General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

International Nuclear Information System (INIS)

Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

2005-01-01

A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

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Ji Juan-Juan

2017-01-01

Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

Method for ion exchange purification of sodium iodide solution from heavy metals and potassium microimpurities

International Nuclear Information System (INIS)

Smirnov, G.I.; Kachur, N.Ya.; Kostromina, O.N.; Ogorodnikova, A.A.; Khajnakov, S.A.

1990-01-01

A method of deep ion exchange purification of sodium iodide solution from heavy metals (iron, nickel, copper, lead) and potassium microimpurities is developed. The method includes multiple sorption of microimpurities on titanium phosphate with their subsequent desorption by sorbent processing with a solution with a solution of 3-6 N nitric acid, first, and then with a neutral solution of 2 % sodium thiosulfate. The given method permits to increase the purification degree of sodium iodide solution by 25-30 %. 2 tabs

Passive Methods as a Solution for Improving Indoor Environments

CERN Document Server

Orosa, José A

2012-01-01

There are many aspects to consider when evaluating or improving an indoor environment; thermal comfort, energy saving, preservation of materials, hygiene and health are all key aspects which can be improved by passive methods of environmental control. Passive Methods as a Solution for Improving Indoor Environments endeavours to fill the lack of analysis in this area by using over ten years of research to illustrate the effects of methods such as thermal inertia and permeable coverings; for example, the use of permeable coverings is a well known passive method, but its effects and ways to improve indoor environments have been rarely analyzed.   Passive Methods as a Solution for Improving Indoor Environments  includes both software simulations and laboratory and field studies. Through these, the main parameters that characterize the behavior of internal coverings are defined. Furthermore, a new procedure is explained in depth which can be used to identify the real expected effects of permeable coverings such ...

Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation

International Nuclear Information System (INIS)

Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.

1989-01-01

The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs

Cost–benefit analysis method for building solutions

International Nuclear Information System (INIS)

Araújo, Catarina; Almeida, Manuela; Bragança, Luís; Barbosa, José Amarilio

2016-01-01

Highlights: • A new cost–benefit method was developed to compare building solutions. • The method considers energy performance, life cycle costs and investment willingness. • The graphical analysis helps stakeholders to easily compare building solutions. • The method was applied to a case study showing consistency and feasibility. - Abstract: The building sector is responsible for consuming approximately 40% of the final energy in Europe. However, more than 50% of this consumption can be reduced through energy-efficient measures. Our society is facing not only a severe and unprecedented environmental crisis but also an economic crisis of similar magnitude. In light of this, EU has developed legislation promoting the use of the Cost-Optimal (CO) method in order to improve building energy efficiency, in which selection criteria is based on life cycle costs. Nevertheless, studies show that the implementation of energy-efficient solutions is far from ideal. Therefore, it is very important to analyse the reasons for this gap between theory and implementation as well as improve selection methods. This study aims to develop a methodology based on a cost-effectiveness analysis, which can be seen as an improvement to the CO method as it considers the investment willingness of stakeholders in the selection process of energy-efficient solutions. The method uses a simple graphical display in which the stakeholders’ investment willingness is identified as the slope of a reference line, allowing easy selection between building solutions. This method will lead to the selection of more desired – from stakeholders’ point of view – and more energy-efficient solutions than those selected through the CO method.

A fast method for optimal reactive power flow solution

Energy Technology Data Exchange (ETDEWEB)

Sadasivam, G; Khan, M A [Anna Univ., Madras (IN). Coll. of Engineering

1990-01-01

A fast successive linear programming (SLP) method for minimizing transmission losses and improving the voltage profile is proposed. The method uses the same compactly stored, factorized constant matrices in all the LP steps, both for power flow solution and for constructing the LP model. The inherent oscillatory convergence of SLP methods is overcome by proper selection of initial step sizes and their gradual reduction. Detailed studies on three systems, including a 109-bus system, reveal the fast and reliable convergence property of the method. (author).

The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

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Yadong Shang

2012-01-01

Full Text Available This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type for n and E, the solitary wave solutions of kink-type for E and bell-type for n, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

International Nuclear Information System (INIS)

Feng Qinghua

2013-01-01

In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)

The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

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H. O. Bakodah

2013-01-01

Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

Accuracy, Precision, Ease-Of-Use, and Cost of Methods to Test Ebola-Relevant Chlorine Solutions.

Directory of Open Access Journals (Sweden)

Emma Wells

Full Text Available To prevent transmission in Ebola Virus Disease (EVD outbreaks, it is recommended to disinfect living things (hands and people with 0.05% chlorine solution and non-living things (surfaces, personal protective equipment, dead bodies with 0.5% chlorine solution. In the current West African EVD outbreak, these solutions (manufactured from calcium hypochlorite (HTH, sodium dichloroisocyanurate (NaDCC, and sodium hypochlorite (NaOCl have been widely used in both Ebola Treatment Unit and community settings. To ensure solution quality, testing is necessary, however test method appropriateness for these Ebola-relevant concentrations has not previously been evaluated. We identified fourteen commercially-available methods to test Ebola-relevant chlorine solution concentrations, including two titration methods, four DPD dilution methods, and six test strips. We assessed these methods by: 1 determining accuracy and precision by measuring in quintuplicate five different 0.05% and 0.5% chlorine solutions manufactured from NaDCC, HTH, and NaOCl; 2 conducting volunteer testing to assess ease-of-use; and, 3 determining costs. Accuracy was greatest in titration methods (reference-12.4% error compared to reference method, then DPD dilution methods (2.4-19% error, then test strips (5.2-48% error; precision followed this same trend. Two methods had an accuracy of <10% error across all five chlorine solutions with good precision: Hach digital titration for 0.05% and 0.5% solutions (recommended for contexts with trained personnel and financial resources, and Serim test strips for 0.05% solutions (recommended for contexts where rapid, inexpensive, and low-training burden testing is needed. Measurement error from test methods not including pH adjustment varied significantly across the five chlorine solutions, which had pH values 5-11. Volunteers found test strip easiest and titration hardest; costs per 100 tests were $14-37 for test strips and $33-609 for titration

75 FR 77664 - Honeywell International, Inc., Automation and Control Solutions Division, Including On-Site...

Science.gov (United States)

2010-12-13

..., Inc., Automation and Control Solutions Division, Including On-Site Leased Workers From Manpower... Solutions Division. The Department has determined that these workers were sufficiently under the control of Honeywell International, Inc., Automation and Control Solutions Division to be considered leased workers...

Redox reactions for group 5 elements, including element 105, in aqueous solutions

International Nuclear Information System (INIS)

Ionova, G.V.; Pershina, V.; Johnson, E.; Fricke, B.; Schaedel, M.

1992-08-01

Standard redox potentials Edeg(M z+x /M z+ ) in acidic solutions for group 5 elements including element 105 (Ha) and the actinide, Pa, have been estimated on the basis of the ionization potentials calculated via the multiconfiguration Dirac-Fock method. Stability of the pentavalent state was shown to increase along the group from V to Ha, while that of the tetra- and trivalent states decreases in this direction. Our estimates have shown no extra stability of the trivalent state of hahnium. Element 105 should form mixed-valence complexes by analogy with Nb due to the similar values of their potentials Edeg(M 3+ /M 2+ ). The stability of the maximum oxidation state of the elements decreases in the direction 103 > 104 > 105. (orig.)

78 FR 19530 - Eastman Kodak Company (GCG), Electrographic Print Solutions, Including On-Site Leased Workers...

Science.gov (United States)

2013-04-01

... Kodak Company (GCG), Electrographic Print Solutions, Including On-Site Leased Workers From Adecco and Datrose, Spencerport, New York; Eastman Kodak Company, IPS, Including On-Site Leased Workers From Adecco..., 2011, applicable to workers of Eastman Kodak Company (GCG), Electrographic Print Solutions, including...

A new solution method for wheel/rail rolling contact.

Science.gov (United States)

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

An investigation of calibration methods for solution calorimetry.

Science.gov (United States)

Yff, Barbara T S; Royall, Paul G; Brown, Marc B; Martin, Gary P

2004-01-28

Solution calorimetry has been used in a number of varying applications within pharmaceutical research as a technique for the physical characterisation of pharmaceutical materials, such as quantifying small degrees of amorphous content, identifying polymorphs and investigating interactions between drugs and carbohydrates or proteins and carbohydrates. A calibration test procedure is necessary to validate the instrumentation; a few of the suggested calibration reactions are the enthalpies of solution associated with dissolving Tris in 0.1 M HCl or NaCl, KCl or propan-1-ol in water. In addition, there are a number of different methods available to determine enthalpies of solution from the experimental data provided by the calorimeter, for example, the Regnault-Pfaundler's method, a graphical extrapolation based on the Dickinson method, or a manual integration-based method. Thus, the aim of the study was to investigate how each of these methods influences the values for the enthalpy of solution. Experiments were performed according to the method outlined by Hogan and Buckton [Int. J. Pharm. 207 (2000) 57] using KCl (samples of 50, 100 and 200 mg), Tris and sucrose as calibrants. For all three materials the manual integration method was found to be the most consistent with the KCl in water (sample mass of 200 mg) being the most precise. Thus, this method is recommended for the validation of solution calorimeters.

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

DEFF Research Database (Denmark)

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

Chemical deposition methods using supercritical fluid solutions

Science.gov (United States)

Sievers, Robert E.; Hansen, Brian N.

1990-01-01

A method for depositing a film of a desired material on a substrate comprises dissolving at least one reagent in a supercritical fluid comprising at least one solvent. Either the reagent is capable of reacting with or is a precursor of a compound capable of reacting with the solvent to form the desired product, or at least one additional reagent is included in the supercritical solution and is capable of reacting with or is a precursor of a compound capable of reacting with the first reagent or with a compound derived from the first reagent to form the desired material. The supercritical solution is expanded to produce a vapor or aerosol and a chemical reaction is induced in the vapor or aerosol so that a film of the desired material resulting from the chemical reaction is deposited on the substrate surface. In an alternate embodiment, the supercritical solution containing at least one reagent is expanded to produce a vapor or aerosol which is then mixed with a gas containing at least one additional reagent. A chemical reaction is induced in the resulting mixture so that a film of the desired material is deposited.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Directory of Open Access Journals (Sweden)

Rahmatullah

2018-03-01

Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

78 FR 25304 - Siemens Medical Solutions, USA, Inc., Oncology Care Systems (Radiation Oncology), Including On...

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2013-04-30

..., USA, Inc., Oncology Care Systems (Radiation Oncology), Including On-Site Leased Workers From Source... Medical Solutions, USA, Inc., Oncology Care Systems (Radiation Oncology), including on- site leased... of February 2013, Siemens Medical Solutions, USA, Inc., Oncology Care Systems (Radiation Oncology...

Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

Science.gov (United States)

Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

2013-08-01

By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

Particular solution of the discrete-ordinate method.

