suggests that most of the land subsidence could be attributed to the unchecked exploitation of groundwater aquifer.
Energy Technology Data Exchange (ETDEWEB)
Morinishi, K.; Satofuka, N. (Kyoto Inst. of Technology., Kyoto (Japan))
1990-07-25
Numerical analysis of the compressible equations for the flow field with low-mach-number is performed. The method using the finite difference method and the rational Runge-Kutta scheme is applied to the compressible Navier-Stokes equations. Numerical computation for the fundamental flow field is carried out in the range of 0.4-0.01 of basic mach-number, and following conclusion is obtained. The results obtained for driven cavity flows and flows past a circular cylinder with Reynolds number of 40 are represented well the numerical solution which is obtained from before through the incompressible Navier-Stokes equations, and are entirely reliable. Though the convergence rate to a steady-state solution becomes slower proportionally as the Mach number is reduced, vibration of the pressure distribution which diverges the numerical computation is not found even at Mach number 0.01. Stable computation can be done. The result of numerical computation of the flow field obtained around the NACA0012 airfoil at Reynolds number 3.0 {times} 10 {sup 6}, is in agreement well with Harris {prime} s experimental data. 14 refs., 11 figs., 2 tabs.
Numerical Methods in Fluid Dynamics.
treatment of time-dependent three-dimensional flows; Un example de modele mathematique complexe en mecanique des fluides ....des equations de Navier-Stokes des fluides visqueux incompressibles; Numerical solution of steady state Navier-Stokes equations; Numerical solution of...dynamics; Application of finite elements methods in fluid dynamics; Computational methods for inviscid transonic flows with inbedded shock waves; Numerical
Digital Repository Service at National Institute of Oceanography (India)
Nakamoto, S.; Kano, M.; PrasannaKumar, S.; Oberhuber, J.M.; Muneyama, K.; Ueyoshi, K.; Subrahmanyam, B.; Nakata, K.; Lai, C.A.; Frouin, R.
. Numerical models experiments suggest an active role of phytoplankton in the equatorial ocean dynamics by modifying density and thus providing conditions favorable to phytoplankton growth, i.e., the potential positive feedback mechanism between the ecosystem...
2017-01-01
Although Arabic numerals (like ‘2016’ and ‘3.14’) are ubiquitous, we show that in interactive computer applications they are often misleading and surprisingly unreliable. We introduce interactive numerals as a new concept and show, like Roman numerals and Arabic numerals, interactive numerals introduce another way of using and thinking about numbers. Properly understanding interactive numerals is essential for all computer applications that involve numerical data entered by users, including finance, medicine, aviation and science. PMID:28484609
CSIR Research Space (South Africa)
Shatalov, M
2011-07-01
Full Text Available New exact solutions of equations of longitudinal vibration of conical and exponential rod are obtained for the Rayleigh-Love model. These solutions are used as reference results for checking accuracy of the method of lines. It is shown...
Numerical approaches to system of fractional partial differential equations
Directory of Open Access Journals (Sweden)
H. F. Ahmed
2017-04-01
Full Text Available In this paper, by introducing the fractional derivative in sense of Caputo, the Laplace- variational iteration method (LVIM and the Laplace-Adomian decomposition method (LADM are directly extended to study the linear and nonlinear systems of fractional partial differential equations, as a result the approximated numerical solutions are acquired in the form of rapidly convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when are applied. Compassions are made between the two methods and exact solutions. Figures are used to show the efficiency as well as the accuracy of the achieved approximated results.
Energy Technology Data Exchange (ETDEWEB)
Steinhauser, Martin O. [Fraunhofer Ernst-Mach-Institut, Freiburg (Germany). Dept. Systems Solutions
2017-05-01
This textbook applies especially to studyings, in the curriculum of which in the bachelor nor master study methods of quantum mechanics. Treated are the non-relativistic quantum mechanics, so the Schroedinger equation and its solution in the central field and in different potentials, the hydrogen atom, the formalism of the creation and annihilation operators, the harmonic oscillator, the electron spin, as well as the electronic structure (Hartree-Fock solution procedure).
Isaacson, Eugene
1994-01-01
This excellent text for advanced undergraduates and graduate students covers norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, and other topics. It offers a careful analysis and stresses techniques for developing new methods, plus many examples and problems. 1966 edition.