Science.gov (United States)

Qin, Yi; Box, Michael A; Jupp, David L

2004-06-20

We present two methods that can be used to derive the particular solution of the discrete-ordinate method (DOM) for an arbitrary source in a plane-parallel atmosphere, which allows us to solve the transfer equation 12-18% faster in the case of a single beam source and is even faster for the atmosphere thermal emission source. We also remove the divide by zero problem that occurs when a beam source coincides with a Gaussian quadrature point. In our implementation, solution for multiple sources can be obtained simultaneously. For each extra source, it costs only 1.3-3.6% CPU time required for a full solution. The GDOM code that we developed previously has been revised to integrate with the DOM. Therefore we are now able to compute the Green's function and DOM solutions simultaneously.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Science.gov (United States)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Computer methods in physics 250 problems with guided solutions

CERN Document Server

Landau, Rubin H

2018-01-01

Our future scientists and professionals must be conversant in computational techniques. In order to facilitate integration of computer methods into existing physics courses, this textbook offers a large number of worked examples and problems with fully guided solutions in Python as well as other languages (Mathematica, Java, C, Fortran, and Maple). It’s also intended as a self-study guide for learning how to use computer methods in physics. The authors include an introductory chapter on numerical tools and indication of computational and physics difficulty level for each problem.

The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions

Directory of Open Access Journals (Sweden)

Mehmet Tarik Atay

2013-01-01

Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.

Patched based methods for adaptive mesh refinement solutions of partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Saltzman, J.

1997-09-02

This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.

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

Science.gov (United States)

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

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

Method for improving solution flow in solution mining of a mineral

International Nuclear Information System (INIS)

Moore, T.

1980-01-01

An improved method for the solution mining of a mineral from a subterranean formation containing same in which an injection and production well are drilled and completed within said formation, leach solution and an oxidant are injected through said injection well into said formation to dissolve said mineral, and said dissolved mineral is recovered via said production well, wherein the improvement comprises pretreating said formation with an acid gas to improve the permeabiltiy thereof

Spectral radiative property control method based on filling solution

International Nuclear Information System (INIS)

Jiao, Y.; Liu, L.H.; Hsu, P.-F.

2014-01-01

Controlling thermal radiation by tailoring spectral properties of microstructure is a promising method, can be applied in many industrial systems and have been widely researched recently. Among various property tailoring schemes, geometry design of microstructures is a commonly used method. However, the existing radiation property tailoring is limited by adjustability of processed microstructures. In other words, the spectral radiative properties of microscale structures are not possible to change after the gratings are fabricated. In this paper, we propose a method that adjusts the grating spectral properties by means of injecting filling solution, which could modify the thermal radiation in a fabricated microstructure. Therefore, this method overcomes the limitation mentioned above. Both mercury and water are adopted as the filling solution in this study. Aluminum and silver are selected as the grating materials to investigate the generality and limitation of this control method. The rigorous coupled-wave analysis is used to investigate the spectral radiative properties of these filling solution grating structures. A magnetic polaritons mechanism identification method is proposed based on LC circuit model principle. It is found that this control method could be used by different grating materials. Different filling solutions would enable the high absorption peak to move to longer or shorter wavelength band. The results show that the filling solution grating structures are promising for active control of spectral radiative properties. -- Highlights: • A filling solution grating structure is designed to adjust spectral radiative properties. • The mechanism of radiative property control is studied for engineering utilization. • Different grating materials are studied to find multi-functions for grating

Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration

Science.gov (United States)

Woollands, Robyn M.; Read, Julie L.; Probe, Austin B.; Junkins, John L.

2017-12-01

We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-shooting method in that integration of the state transition matrix (36 additional differential equations) is not required, and instead it makes use of a reference trajectory and a set of n particular solutions. Any numerical integrator can be used for solving two-point boundary problems with the method of particular solutions, however we show that using modified Chebyshev-Picard iteration affords an avenue for increased efficiency that is not available with other step-by-step integrators. We take advantage of the path approximation nature of modified Chebyshev-Picard iteration (nodes iteratively converge to fixed points in space) and utilize a variable fidelity force model for propagating the reference trajectory. Remarkably, we demonstrate that computing the particular solutions with only low fidelity function evaluations greatly increases the efficiency of the algorithm while maintaining machine precision accuracy. Our study reveals that solving the perturbed Lambert's problem using the method of particular solutions with modified Chebyshev-Picard iteration is about an order of magnitude faster compared with the classical shooting method and a tenth-twelfth order Runge-Kutta integrator. It is well known that the solution to Lambert's problem over multiple revolutions is not unique and to ensure that all possible solutions are considered we make use of a reliable preexisting Keplerian Lambert solver to warm start our perturbed algorithm.

Solution of the porous media equation by Adomian's decomposition method

International Nuclear Information System (INIS)

Pamuk, Serdal

2005-01-01

The particular exact solutions of the porous media equation that usually occurs in nonlinear problems of heat and mass transfer, and in biological systems are obtained using Adomian's decomposition method. Also, numerical comparison of particular solutions in the decomposition method indicate that there is a very good agreement between the numerical solutions and particular exact solutions in terms of efficiency and accuracy

Method for Non-Invasive Determination of Chemical Properties of Aqueous Solutions

Science.gov (United States)

Todd, Paul W. (Inventor); Jones, Alan (Inventor); Thomas, Nathan A. (Inventor)

2016-01-01

A method for non-invasively determining a chemical property of an aqueous solution is provided. The method provides the steps of providing a colored solute having a light absorbance spectrum and transmitting light through the colored solute at two different wavelengths. The method further provides the steps of measuring light absorbance of the colored solute at the two different transmitted light wavelengths, and comparing the light absorbance of the colored solute at the two different wavelengths to determine a chemical property of an aqueous solution.

Perturbation method for periodic solutions of nonlinear jerk equations

International Nuclear Information System (INIS)

Hu, H.

2008-01-01

A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

Modified harmonic balance method for the solution of nonlinear jerk equations

Science.gov (United States)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Method for Cs-137 separation from the decontamination solutions

International Nuclear Information System (INIS)

Toropov, I.G.; Efremenkov, V.M.; Toropova, V.V.; Satsukevich, V.M.; Davidov, Yu.P.

1995-01-01

In this work results of investigations are presented on separation of radiocaesium from the decontamination solutions containing reducing agents (thiocarbamide). The scientific basis for radiocaesium removal from the solution focuses on the state of the radionuclide and its sorption behavior in the solution with a complicated composition. Then using a combination of sorption and ultrafiltration methods it would be possible to concentrate the radionuclide in a small volume and to purify the main part of the solution. As a sorbent for radiocaesium removal from the solution, a ferrocyanide based sorbent is proposed. Use of this sorbent is justified since its high selectivity and effectiveness for radiocaesium sorption from the solutions of different composition is well known. When synthesis of the sorbent is performed directly in the treating solution, two components as a minimum should be added to it, namely K 4 Fe(CN) 6 and metal ions of Ni-II, Co-II, Cu-II, etc. The results are presented which show the possibility of radiocaesium separation from the decontamination solutions (containing 60--100 g/l of salts) using sorption and membrane separation methods without the use of metal salts. At the same time by using FE-2 in solution in the presence of cyanide ions and thiocarbamide, it is possible to avoid the addition of metal salts (Ni, Cu, etc.). Utilization of the proposed method for spent decontamination solution treatment allows a relatively easy way to reduce the concentration of radiocaesium in solution on 2--4 orders of magnitudes, and to exclude the utilization of relatively expensive metal salts

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

Science.gov (United States)

Felici, Helene Marie

1992-01-01

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

The Method of Manufactured Solutions for RattleSnake A SN Radiation Transport Solver Inside the MOOSE Framework

International Nuclear Information System (INIS)

Wang, Yaqi

2012-01-01

The Method of Manufactured Solutions (MMS) is an accepted technique to verify that a numerical discretization for the radiation transport equation has been implemented correctly. This technique offers a few advantages over other methods such as benchmark problems or analytical solutions. The solution can be manufactured such that properties for the angular flux are either stressed or preserved. For radiation transport, these properties can include desired smoothness, positiveness and arbitrary order of anisotropy in angle. Another advantage is that the angular flux solution can be manufactured for multidimensional problems where analytical solutions are difficult to obtain in general.

Determination of humic acid in alkali leaching solution of uranium by spectophotrometry-COD method

International Nuclear Information System (INIS)

Feng Yu; An Wei; Chen Shusen

2014-01-01

It is one of the main causes of extraction emulsification or resin toxicosis during alkali leaching process in uranium metallurgy which organic matters including humic acid exist in lixiviums. In order to study the effect of humic acid in uranium metallurgy, a method for determination of content of humic acid in aqueous solution need to be established. Spectrophotometry is a simple and convenient method in humic acid analysis. However, accuracy of spectrophotometry can be reduced greatly because of interference of uranium and other elements in the humic acid solutions. Although chemical oxygen demand (COD) method is a common analysis way of organic matters in aqueous solutions, the concentration of humic acid cannot be directly measured. In this paper, COD method is related with spectrophotometry to avoid the interference of uranium and ensure the accurate analysis of humic acid. The results showed that the detection limit of the method was 1.78 mg/L and the recovery rate was 101.2%. (authors)

Method of lines solution of Richards` equation

Energy Technology Data Exchange (ETDEWEB)

Kelley, C.T.; Miller, C.T.; Tocci, M.D.

1996-12-31

We consider the method of lines solution of Richard`s equation, which models flow through porous media, as an example of a situation in which the method can give incorrect results because of premature termination of the nonlinear corrector iteration. This premature termination arises when the solution has a sharp moving front and the Jacobian is ill-conditioned. While this problem can be solved by tightening the tolerances provided to the ODE or DAE solver used for the temporal integration, it is more efficient to modify the termination criteria of the nonlinear solver and/or recompute the Jacobian more frequently. In this paper we continue previous work on this topic by analyzing the modifications in more detail and giving a strategy on how the modifications can be turned on and off in response to changes in the character of the solution.

76 FR 13666 - Pitney Bowes, Inc., Mailing Solutions Management, Global Engineering Group, Including On-Site...

Science.gov (United States)

2011-03-14

...., Mailing Solutions Management, Global Engineering Group, Including On-Site Leased Workers From Guidant... workers and former workers of Pitney Bowes, Inc., Mailing Solutions Management Division, Engineering... reviewed the certification to clarify the subject worker group's identity. Additional information revealed...

Properties and solution methods for large location-allocation problems

DEFF Research Database (Denmark)

Juel, Henrik; Love, Robert F.

1982-01-01

Location-allocation with l$ _p$ distances is studied. It is shown that this structure can be expressed as a concave minimization programming problem. Since concave minimization algorithms are not yet well developed, five solution methods are developed which utilize the special properties of the l......Location-allocation with l$ _p$ distances is studied. It is shown that this structure can be expressed as a concave minimization programming problem. Since concave minimization algorithms are not yet well developed, five solution methods are developed which utilize the special properties...... of the location-allocation problem. Using the rectilinear distance measure, two of these algorithms achieved optimal solutions in all 102 test problems for which solutions were known. The algorithms can be applied to much larger problems than any existing exact methods....

Approximate solution fuzzy pantograph equation by using homotopy perturbation method

Science.gov (United States)

Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.

2017-09-01

In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.

Nonclassical pseudospectral method for the solution of brachistochrone problem

International Nuclear Information System (INIS)

Alipanah, A.; Razzaghi, M.; Dehghan, M.

2007-01-01

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature

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

Directory of Open Access Journals (Sweden)

De-Gang Wang

2012-01-01

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

Variation Iteration Method for The Approximate Solution of Nonlinear ...

African Journals Online (AJOL)

In this study, we considered the numerical solution of the nonlinear Burgers equation using the Variational Iteration Method (VIM). The method seeks to examine the convergence of solutions of the Burgers equation at the expense of the parameters x and t of which the amount of errors depends. Numerical experimentation ...

expansion method and travelling wave solutions for the perturbed ...

Indian Academy of Sciences (India)

Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...

Local existence of solutions to the Euler-Poisson system, including densities without compact support

Science.gov (United States)

Brauer, Uwe; Karp, Lavi

2018-01-01

Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density ρ which either falls off at infinity or has compact support. The solutions have finite mass, finite energy functional and include the static spherical solutions for γ = 6/5. The result is achieved by using weighted Sobolev spaces of fractional order and a new non-linear estimate which allows to estimate the physical density by the regularised non-linear matter variable. Gamblin also has studied this setting but using very different functional spaces. However we believe that the functional setting we use is more appropriate to describe a physical isolated body and more suitable to study the Newtonian limit.

Methods of Uranium Determination in solutions of Tributyl Phosphate and Kerosene

International Nuclear Information System (INIS)

Petrement Eguiluz, J.; Palomares Delgado, F.

1962-01-01

A new analytical method for the determination of uranium in organic solutions of tributyl phosphate and kerosene is proposed. In this method the uranium is reextracted from the aqueous phase by reduction with cadmium in acid solution. The uranium can be determined in this solution by the usual methods. In case of very diluted solutions, a direct spectrophtometrical determination of uranium in the organic phase with dibenzoylmethane is proposed. (Author) 21 refs

Properties of gases, liquids, and solutions principles and methods

CERN Document Server

Mason, Warren P

2013-01-01

Physical Acoustics: Principles and Methods, Volume ll-Part A: Properties of Gases, Liquids, and Solutions ponders on high frequency sound waves in gases, liquids, and solids that have been proven as effective tools in examining the molecular, domain wall, and other types of motions. The selection first offers information on the transmission of sound waves in gases at very low pressures and the phenomenological theory of the relaxation phenomena in gases. Topics include free molecule propagation, phenomenological thermodynamics of irreversible processes, and simultaneous multiple relaxation pro

Finite element method solution of simplified P3 equation for flexible geometry handling

International Nuclear Information System (INIS)

Ryu, Eun Hyun; Joo, Han Gyu

2011-01-01

In order to obtain efficiently core flux solutions which would be much closer to the transport solution than the diffusion solution is, not being limited by the geometry of the core, the simplified P 3 (SP 3 ) equation is solved with the finite element method (FEM). A generic mesh generator, GMSH, is used to generate linear and quadratic mesh data. The linear system resulting from the SP 3 FEM discretization is solved by Krylov subspace methods (KSM). A symmetric form of the SP 3 equation is derived to apply the conjugate gradient method rather than the KSMs for nonsymmetric linear systems. An optional iso-parametric quadratic mapping scheme, which is to selectively model nonlinear shapes with a quadratic mapping to prevent significant mismatch in local domain volume, is also implemented for efficient application of arbitrary geometry handling. The gain in the accuracy attainable by the SP 3 solution over the diffusion solution is assessed by solving numerous benchmark problems having various core geometries including the IAEA PWR problems involving rectangular fuels and the Takeda fast reactor problems involving hexagonal fuels. The reference transport solution is produced by the McCARD Monte Carlo code and the multiplication factor and power distribution errors are assessed. In addition, the effect of quadratic mapping is examined for circular cell problems. It is shown that significant accuracy gain is possible with the SP 3 solution for the fast reactor problems whereas only marginal improvement is noted for thermal reactor problems. The quadratic mapping is also quite effective handling geometries with curvature. (author)

The method of lines solution of discrete ordinates method for non-grey media

International Nuclear Information System (INIS)

Cayan, Fatma Nihan; Selcuk, Nevin

2007-01-01

A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach

Systems and methods for laser assisted sample transfer to solution for chemical analysis

Science.gov (United States)

Van Berkel, Gary J; Kertesz, Vilmos; Ovchinnikova, Olga S

2013-08-27

Systems and methods are described for laser ablation of an analyte from a specimen and capturing of the analyte in a dispensed solvent to form a testing solution. A solvent dispensing and extraction system can form a liquid microjunction with the specimen. The solvent dispensing and extraction system can include a surface sampling probe. The laser beam can be directed through the surface sampling probe. The surface sampling probe can also serve as an atomic force microscopy probe. The surface sampling probe can form a seal with the specimen. The testing solution including the analyte can then be analyzed using an analytical instrument or undergo further processing.

Solution of the Schroedinger equation by a spectral method

International Nuclear Information System (INIS)

Feit, M.D.; Fleck, J.A. Jr.; Steiger, A.

1982-01-01

A new computational method for determining the eigenvalues and eigenfunctions of the Schroedinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schroedinger equation. The method requires the computation of a correlation function from a numerical solution psi(r, t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of psi(r, t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Henon--Heiles potential

Comparison of different methods for the solution of sets of linear equations

International Nuclear Information System (INIS)

Bilfinger, T.; Schmidt, F.

1978-06-01

The application of the conjugate-gradient methods as novel general iterative methods for the solution of sets of linear equations with symmetrical systems matrices led to this paper, where a comparison of these methods with the conventional differently accelerated Gauss-Seidel iteration was carried out. In additon, the direct Cholesky method was also included in the comparison. The studies referred mainly to memory requirement, computing time, speed of convergence, and accuracy of different conditions of the systems matrices, by which also the sensibility of the methods with respect to the influence of truncation errors may be recognized. (orig.) 891 RW [de

Optimisation-Based Solution Methods for Set Partitioning Models

DEFF Research Database (Denmark)

Rasmussen, Matias Sevel

The scheduling of crew, i.e. the construction of work schedules for crew members, is often not a trivial task, but a complex puzzle. The task is complicated by rules, restrictions, and preferences. Therefore, manual solutions as well as solutions from standard software packages are not always su......_cient with respect to solution quality and solution time. Enhancement of the overall solution quality as well as the solution time can be of vital importance to many organisations. The _elds of operations research and mathematical optimisation deal with mathematical modelling of di_cult scheduling problems (among...... other topics). The _elds also deal with the development of sophisticated solution methods for these mathematical models. This thesis describes the set partitioning model which has been widely used for modelling crew scheduling problems. Integer properties for the set partitioning model are shown...

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

Science.gov (United States)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

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

International Nuclear Information System (INIS)

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

1999-01-01

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

Construct solitary solutions of discrete hybrid equation by Adomian Decomposition Method

International Nuclear Information System (INIS)

Wang Zhen; Zhang Hongqing

2009-01-01

In this paper, we apply the Adomian Decomposition Method to solving the differential-difference equations. A typical example is applied to illustrate the validity and the great potential of the Adomian Decomposition Method in solving differential-difference equation. Kink shaped solitary solution and Bell shaped solitary solution are presented. Comparisons are made between the results of the proposed method and exact solutions. The results show that the Adomian Decomposition Method is an attractive method in solving the differential-difference equations.

Algebraic methods for solution of polyhedra

Energy Technology Data Exchange (ETDEWEB)

Sabitov, Idzhad Kh [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2011-06-30

By analogy with the solution of triangles, the solution of polyhedra means a theory and methods for calculating some geometric parameters of polyhedra in terms of other parameters of them. The main content of this paper is a survey of results on calculating the volumes of polyhedra in terms of their metrics and combinatorial structures. It turns out that a far-reaching generalization of Heron's formula for the area of a triangle to the volumes of polyhedra is possible, and it underlies the proof of the conjecture that the volume of a deformed flexible polyhedron remains constant. Bibliography: 110 titles.

A general solution strategy of modified power method for higher mode solutions

International Nuclear Information System (INIS)

Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung

2016-01-01

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the new strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.

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

KAUST Repository

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

2015-01-01

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

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

KAUST Repository

Frohne, Jörg

2015-08-06

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

Monte Carlo methods for flux expansion solutions of transport problems

International Nuclear Information System (INIS)

Spanier, J.

1999-01-01

Adaptive Monte Carlo methods, based on the use of either correlated sampling or importance sampling, to obtain global solutions to certain transport problems have recently been described. The resulting learning algorithms are capable of achieving geometric convergence when applied to the estimation of a finite number of coefficients in a flux expansion representation of the global solution. However, because of the nonphysical nature of the random walk simulations needed to perform importance sampling, conventional transport estimators and source sampling techniques require modification to be used successfully in conjunction with such flux expansion methods. It is shown how these problems can be overcome. First, the traditional path length estimators in wide use in particle transport simulations are generalized to include rather general detector functions (which, in this application, are the individual basis functions chosen for the flus expansion). Second, it is shown how to sample from the signed probabilities that arise as source density functions in these applications, without destroying the zero variance property needed to ensure geometric convergence to zero error

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

Science.gov (United States)

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

CFD code verification and the method of manufactured solutions

International Nuclear Information System (INIS)

Pelletier, D.; Roache, P.J.

2002-01-01

This paper presents the Method of Manufactured Solutions (MMS) for CFD code verification. The MMS provides benchmark solutions for direct evaluation of the solution error. The best benchmarks are exact analytical solutions with sufficiently complex solution structure to ensure that all terms of the differential equations are exercised in the simulation. The MMS provides a straight forward and general procedure for generating such solutions. When used with systematic grid refinement studies, which are remarkably sensitive, the MMS provides strong code verification with a theorem-like quality. The MMS is first presented on simple 1-D examples. Manufactured solutions for more complex problems are then presented with sample results from grid convergence studies. (author)

On numerical solution of Burgers' equation by homotopy analysis method

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

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

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

Science.gov (United States)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

76 FR 2710 - Pitney Bowes, Inc., Mailing Solutions Management Division Including On-Site Leased Workers of...

Science.gov (United States)

2011-01-14

...., Mailing Solutions Management Division Including On-Site Leased Workers of Guidant Group, and Teleworkers... Bowes, Inc., Mailing Solutions Management Division, Engineering Quality Assurance, Shelton, Connecticut... identity of the subject worker group. The worker group consists of workers of Pitney Bowes, Inc., the...