Simulation Model of Bus Rapid Transit
Directory of Open Access Journals (Sweden)
Gunawan Fergyanto E.
2014-03-01
Full Text Available Bus rapid transit system is modern solution for mass transportation system. The system, in comparison to the rail-based transportation system, is significantly cheaper and requires shorter development time, but lower performance. The BRT system performance strongly depends on variables related to station design and infrastructure. A numerical model offers an effective and efficient means to evaluate the system performance. This article offers a detailed numerical model on the basis of the discrete-event approach and demonstrates its application.
Energy Technology Data Exchange (ETDEWEB)
Nourtier-Mazauric, E.
2003-03-15
This thesis presents a thermodynamic and kinetic model of interactions between a fluid and ideal solid solutions represented by several end-members. The reaction between a solid solution and the aqueous solution results from the competition between the stoichiometric dissolution of the initial solid solution and the co-precipitation of the least soluble solid solution in the fluid at considered time. This model was implemented in ARCHIMEDE, a computer code of reactive transport in porous media, then applied to various examples. In the case of binary solid solutions, a graphical method allowed to determine the compositions of the precipitating solid solutions, with the aid of the end-member chemical potentials. The obtained program could be used to notably model the diagenesis of clayey or carbonated oil reservoirs, or the ground pollutant dispersion. (author)
Alolyan, Ibraheem; Simos, T. E.
2016-12-01
A family of eighth algebraic order embedded explicit six-step methods with vanished phase-lag and its derivatives for the numerical integration of second order periodic initial or boundary-value problems is studied in this paper. The development of the new family of embedded methods is based on: • the vanishing phase-lag and • the vanishing of its derivatives.For the obtained methods of the new family of embedded methods, we studied their local truncation error and we calculate its asymptotic form after its application to a test problem which is equivalent with the radial Schrödinger equation. A comparison of the asymptotic forms of the resulting (after application to the test problem) formulae of the local truncation errors are compared in order to lead to summaries about the efficiency of each method of the family. We also investigated the stability and the interval of periodicity of the obtained methods of the new family of embedded methods. Finally, we applied the new produced family of embedded methods to the numerical solution of the radial Schrödinger equation in order to show their efficiency. The article "A Family of Implicit Six-Step Methods with Vanished Phase-Lag and its Derivatives for the Numerical Solution of the Schrödinger Equation and Related Problems" is being replaced with this new article titled "A Family of High Algebraic Order Embedded Explicit Six-Step Methods with Vanished Phase-Lag and its Derivatives for the Numerical Solution of the Schrödinger Equation and Related Problems." The first article was previously published in Conference Proceedings Volume 1702 and was published in Conference Proceedings Volume 1790 in error. Volume 1790 was updated with the correct article on 12 April 2017. The authors and proceedings editor agree with this change.
Numerical methods using Matlab
Lindfield, George
2012-01-01
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board. Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of use
Brem, Gerrit; Brouwers, J.J.H.
1990-01-01
In Part I, analytical solutions were given for the non-linear isothermal heterogeneous conversion of a porous solid particle. Account was taken of a reaction rate of general order with respect to the gas reactant, intrinsic reaction surface area and effective pore diffusion, which change with solid
Westphalen, H.; Spjeldvik, W. N.
1982-01-01
A theoretical method by which the energy dependence of the radial diffusion coefficient may be deduced from spectral observations of the particle population at the inner edge of the earth's radiation belts is presented. This region has previously been analyzed with numerical techniques; in this report an analytical treatment that illustrates characteristic limiting cases in the L shell range where the time scale of Coulomb losses is substantially shorter than that of radial diffusion (L approximately 1-2) is given. It is demonstrated both analytically and numerically that the particle spectra there are shaped by the energy dependence of the radial diffusion coefficient regardless of the spectral shapes of the particle populations diffusing inward from the outer radiation zone, so that from observed spectra the energy dependence of the diffusion coefficient can be determined. To insure realistic simulations, inner zone data obtained from experiments on the DIAL, AZUR, and ESRO 2 spacecraft have been used as boundary conditions. Excellent agreement between analytic and numerical results is reported.
National Oceanic and Atmospheric Administration, Department of Commerce — The Rapid Refresh (RAP) numerical weather model took the place of the Rapid Update Cycle (RUC) on May 1, 2012. Run by the National Centers for Environmental...