Collection of proceedings of the international conference on programming and mathematical methods for solution of physical problems

International Nuclear Information System (INIS)

1994-01-01

Traditional International Conference on programming and mathematical methods for solution of physical problems took place in Dubna in Jun, 14-19, 1993. More than 160 scientists from 14 countries participated in the Conference. They presented about 120 reports, the range of problems including computerized information complexes, experimental data acquisition and processing systems, mathematical simulation and calculation experiment in physics, analytical and numerical methods for solution of physical problems

New numerical method for solving the solute transport equation

International Nuclear Information System (INIS)

Ross, B.; Koplik, C.M.

1978-01-01

The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

The functional variable method for finding exact solutions of some ...

Indian Academy of Sciences (India)

Abstract. In this paper, we implemented the functional variable method and the modified. Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled. KdV system. This method is extremely simple ...

Method of continuously regenerating decontaminating electrolytic solution

International Nuclear Information System (INIS)

Sasaki, Takashi; Kobayashi, Toshio; Wada, Koichi.

1985-01-01

Purpose: To continuously recover radioactive metal ions from the electrolytic solution used for the electrolytic decontamination of radioactive equipment and increased with the radioactive dose, as well as regenerate the electrolytic solution to a high concentration acid. Method: A liquid in an auxiliary tank is recycled to a cathode chamber containing water of an electro depositing regeneration tank to render pH = 2 by way of a pH controller and a pH electrode. The electrolytic solution in an electrolytic decontaminating tank is introduced by way of an injection pump to an auxiliary tank and, interlocking therewith, a regenerating solution is introduced from a regenerating solution extracting pump by way of a extraction pipeway to an electrolytic decontaminating tank. Meanwhile, electric current is supplied to the electrode to deposit radioactive metal ions dissolved in the cathode chamber on the capturing electrode. While on the other hand, anions are transferred by way of a partition wall to an anode chamber to regenerate the electrolytic solution to high concentration acid solution. While on the other hand, water is supplied by way of an electromagnetic valve interlocking with the level meter to maintain the level meter constant. This can decrease the generation of the liquid wastes and also reduce the amount of the radioactive secondary wastes. (Horiuchi, T.)

Composition and method for solution mining of uranium ores

International Nuclear Information System (INIS)

Lawes, B.C.; Watts, J.C.

1981-01-01

It has been found that, in the solution mining of uranium ores using ammonium carbonate solutions containing hydrogen peroxide or ozone as an oxidant, the tendency of the formation being treated to become less permeable during the leaching process can be overcome by including in the leaching solution a very small concentration of sodium silicate

A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

OpenAIRE

Mehmet Ali Akinlar; Muhammet Kurulay

2013-01-01

A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...

78 FR 28642 - Eastman Kodak Company, Electrographic Print Solutions, Including On-Site Leased Workers From...

Science.gov (United States)

2013-05-15

... Kodak Company, Electrographic Print Solutions, Including On-Site Leased Workers From Adecco and Datrose, Spencerport, New York; Eastman Kodak Company, IPS, Including On-Site Leased Workers From Adecco, Dayton, Ohio... Trade Adjustment Assistance (TAA) filed on behalf of Eastman Kodak Company, Electrographic Print...

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity.

Science.gov (United States)

Atroshchenko, Elena; Bordas, Stéphane P A

2015-07-08

In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

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

2015-01-01

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

Defining collaborative business rules management solutions : framework and method

NARCIS (Netherlands)

dr. Martijn Zoet; Johan Versendaal

2014-01-01

From the publishers' website: The goal of this research is to define a method for configuring a collaborative business rules management solution from a value proposition perspective. In an earlier published study (Business rules management solutions: added value by means of business

The method of determination of micro quantities of labeled iodide in carrier free Na125 solution

International Nuclear Information System (INIS)

Kholbaev, A.Kh.; Shilin, E.A.

1996-01-01

The method of determination of microquantities of labelled iodide in Na 125 carrier-free solution was elaborated. This method permits to increase the sensitivity and radiation protection of the determination of labeled iodide. It includes oxidation of iodide by iodate in diluted sulphuric acid with molar concentration 0,03-0,04 mole/l. The extraction of I 2 is made by toluene. The coloured solution is made and optical density is measured at λ=640 nm at the 10 mm optical path .(A.A.D.)

Milestones in the Development of Iterative Solution Methods

Czech Academy of Sciences Publication Activity Database

Axelsson, Owe

2010-01-01

Roč. 2010, - (2010), s. 1-33 ISSN 2090-0147 Institutional research plan: CEZ:AV0Z30860518 Keywords : iterative solution methods * convergence acceleration methods * linear systems Subject RIV: JC - Computer Hardware ; Software http://www.hindawi.com/journals/jece/2010/972794.html

Higher-order approximate solutions to the relativistic and Duffing-harmonic oscillators by modified He's homotopy methods

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T

2008-01-01

A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient

Compacton solutions and multiple compacton solutions for a continuum Toda lattice model

International Nuclear Information System (INIS)

Fan Xinghua; Tian Lixin

2006-01-01

Some special solutions of the Toda lattice model with a transversal degree of freedom are obtained. With the aid of Mathematica and Wu elimination method, more explicit solitary wave solutions, including compacton solutions, multiple compacton solutions, peakon solutions, as well as periodic solutions are found in this paper

Numerical Solution of Nonlinear Fredholm Integro-Differential Equations Using Spectral Homotopy Analysis Method

Directory of Open Access Journals (Sweden)

Z. Pashazadeh Atabakan

2013-01-01

Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.

An Adaptive Physics-Based Method for the Solution of One-Dimensional Wave Motion Problems

Directory of Open Access Journals (Sweden)

Masoud Shafiei

2015-12-01

Full Text Available In this paper, an adaptive physics-based method is developed for solving wave motion problems in one dimension (i.e., wave propagation in strings, rods and beams. The solution of the problem includes two main parts. In the first part, after discretization of the domain, a physics-based method is developed considering the conservation of mass and the balance of momentum. In the second part, adaptive points are determined using the wavelet theory. This part is done employing the Deslauries-Dubuc (D-D wavelets. By solving the problem in the first step, the domain of the problem is discretized by the same cells taking into consideration the load and characteristics of the structure. After the first trial solution, the D-D interpolation shows the lack and redundancy of points in the domain. These points will be added or eliminated for the next solution. This process may be repeated for obtaining an adaptive mesh for each step. Also, the smoothing spline fit is used to eliminate the noisy portion of the solution. Finally, the results of the proposed method are compared with the results available in the literature. The comparison shows excellent agreement between the obtained results and those already reported.

A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

Directory of Open Access Journals (Sweden)

Mehmet Ali Akinlar

2013-01-01

Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.

Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

Directory of Open Access Journals (Sweden)

Daniel Olvera

2014-01-01

Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

Science.gov (United States)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Acceleration of monte Carlo solution by conjugate gradient method

International Nuclear Information System (INIS)

Toshihisa, Yamamoto

2005-01-01

The conjugate gradient method (CG) was applied to accelerate Monte Carlo solutions in fixed source problems. The equilibrium model based formulation enables to use CG scheme as well as initial guess to maximize computational performance. This method is available to arbitrary geometry provided that the neutron source distribution in each subregion can be regarded as flat. Even if it is not the case, the method can still be used as a powerful tool to provide an initial guess very close to the converged solution. The major difference of Monte Carlo CG to deterministic CG is that residual error is estimated using Monte Carlo sampling, thus statistical error exists in the residual. This leads to a flow diagram specific to Monte Carlo-CG. Three pre-conditioners were proposed for CG scheme and the performance was compared with a simple 1-D slab heterogeneous test problem. One of them, Sparse-M option, showed an excellent performance in convergence. The performance per unit cost was improved by four times in the test problem. Although direct estimation of efficiency of the method is impossible mainly because of the strong problem-dependence of the optimized pre-conditioner in CG, the method seems to have efficient potential as a fast solution algorithm for Monte Carlo calculations. (author)

Interaction of sodium monoborate and boric acid with some mono- and disaccharides in aqueous solutions (from data on isomolar solutions method)

International Nuclear Information System (INIS)

Shvarts, E.M.; Ignash, R.T.; Belousova, R.G.

2000-01-01

Interaction of sodium monoborate Na[B(OH) 4 ] and boric acid with D-glucose, D-fructose, D-saccharose and D-lactose in aqueous solution depending on the solution total concentration is studied through the method of isomolar solutions with application of conductometry and polarimetry. It is shown by the D-glucose and D-fructose examples that the method of isomolar solutions leads to results compatible with the data obtained by other methods and it may be applied to other saccharides [ru

Hydrogen/deuterium substitution methods: understanding water structure in solution

International Nuclear Information System (INIS)

Soper, A.K.

1993-01-01

The hydrogen/deuterium substitution method has been used for different applications, such as the short range order between water molecules in a number of different environments (aqueous solutions of organic molecules), or to study the partial structure factors of water at high pressure and temperature. The absolute accuracy that can be obtained remains uncertain, but important qualitative information can be obtained on the local organization of water in aqueous solution. Some recent results with pure water, methanol and dimethyl sulphoxide (DMSO) solutions are presented. It is shown that the short range water structure is not greatly affected by most solutes except at high concentrations and when the solute species has its own distinctive interaction with water (such as a dissolved small ion). 3 figs., 14 refs

System and method for laser assisted sample transfer to solution for chemical analysis

Science.gov (United States)

Van Berkel, Gary J; Kertesz, Vilmos

2014-01-28

A system and method for laser desorption of an analyte from a specimen and capturing of the analyte in a suspended solvent to form a testing solution are described. The method can include providing a specimen supported by a desorption region of a specimen stage and desorbing an analyte from a target site of the specimen with a laser beam centered at a radiation wavelength (.lamda.). The desorption region is transparent to the radiation wavelength (.lamda.) and the sampling probe and a laser source emitting the laser beam are on opposite sides of a primary surface of the specimen stage. The system can also be arranged where the laser source and the sampling probe are on the same side of a primary surface of the specimen stage. The testing solution can then be analyzed using an analytical instrument or undergo further processing.

Solutions of hyperbolic equations with the CIP-BS method

International Nuclear Information System (INIS)

Utsumi, Takayuki; Koga, James; Yamagiwa, Mitsuru; Yabe, Takashi; Aoki, Takayuki

2004-01-01

In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve general hyperbolic equations efficiently. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution owing to the constraints from the spatial derivatives of the master equations. Then, introducing scalar products, the linear and nonlinear partial differential equations are uniquely reduced to the ordinary differential equations for values and spatial derivatives at the grid points. The method gives stable, less diffusive, and accurate results. It is successfully applied to the continuity equation, the Burgers equation, the Korteweg-de Vries equation, and one-dimensional shock tube problems. (author)

Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

Directory of Open Access Journals (Sweden)

Sadaf Bibi

2014-03-01

Full Text Available Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme.

Recovery of iron/iron oxide nanoparticles from solution: comparison of methods and their effects

International Nuclear Information System (INIS)

Nurmi, James T.; Sarathy, Vaishnavi; Tratnyek, Paul G.; Baer, Donald R.; Amonette, James E.; Karkamkar, Abhi

2011-01-01

Most methods currently being used to recover Fe 0 -core/oxide-shell nanoparticles from solutions (including the solvents they are synthesized or stored in) are potentially problematic because they may alter the particle composition (e.g., depositing salts formed from solutes) or leave the particles prone to transformations during subsequent storage and handling (e.g., due to residual moisture). In this study, several methods for recovery of nanoparticles from aqueous solution were studied to determine how they affect the structure and reactivity of the recovered materials. Simple washing of the nanoparticles during vacuum filtration (i.e., “flash drying”) can leave up to ∼17 wt% residual moisture. Modeling calculations suggest this moisture is mostly capillary or matric water held between particles and particle aggregates, which can be removed by drying for short periods at relative vapor pressures below 0.9. Flash drying followed by vacuum drying, all under N 2 , leaves no detectable residue from precipitation of solutes (detectable by X-ray photoelectron spectroscopy, XPS), no significant changes in overall particle composition or structure (determined by transmission electron microscopy, TEM), and negligible residual moisture (by thermogravimetric analysis, TGA). While this improved flash-drying protocol may be the preferred method for recovering nanoparticles for many purposes, we found that Fe 0 -core/oxide-shell nanoparticles still exhibit gradual aging during storage when characterized electrochemically with voltammetry.

Novel method for solution of coupled radial Schrödinger equations

International Nuclear Information System (INIS)

Ershov, S. N.; Vaagen, J. S.; Zhukov, M. V.

2011-01-01

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.

A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

OpenAIRE

Filatovas, Ernestas; Podkopaev, Dmitry; Kurasova, Olga

2015-01-01

Interactive methods of multiobjective optimization repetitively derive Pareto optimal solutions based on decision maker’s preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the Pareto optimal set and learning about the op...

Differential and difference equations a comparison of methods of solution

CERN Document Server

Maximon, Leonard C

2016-01-01

This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associat...

Method for separation of Cs from acid solution dissolving radionuclides and microanalysis of solution with ICP-AES

International Nuclear Information System (INIS)

Kanazawa, Toru; Hidaka, Akihide; Kudo, Tamotsu; Nakamura, Takehiko; Fuketa, Toyoshi

2004-06-01

The VEGA (Verification Experiments of radionuclides Gas/Aerosol release) program is being performed at JAERI to understand mechanisms of radionuclides release from irradiated fuel during severe accidents. As a part of evaluation in the program, the mass balances of released and deposited FP (Fission Products) onto the test apparatus are estimated from gamma ray measurement for acid solution leached from the apparatus, but short-life nuclides are difficult to be measured because those in the VEGA fuel have been mostly depleted due to cooling for several years. Moreover, the radionuclides without emitting gamma rays and very small quantity of elements cannot be quantified by gamma ray measurement. Therefore, a microanalysis by ICP-AES (Inductively Coupled Plasma - Atomic Emission Spectrometry) for the acid solution leached from VEGA apparatuses is being applied to evaluate the released and deposited masses for those elements. Since Cs-134 and -137, which are major FP dissolved in the solution, have high intensity of gamma ray spectrum, they have to be removed from the solution before the microanalysis in order to avoid contamination of ICP system and to decrease exposure to gamma ray. In this report, methods for separation of Cs from acid solution were reviewed and the applicability of them to the ICP-AES analysis was discussed. The method for Cs separation using the inorganic ion exchanger, AMP (Ammonium Molybdate Phosphate) was applied to the solutions of cold and hot test and the effectiveness was examined. The results showed that more than 99.9% of Cs could be removed from the test solutions, and once removed Sb by AMP was recovered by using a complexing agent such as citric acid. Next, the method was applied to an acid solution leached from VEGA-3 apparatus, and ICP-AES analysis was performed for it. The analysis showed that amount of U, Sr and Zr were successfully quantified. Most of elements to be analyzed were measurable except for Sb, Ag and Sn, although

Regularization and computational methods for precise solution of perturbed orbit transfer problems

Science.gov (United States)

Woollands, Robyn Michele

The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these

Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method

Directory of Open Access Journals (Sweden)

Hassan A. Zedan

2012-01-01

Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.

Fundamental solution of the problem of linear programming and method of its determination

Science.gov (United States)

Petrunin, S. V.

1978-01-01

The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method

Directory of Open Access Journals (Sweden)

Olumuyiwa A. Agbolade

2017-01-01

Full Text Available The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobatto collocation points were, respectively, chosen to collocate the approximate solution. Numerical experiments are performed on some sample problems already solved by homotopy analysis method and finite difference methods. Comparison of the absolute error is obtained from the present method and those from aforementioned methods. It is also observed that the absolute errors obtained are very low establishing convergence and computational efficiency.

Exercises in experimental physics including complete solutions

International Nuclear Information System (INIS)

Fleischmann, R.; Loos, G.

1978-01-01

This collection of exercises is not only addressed to students of physics but also to scientists of other branches and to engineers. Possibilities are offered to the student to gain control on his growing knowledge from the beginning of his studies until the examination. The individual exercises are linked thematically and are mostly composed by several single tasks. Complete and detailed numerical solutions are presented. The topics covered are: (1) Mechanics, (2) thermodynamics, (3) oscillations and their propagation, (4) electricity and magnetism, (5) atomic physics, and (6) nuclear physics. (KBE)

ANALYSIS AND PERFORMANCE MEASUREMENT OF EXISTING SOLUTION METHODS OF QUADRATIC ASSIGNMENT PROBLEM

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Morteza KARAMI

2014-01-01

Full Text Available Quadratic Assignment Problem (QAP is known as one of the most difficult combinatorial optimization problems that is classified in the category of NP-hard problems. Quadratic Assignment Problem Library (QAPLIB is a full database of QAPs which contains several problems from different authors and different sizes. Many exact and meta-heuristic solution methods have been introduced to solve QAP. In this study we focus on previously introduced solution methods of QAP e.g. Branch and Bound (B&B, Simulated Annealing (SA Algorithm, Greedy Randomized Adaptive Search Procedure (GRASP for dense and sparse QAPs. The codes of FORTRAN for these methods were downloaded from QAPLIB. All problems of QAPLIB were solved by the abovementioned methods. Several results were obtained from the computational experiments part. The Results show that the Branch and Bound method is able to introduce a feasible solution for all problems while Simulated Annealing Algorithm and GRASP methods are not able to find any solution for some problems. On the other hand, Simulated Annealing and GRASP methods have shorter run time comparing to the Branch and Bound method. In addition, the performance of the methods on the objective function value is discussed.

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

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Yusuf Pandir

2018-02-01

Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies.

Science.gov (United States)

Rukhin, Andrew L

2011-01-01

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.

Methods of pretreating comminuted cellulosic material with carbonate-containing solutions

Energy Technology Data Exchange (ETDEWEB)

Francis, Raymond

2012-11-06

Methods of pretreating comminuted cellulosic material with an acidic solution and then a carbonate-containing solution to produce a pretreated cellulosic material are provided. The pretreated material may then be further treated in a pulping process, for example, a soda-anthraquinone pulping process, to produce a cellulose pulp. The pretreatment solutions may be extracted from the pretreated cellulose material and selectively re-used, for example, with acid or alkali addition, for the pretreatment solutions. The resulting cellulose pulp is characterized by having reduced lignin content and increased yield compared to prior art treatment processes.

An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method

International Nuclear Information System (INIS)

Yabushita, Kazuki; Yamashita, Mariko; Tsuboi, Kazuhiro

2007-01-01

We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 x 10 3 ∼ 2 x 10 5 (for instance, a sphere) for practical situations, such as throwing a ball. It has been considered that the equations of motion of this case are unsolvable for a general projectile angle, although some solutions have been obtained for a small projectile angle using perturbation techniques. To obtain a general analytic solution, we apply Liao's homotopy analysis method to this problem. The homotopy analysis method, which is different from a perturbation technique, can be applied to a problem which does not include small parameters. We apply the homotopy analysis method for not only governing differential equations, but also an algebraic equation of a velocity vector to extend the radius of convergence. Ultimately, we obtain the analytic solution to this problem and investigate the validation of the solution

An evaluation of solutions to moment method of biochemical oxygen ...

African Journals Online (AJOL)

This paper evaluated selected solutions of moment method in respect to Biochemical Oxygen Demand (BOD) kinetics with the aim of ascertain error free solution. Domestic - institutional wastewaters were collected two - weekly for three months from waste - stabilization ponds in Obafemi Awolowo University, Ile - Ife.

Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

Directory of Open Access Journals (Sweden)

R. Darzi

2013-01-01

Full Text Available We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D0+αut+ft,ut=0, 0

The Telegraph Equation and Its Solution by Reduced Differential Transform Method

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2013-01-01

Full Text Available One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM. Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

A Marker Method for the Solution of the Damped Burgers' Equation

International Nuclear Information System (INIS)

Jerome L.V. Lewandowski

2005-01-01

A new method for the solution of the damped Burgers equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

Science.gov (United States)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Solidification method for organic solution and processing method of aqueous solution

International Nuclear Information System (INIS)

Kamoshida, Mamoru; Fukazawa, Tetsuo; Yazawa, Noriko; Hasegawa, Toshihiko

1998-01-01

The relative dielectric constant of an organic solution containing polar ingredients is controlled to 13 or less to enable its solidification. The polarity of the organic solution can be evaluated quantitatively by using the relative dielectric constant. If the relative dielectric constant is high, it can be controlled by dilution using a non-polar organic solvent of low relative dielectric constant. With such procedures, solidification can be conducted by using an economical 12-hydroxy stearic acid, process of liquid wastes can be facilitated and the safety can be ensured. (T.M.)

Soliton-like solutions to the GKdV equation by extended mapping method

International Nuclear Information System (INIS)

Wu Ranchao; Sun Jianhua

2007-01-01

In this note, many new exact solutions of the generalized KdV equation, such as rational solutions, periodic solutions like Jacobian elliptic and triangular functions, soliton-like solutions, are constructed by symbolic computation and the extended mapping method, with the auxiliary ordinary equation replaced by a more general one

Comparative analysis of solution methods of the punctual kinetic equations

International Nuclear Information System (INIS)

Hernandez S, A.

2003-01-01

The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)

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

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

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

76 FR 72978 - Whirlpool Corporation Including On-Site Leased Workers From Career Solutions TEC Staffing...

Science.gov (United States)

2011-11-28

... DEPARTMENT OF LABOR Employment and Training Administration [TA-W-74,593] Whirlpool Corporation Including On-Site Leased Workers From Career Solutions TEC Staffing, Andrews International, IBM Corporation... workers are engaged in the production of refrigerators and trash compactors. The notice was published in...

Technetium recovery from high alkaline solution

Energy Technology Data Exchange (ETDEWEB)

Nash, Charles A.

2016-07-12

Disclosed are methods for recovering technetium from a highly alkaline solution. The highly alkaline solution can be a liquid waste solution from a nuclear waste processing system. Methods can include combining the solution with a reductant capable of reducing technetium at the high pH of the solution and adding to or forming in the solution an adsorbent capable of adsorbing the precipitated technetium at the high pH of the solution.

Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions

Science.gov (United States)

Barkeshli, Kasra; Volakis, John L.

1991-01-01

The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.

Solution of problems in calculus of variations via He's variational iteration method

International Nuclear Information System (INIS)

Tatari, Mehdi; Dehghan, Mehdi

2007-01-01

In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years He's variational iteration method has been attracted a lot of attention of the researchers for solving nonlinear problems. This method finds the solution of the problem without any discretization of the equation. Since this method gives a closed form solution of the problem and avoids the round off errors, it can be considered as an efficient method for solving various kinds of problems. In this research He's variational iteration method will be employed for solving some problems in calculus of variations. Some examples are presented to show the efficiency of the proposed technique

Solution Methods for the Periodic Petrol Station Replenishment Problem

Directory of Open Access Journals (Sweden)

C Triki

2013-12-01

Full Text Available In this paper we introduce the Periodic Petrol Station Replenishment Problem (PPSRP over a T-day planning horizon and describe four heuristic methods for its solution. Even though all the proposed heuristics belong to the common partitioning-then-routing paradigm, they differ in assigning the stations to each day of the horizon. The resulting daily routing problems are then solved exactly until achieving optimalization. Moreover, an improvement procedure is also developed with the aim of ensuring a better quality solution. Our heuristics are tested and compared in two real-life cases, and our computational results show encouraging improvements with respect to a human planning solution

Parallel Jacobian-free Newton Krylov solution of the discrete ordinates method with flux limiters for 3D radiative transfer

International Nuclear Information System (INIS)

Godoy, William F.; Liu Xu

2012-01-01

The present study introduces a parallel Jacobian-free Newton Krylov (JFNK) general minimal residual (GMRES) solution for the discretized radiative transfer equation (RTE) in 3D, absorbing, emitting and scattering media. For the angular and spatial discretization of the RTE, the discrete ordinates method (DOM) and the finite volume method (FVM) including flux limiters are employed, respectively. Instead of forming and storing a large Jacobian matrix, JFNK methods allow for large memory savings as the required Jacobian-vector products are rather approximated by semiexact and numerical formulations, for which convergence and computational times are presented. Parallelization of the GMRES solution is introduced in a combined memory-shared/memory-distributed formulation that takes advantage of the fact that only large vector arrays remain in the JFNK process. Results are presented for 3D test cases including a simple homogeneous, isotropic medium and a more complex non-homogeneous, non-isothermal, absorbing–emitting and anisotropic scattering medium with collimated intensities. Additionally, convergence and stability of Gram–Schmidt and Householder orthogonalizations for the Arnoldi process in the parallel GMRES algorithms are discussed and analyzed. Overall, the introduction of JFNK methods results in a parallel, yet scalable to the tested 2048 processors, and memory affordable solution to 3D radiative transfer problems without compromising the accuracy and convergence of a Newton-like solution.

76 FR 73683 - Whirlpool Corporation, Including On-Site Leased Workers From Career Solutions TEC Staffing...

Science.gov (United States)

2011-11-29

... DEPARTMENT OF LABOR Employment and Training Administration [TA-W-74,593] Whirlpool Corporation, Including On-Site Leased Workers From Career Solutions TEC Staffing, Andrews International, IBM Corporation... refrigerators and trash compactors. The notice was published in the Federal Register on October 25, 2010 (75 FR...

Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method

Directory of Open Access Journals (Sweden)

Shaheed N. Huseen

2013-01-01

Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

Two new solutions to the third-order symplectic integration method

International Nuclear Information System (INIS)

Iwatsu, Reima

2009-01-01

Two new solutions are obtained for the symplecticity conditions of explicit third-order partitioned Runge-Kutta time integration method. One of them has larger stability limit and better dispersion property than the Ruth's method.

An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

DEFF Research Database (Denmark)

Larsen, Niels Vesterdal; Breinbjerg, Olav

2004-01-01

Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

Solution methods for large systems of linear equations in BACCHUS

International Nuclear Information System (INIS)

Homann, C.; Dorr, B.

1993-05-01

The computer programme BACCHUS is used to describe steady state and transient thermal-hydraulic behaviour of a coolant in a fuel element with intact geometry in a fast breeder reactor. In such computer programmes generally large systems of linear equations with sparse matrices of coefficients, resulting from discretization of coolant conservation equations, must be solved thousands of times giving rise to large demands of main storage and CPU time. Direct and iterative solution methods of the systems of linear equations, available in BACCHUS, are described, giving theoretical details and experience with their use in the programme. Besides use of a method of lines, a Runge-Kutta-method, for solution of the partial differential equation is outlined. (orig.) [de

On the method of solution of the differential-delay Toda equation

Science.gov (United States)

Villarroel, Javier; Ablowitz, Mark J.

1993-09-01

The method of solution of the Toda differential-delay equation, which is a reduction of the Toda equation in 2+1 dimensions, is described. An important feature of the solution process is to obtain and study a novel Riemann-Hilbert problem. The latter problem requires factorization across an infinite number of strips with a suitable branching structure. Explicit soliton solutions are given.

Gas storage materials, including hydrogen storage materials

Science.gov (United States)

Mohtadi, Rana F; Wicks, George G; Heung, Leung K; Nakamura, Kenji

2013-02-19

A material for the storage and release of gases comprises a plurality of hollow elements, each hollow element comprising a porous wall enclosing an interior cavity, the interior cavity including structures of a solid-state storage material. In particular examples, the storage material is a hydrogen storage material such as a solid state hydride. An improved method for forming such materials includes the solution diffusion of a storage material solution through a porous wall of a hollow element into an interior cavity.

Solution of the isotopic depletion equation using decomposition method and analytical solution

Energy Technology Data Exchange (ETDEWEB)

Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S., E-mail: fprata@con.ufrj.br, E-mail: fernando@con.ufrj.br, E-mail: aquilino@lmp.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (PEN/COPPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear

2011-07-01

In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)

Solution of the isotopic depletion equation using decomposition method and analytical solution

International Nuclear Information System (INIS)

Prata, Fabiano S.; Silva, Fernando C.; Martinez, Aquilino S.

2011-01-01

In this paper an analytical calculation of the isotopic depletion equations is proposed, featuring a chain of major isotopes found in a typical PWR reactor. Part of this chain allows feedback reactions of (n,2n) type. The method is based on decoupling the equations describing feedback from the rest of the chain by using the decomposition method, with analytical solutions for the other isotopes present in the chain. The method was implemented in a PWR reactor simulation code, that makes use of the nodal expansion method (NEM) to solve the neutron diffusion equation, describing the spatial distribution of neutron flux inside the reactor core. Because isotopic depletion calculation module is the most computationally intensive process within simulation systems of nuclear reactor core, it is justified to look for a method that is both efficient and fast, with the objective of evaluating a larger number of core configurations in a short amount of time. (author)

Method for assessment of stormwater treatment facilities - Synthetic road runoff addition including micro-pollutants and tracer.

Science.gov (United States)

Cederkvist, Karin; Jensen, Marina B; Holm, Peter E

2017-08-01

Stormwater treatment facilities (STFs) are becoming increasingly widespread but knowledge on their performance is limited. This is due to difficulties in obtaining representative samples during storm events and documenting removal of the broad range of contaminants found in stormwater runoff. This paper presents a method to evaluate STFs by addition of synthetic runoff with representative concentrations of contaminant species, including the use of tracer for correction of removal rates for losses not caused by the STF. A list of organic and inorganic contaminant species, including trace elements representative of runoff from roads is suggested, as well as relevant concentration ranges. The method was used for adding contaminants to three different STFs including a curbstone extension with filter soil, a dual porosity filter, and six different permeable pavements. Evaluation of the method showed that it is possible to add a well-defined mixture of contaminants despite different field conditions by having a flexibly system, mixing different stock-solutions on site, and use bromide tracer for correction of outlet concentrations. Bromide recovery ranged from only 12% in one of the permeable pavements to 97% in the dual porosity filter, stressing the importance of including a conservative tracer for correction of contaminant retention values. The method is considered useful in future treatment performance testing of STFs. The observed performance of the STFs is presented in coming papers. Copyright © 2017 Elsevier Ltd. All rights reserved.

A generalised solution for step-drawdown tests including flow ...

African Journals Online (AJOL)

drinie

2001-07-03

Jul 3, 2001 ... interpreted as the theoretical solution of the groundwater flow equation for the .... and gravity force the water to flow from the rock matrix to the fracture. ..... Computational Mechanics Publications, Southampton. CLOOT AHJ ...

Rapid processing method for solution deposited YBa2Cu3O7-δ thin films

International Nuclear Information System (INIS)

Dawley, J.T.; Clem, P.G.; Boyle, T.J.; Ottley, L.M.; Overmyer, D.L.; Siegal, M.P.

2004-01-01

YBa 2 Cu 3 O 7-δ (YBCO) films, deposited on buffered metal substrates, are the primary candidate for second-generation superconducting (SC) wires, with applications including expanded power grid transmission capability, compact motors, and enhanced sensitivity magnetic resonance imaging. Feasibility of manufacturing such superconducting wires is dependent on high processing speed, often a limitation of vapor and solution-based YBCO deposition processes. In this work, YBCO films were fabricated via a new diethanolamine-modified trifluoroacetic film solution deposition method. Modifying the copper chemistry of the YBCO precursor solution with diethanolamine enables a hundredfold decrease in the organic pyrolysis time required for MA/cm 2 current density (J c ) YBCO films, from multiple hours to ∼20 s in atmospheric pressure air. High quality, ∼0.2 μm thick YBCO films with J c (77 K) values ≥2 MA/cm 2 at 77 K are routinely crystallized from these rapidly pyrolyzed films deposited on LaAlO 3 . This process has also enabled J c (77 K)=1.1 MA/cm 2 YBCO films via 90 m/h dip-coating on Oak Ridge National Laboratory RABiTS textured metal tape substrates. This new YBCO solution deposition method suggests a route toward inexpensive and commercializable ∼$10/kA m solution deposited YBCO coated conductor wires

Modelling with the master equation solution methods and applications in social and natural sciences

CERN Document Server

Haag, Günter

2017-01-01

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience...

Semi-exact solution of elastic non-uniform thickness and density rotating disks by homotopy perturbation and Adomian's decomposition methods. Part I: Elastic solution

International Nuclear Information System (INIS)

Hojjati, M.H.; Jafari, S.

2008-01-01

In this work, two powerful analytical methods, namely homotopy perturbation method (HPM) and Adomian's decomposition method (ADM), are introduced to obtain distributions of stresses and displacements in rotating annular elastic disks with uniform and variable thicknesses and densities. The results obtained by these methods are then compared with the verified variational iteration method (VIM) solution. He's homotopy perturbation method which does not require a 'small parameter' has been used and a homotopy with an imbedding parameter p element of [0,1] is constructed. The method takes the full advantage of the traditional perturbation methods and the homotopy techniques and yields a very rapid convergence of the solution. Adomian's decomposition method is an iterative method which provides analytical approximate solutions in the form of an infinite power series for nonlinear equations without linearization, perturbation or discretization. Variational iteration method, on the other hand, is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This study demonstrates the ability of the methods for the solution of those complicated rotating disk cases with either no or difficult to find fairly exact solutions without the need to use commercial finite element analysis software. The comparison among these methods shows that although the numerical results are almost the same, HPM is much easier, more convenient and efficient than ADM and VIM

Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

International Nuclear Information System (INIS)

Lewandowski, Jerome L.V.

2005-01-01

A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details

A new method for determining the bioavailability of radionuclides in the soil solution

International Nuclear Information System (INIS)

Jouve, A.; Lejeune, M.; Rey, J.

1999-01-01

A new method for determining the pool of radionuclides in the soil solution, available for root uptake, has been compared to existing methods. The new method is based on extracting the soil solution at a soil moisture below saturation. It uses the soaking capacity of a polyacrylamide resin deposited on a cellulose acetate membrane laid on the soil surface. The new method exhibited the best reproductibility amongst the methods tested. It allowed us to extract more 134 Cs and a similar amount of 85 Sr relative to the other methods. The correlation between the observed ratio of radionuclide concentrations in soil and plants and the radionuclide concentration of the soil solution using the new method was better than using the existing methods. Using the measurement of 134 Cs and natural potassium in the soil solution by the new method, based on a multiple regression equation involving an exponential form, the uptake of 134 Cs by bean and wheat was predicted with a 0.9 determination coefficient. As far as the uptake of 85 Sr is considered, this method was not very successful since the equation with a linear form involved a large number of parameters. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

A linear complementarity method for the solution of vertical vehicle-track interaction

Science.gov (United States)

Zhang, Jian; Gao, Qiang; Wu, Feng; Zhong, Wan-Xie

2018-02-01

A new method is proposed for the solution of the vertical vehicle-track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel-rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel-rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel-rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle-track interaction including a separation between wheel and rail.

Method for improved decomposition of metal nitrate solutions

Science.gov (United States)

Haas, Paul A.; Stines, William B.

1983-10-11

A method for co-conversion of aqueous solutions of one or more heavy metal nitrates wherein thermal decomposition within a temperature range of about 300.degree. to 800.degree. C. is carried out in the presence of about 50 to 500% molar concentration of ammonium nitrate to total metal.

Exact solutions for nonlinear evolution equations using Exp-function method

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2008-01-01

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

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

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

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

Exact Solutions of the Time Fractional BBM-Burger Equation by Novel (G′/G-Expansion Method

Directory of Open Access Journals (Sweden)

Muhammad Shakeel

2014-01-01

Full Text Available The fractional derivatives are used in the sense modified Riemann-Liouville to obtain exact solutions for BBM-Burger equation of fractional order. This equation can be converted into an ordinary differential equation by using a persistent fractional complex transform and, as a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions are attained. The performance of the method is reliable, useful, and gives newer general exact solutions with more free parameters than the existing methods. Numerical results coupled with the graphical representation completely reveal the trustworthiness of the method.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

Science.gov (United States)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

An approximate JKR solution for a general contact, including rough contacts

Science.gov (United States)

Ciavarella, M.

2018-05-01

In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is δ =δ1 -√{ 2 wA‧ /P″ } where w is surface energy, δ1 is the adhesiveless indentation, A‧ is the first derivative of contact area and P‧‧ the second derivative of the load with respect to δ1. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts, but also sinusoidal waves contact and correctly predicts some features of an ideal asperity model used as a test case and not as a real description of a rough contact problem. The solution permits therefore an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The result turns out to depend only on rms amplitude and slopes of the surface, and as in the fractal limit, slopes would grow without limit, tends to the adhesiveless result - although in this limit the JKR model is inappropriate. The solution would also go to adhesiveless result for large rms amplitude of roughness hrms, irrespective of the small scale details, and in agreement with common sense, well known experiments and previous models by the author.

Methods for partial differential equations qualitative properties of solutions, phase space analysis, semilinear models

CERN Document Server

Ebert, Marcelo R

2018-01-01

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes...

The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

Directory of Open Access Journals (Sweden)

Hasibun Naher

2011-01-01

Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Directory of Open Access Journals (Sweden)

A. M. El-Naggar

2015-11-01

Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.

A simple high performance liquid chromatography method for analyzing paraquat in soil solution samples.

Science.gov (United States)

Ouyang, Ying; Mansell, Robert S; Nkedi-Kizza, Peter

2004-01-01

A high performance liquid chromatography (HPLC) method with UV detection was developed to analyze paraquat (1,1'-dimethyl-4,4'-dipyridinium dichloride) herbicide content in soil solution samples. The analytical method was compared with the liquid scintillation counting (LSC) method using 14C-paraquat. Agreement obtained between the two methods was reasonable. However, the detection limit for paraquat analysis was 0.5 mg L(-1) by the HPLC method and 0.05 mg L(-1) by the LSC method. The LSC method was, therefore, 10 times more precise than the HPLC method for solution concentrations less than 1 mg L(-1). In spite of the high detection limit, the UC (nonradioactive) HPLC method provides an inexpensive and environmentally safe means for determining paraquat concentration in soil solution compared with the 14C-LSC method.

The method of determination of micro quantities of labelled iodide in Na125 I carrier free solution

International Nuclear Information System (INIS)

Kholbaev, A.Kh.; Shilin, E.A.

1996-01-01

The analytical method was elaborated with the purpose to increase detection limit and radiation safety of labelled iodide determination. The method includes oxidation of iodide by iodate in diluted sulphur acid solution with molar concentration 0,03-0,04/moles/litre at molar ratio of iodide to iodate I - :IO - 3 1:12,5. The extraction of I 2 produced is done by toluene. (author)

Mobility of arsenic and its compounds in soil and soil solution: the effect of soil pretreatment and extraction methods.

Science.gov (United States)

Száková, J; Tlustos, P; Goessler, W; Frková, Z; Najmanová, J

2009-12-30

The effect of soil extraction procedures and/or sample pretreatment (drying, freezing of the soil sample) on the extractability of arsenic and its compounds was tested. In the first part, five extraction procedures were compared with following order of extractable arsenic portions: 2M HNO(3)>0.43 M CH(3)COOH>or=0.05 M EDTA>or=Mehlich III (0.2M CH(3)COOH+0.25 M NH(4)NO(3)+0.013 M HNO(3)+0.015 M NH(4)F+0.001 M EDTA) extraction>water). Additionally, two methods of soil solution sampling were compared, centrifugation of saturated soil and the use of suction cups. The results showed that different sample pretreatments including soil solution sampling could lead to different absolute values of mobile arsenic content in soils. However, the interpretation of the data can lead to similar conclusions as apparent from the comparison of the soil solution sampling methods (r=0.79). For determination of arsenic compounds mild extraction procedures (0.05 M (NH(4))(2)SO(4), 0.01 M CaCl(2), and water) and soil solution sampling using suction cups were compared. Regarding the real soil conditions the extraction of fresh samples and/or in situ collection of soil solution are preferred among the sample pretreatments and/or soil extraction procedures. However, chemical stabilization of the solutions should be allowed and included in the analytical procedures for determination of individual arsenic compounds.

Solution of two group neutron diffusion equation by using homotopy analysis method

International Nuclear Information System (INIS)

Cavdar, S.

2010-01-01

The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.

Solution of the radiative enclosure with a hybrid inverse method

Energy Technology Data Exchange (ETDEWEB)

Silva, Rogerio Brittes da; Franca, Francis Henrique Ramos [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica], E-mail: frfranca@mecanica.ufrgs.br

2010-07-01

This work applies the inverse analysis to solve a three-dimensional radiative enclosure - which the surfaces are diffuse-grays - filled with transparent medium. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A hybrid solution that couples two methods, the generalized extremal optimization (GEO) and the truncated singular value decomposition (TSVD) is proposed. The determination of the heat sources distribution is treated as an optimization problem, by GEO algorithm , whereas the solution of the system of equation, that embodies the Fredholm equation of first kind and therefore is expected to be ill conditioned, is build up through TSVD regularization method. The results show that the hybrid method can lead to a heat flux on the design surface that satisfies the imposed conditions with maximum error of less than 1,10%. The results illustrated the relevance of a hybrid method as a prediction tool. (author)

75 FR 77665 - Whirlpool Corporation, Including On-Site Leased Workers From Career Solutions TEC Staffing and...

Science.gov (United States)

2010-12-13

... DEPARTMENT OF LABOR Employment and Training Administration [TA-W-74,593] Whirlpool Corporation, Including On-Site Leased Workers From Career Solutions TEC Staffing and Andrews International, Fort Smith... subject firm. The workers are engaged in the production of refrigerators and trash compactors. The company...

New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods

Science.gov (United States)

S Saha, Ray

2016-04-01

In this paper, new exact solutions of the time fractional KdV-Khokhlov-Zabolotskaya-Kuznetsov (KdV-KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann-Liouville derivative is used to convert the nonlinear time fractional KdV-KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV-KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV-KZK equation.

Evaluation of element migration from food plastic packagings into simulated solutions using radiometric method

International Nuclear Information System (INIS)

Soares, Eufemia Paez; Saiki, Mitiko; Wiebeck, Helio

2005-01-01

In the present study a radiometric method was established to determine the migration of elements from food plastic packagings to a simulated acetic acid solution. This radiometric method consisted of irradiating plastic samples with neutrons at IEA-R1 nuclear reactor for a period of 16 hours under a neutron flux of 10 12 n cm -2 s -1 and, then to expose them to the element migration into a simulated solution. The radioactivity of the activated elements transferred to the solutions was measured to evaluate the migration. The experimental conditions were: time of exposure of 10 days at 40 deg C and 3% acetic acid solution was used as simulated solution, according to the procedure established by the National Agency of Sanitary Monitoring (ANVISA). The migration study was applied for plastic samples from soft drink and juice packagings. The results obtained indicated the migration of elements Co, Cr and Sb. The advantage of this methodology was no need to analyse the blank of simulantes, as well as the use of high purity simulated solutions. Besides, the method allows to evaluate the migration of the elements into the food content instead of simulated solution. The detention limits indicated high sensitivity of the radiometric method. (author)

Direct methods of solution for problems in mechanics from invariance principles

International Nuclear Information System (INIS)

Rajan, M.

1986-01-01

Direct solutions to problems in mechanics are developed from variational statements derived from the principle of invariance of the action integral under a one-parameter family of infinitesimal transformations. Exact, direct solution procedures for linear systems are developed by a careful choice of the arbitrary functions used to generate the infinitesimal transformations. It is demonstrated that the well-known methods for the solution of differential equations can be directly adapted to the required variational statements. Examples in particle and continuum mechanics are presented

Comparing numerical methods for the solutions of the Chen system

International Nuclear Information System (INIS)

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

2007-01-01

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

A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation

International Nuclear Information System (INIS)

Ma Wenxiu; Lee, J.-H.

2009-01-01

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanh-function type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type methods. Its key point is to search for rational solutions to variable-coefficient ordinary differential equations transformed from given partial differential equations. As an application, the construction problem of exact solutions to the 3+1 dimensional Jimbo-Miwa equation is treated, together with a Baecklund transformation.

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

Science.gov (United States)

Crevoisier, David; Voltz, Marc

2013-04-01

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

Benchmarking the invariant embedding method against analytical solutions in model transport problems

International Nuclear Information System (INIS)

Malin, Wahlberg; Imre, Pazsit

2005-01-01

The purpose of this paper is to demonstrate the use of the invariant embedding method in a series of model transport problems, for which it is also possible to obtain an analytical solution. Due to the non-linear character of the embedding equations, their solution can only be obtained numerically. However, this can be done via a robust and effective iteration scheme. In return, the domain of applicability is far wider than the model problems investigated in this paper. The use of the invariant embedding method is demonstrated in three different areas. The first is the calculation of the energy spectrum of reflected (sputtered) particles from a multiplying medium, where the multiplication arises from recoil production. Both constant and energy dependent cross sections with a power law dependence were used in the calculations. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel and unexpected application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and a half-space are interrelated through embedding-like integral equations, by the solution of which the reflected flux from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases the invariant embedding method proved to be robust, fast and monotonically converging to the exact solutions. (authors)

Microfluidic devices and methods including porous polymer monoliths

Science.gov (United States)

Hatch, Anson V; Sommer, Gregory J; Singh, Anup K; Wang, Ying-Chih; Abhyankar, Vinay V

2014-04-22

Microfluidic devices and methods including porous polymer monoliths are described. Polymerization techniques may be used to generate porous polymer monoliths having pores defined by a liquid component of a fluid mixture. The fluid mixture may contain iniferters and the resulting porous polymer monolith may include surfaces terminated with iniferter species. Capture molecules may then be grafted to the monolith pores.

Finding all solutions of nonlinear equations using the dual simplex method

Science.gov (United States)

Yamamura, Kiyotaka; Fujioka, Tsuyoshi

2003-03-01

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using linear programming. This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations using the dual simplex method. In this letter, an improved version of the LP test algorithm is proposed. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 300 nonlinear equations in practical computation time.

Synthesis method based on solution regions for planar four bar straight line linkages

International Nuclear Information System (INIS)

Lai Rong, Yin; Cong, Mao; Jian you, Han; Tong, Yang; Juan, Huang

2012-01-01

An analytical method for synthesizing and selecting desired four-bar straight line mechanisms based on solution regions is presented. Given two fixed pivots, the point position and direction of the target straight line, an infinite number of mechanism solutions can be produced by employing this method, both in the general case and all three special cases. Unifying the straight line direction and the displacement from the given point to the instant center into the same form with different angles as parameters, infinite mechanism solutions can be expressed with different solution region charts. The mechanism property graphs have been computed to enable the designers to find out the involved mechanism information more intuitively and avoid aimlessness in selecting optimal mechanisms

Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

Science.gov (United States)

Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

2013-01-01

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

New analytical exact solutions of time fractional KdV–KZK equation by Kudryashov methods

International Nuclear Information System (INIS)

Saha Ray, S

2016-01-01

In this paper, new exact solutions of the time fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov (KdV–KZK) equation are obtained by the classical Kudryashov method and modified Kudryashov method respectively. For this purpose, the modified Riemann–Liouville derivative is used to convert the nonlinear time fractional KdV–KZK equation into the nonlinear ordinary differential equation. In the present analysis, the classical Kudryashov method and modified Kudryashov method are both used successively to compute the analytical solutions of the time fractional KdV–KZK equation. As a result, new exact solutions involving the symmetrical Fibonacci function, hyperbolic function and exponential function are obtained for the first time. The methods under consideration are reliable and efficient, and can be used as an alternative to establish new exact solutions of different types of fractional differential equations arising from mathematical physics. The obtained results are exhibited graphically in order to demonstrate the efficiencies and applicabilities of these proposed methods of solving the nonlinear time fractional KdV–KZK equation. (paper)

The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

OpenAIRE

Efimova, Olga Yu.

2010-01-01

The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

Exact Solutions to (2+1)-Dimensional Kaup-Kupershmidt Equation

International Nuclear Information System (INIS)

Lu Hailing; Liu Xiqiang

2009-01-01

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G'/G)-expansion method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, including similarity solutions, solitary wave solutions, and periodic solutions. (general)

New exact solutions of the (2 + 1)-dimensional breaking soliton system via an extended mapping method

International Nuclear Information System (INIS)

Ma Songhua; Fang Jianping; Zheng Chunlong

2009-01-01

By means of an extended mapping method and a variable separation method, a series of solitary wave solutions, periodic wave solutions and variable separation solutions to the (2 + 1)-dimensional breaking soliton system is derived.

Preface of "The Second Symposium on Border Zones Between Experimental and Numerical Application Including Solution Approaches By Extensions of Standard Numerical Methods"

Science.gov (United States)

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.

Solution of axisymmetric transient inverse heat conduction problems using parameter estimation and multi block methods

International Nuclear Information System (INIS)

Azimi, A.; Hannani, S.K.; Farhanieh, B.

2005-01-01

In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)

Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

Directory of Open Access Journals (Sweden)

Xiao-Ying Qin

2014-01-01

Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

Adjusted permutation method for multiple attribute decision making with meta-heuristic solution approaches

Directory of Open Access Journals (Sweden)

Hossein Karimi

2011-04-01

Full Text Available The permutation method of multiple attribute decision making has two significant deficiencies: high computational time and wrong priority output in some problem instances. In this paper, a novel permutation method called adjusted permutation method (APM is proposed to compensate deficiencies of conventional permutation method. We propose Tabu search (TS and particle swarm optimization (PSO to find suitable solutions at a reasonable computational time for large problem instances. The proposed method is examined using some numerical examples to evaluate the performance of the proposed method. The preliminary results show that both approaches provide competent solutions in relatively reasonable amounts of time while TS performs better to solve APM.

Unified solution of a non-convex SCUC problem using combination of modified Branch-and-Bound method with Quadratic Programming

International Nuclear Information System (INIS)

Shafie-khah, M.; Parsa Moghaddam, M.; Sheikh-El-Eslami, M.K.

2011-01-01

Highlights: → A hybrid SCUC solution is developed to deal with large-scale, real-time and long-term problems. → New formulations are proposed for considering valve point effect and warmth-dependent start-up cost. → A new algorithm is developed for modeling the AC power flow in SCUC problems. → Using the power flow algorithm both steps in traditional SCUC is done simultaneously. → The proposed method provides better solutions than previous ones with a fast speed. - Abstract: In this paper, a new practical method is presented for solving the non-convex security constraint unit commitment (SCUC) problem in power systems. The accuracy of the proposed method is desirable while the shorter computation time makes it useful for SCUC solution of large-scale power systems, real-time market operation and long-term SCUC problems. The proposed framework allows inclusion of the valve point effects, warmth-dependent start-up costs, ramp rates, minimum up/down time constraints, multiple fuels costs, emission costs, prohibited operating zones and AC power flow limits in normal and contingency conditions. To solve the non-convex problem, combination of a modified Branch-and-Bound method with the Quadratic Programming is used as an optimization tool and a developed AC power flow algorithm is applied for considering the security and contingency concerns using the nonlinear/linear AC model. These modifications improve the convergence speed and solution precision of SCUC problem. In the proposed method, in contrast with traditional SCUC algorithms, unit commitment solution, checking and satisfying the security constraints are managed simultaneously. The obtained results are compared with other reported methods for investigating the effectiveness of the proposed method. Also, the proposed method is applied to an Iranian power system including 493 thermal units.

Method for recovering palladium and technetium values from nuclear fuel reprocessing waste solutions

Science.gov (United States)

Horwitz, E. Philip; Delphin, Walter H.

1979-07-24

A method for recovering palladium and technetium values from nuclear fuel reprocessing waste solutions containing these and other values by contacting the waste solution with an extractant of tricaprylmethylammonium nitrate in an inert hydrocarbon diluent which extracts the palladium and technetium values from the waste solution. The palladium and technetium values are recovered from the extractant and from any other coextracted values with a strong nitric acid strip solution.

Modified micro-diffusion method for 15N-enriched soil solutions

International Nuclear Information System (INIS)

Aigner, M.

2000-01-01

The preparation of solutions for determination of 15 N/ 14 N isotope ratios is described, with special reference to dilute samples. A micro-diffusion method has been simplified to be more suitable for rapid isotope-ratio determination in soil solutions collected in tensionics. Ammonia expelled during micro-diffusion is captured on acidified filter discs fixed to the caps of gas-tight vials. The discs are transferred to tin capsules for shipment to the Soil Science Unit for 15 N-enrichment determination. (author)

Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

Science.gov (United States)

Cockrell, C. R.

1989-01-01

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions.

Symbolic computation and abundant travelling wave solutions to ...

Indian Academy of Sciences (India)

The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometricand rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and ...

An induced current method for measuring zeta potential of electrolyte solution-air interface.

Science.gov (United States)

Song, Yongxin; Zhao, Kai; Wang, Junsheng; Wu, Xudong; Pan, Xinxiang; Sun, Yeqing; Li, Dongqing

2014-02-15

This paper reports a novel and very simple method for measuring the zeta potential of electrolyte solution-air interface. When a measuring electrode contacts the electrolyte solution-air interface, an electrical current will be generated due to the potential difference between the electrode-air surface and the electrolyte solution-air interface. The amplitude of the measured electric signal is linearly proportional to this potential difference; and depends only on the zeta potential at the electrolyte solution-air interface, regardless of the types and concentrations of the electrolyte. A correlation between the zeta potential and the measured voltage signal is obtained based on the experimental data. Using this equation, the zeta potential of any electrolyte solution-air interface can be evaluated quickly and easily by inserting an electrode through the electrolyte solution-air interface and measuring the electrical signal amplitude. This method was verified by comparing the obtained results of NaCl, MgCl2 and CaCl2 solutions of different pH values and concentrations with the zeta potential data reported in the published journal papers. Copyright © 2013 Elsevier Inc. All rights reserved.

New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F -Expansion Method

International Nuclear Information System (INIS)

Pandir, Yusuf; Duzgun, Hasan Huseyin

2017-01-01

In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. (paper)

A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.

Improved parallel solution techniques for the integral transport matrix method

Energy Technology Data Exchange (ETDEWEB)

Zerr, R. Joseph, E-mail: rjz116@psu.edu [Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA (United States); Azmy, Yousry Y., E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Burlington Engineering Laboratories, Raleigh, NC (United States)

2011-07-01

Alternative solution strategies to the parallel block Jacobi (PBJ) method for the solution of the global problem with the integral transport matrix method operators have been designed and tested. The most straightforward improvement to the Jacobi iterative method is the Gauss-Seidel alternative. The parallel red-black Gauss-Seidel (PGS) algorithm can improve on the number of iterations and reduce work per iteration by applying an alternating red-black color-set to the subdomains and assigning multiple sub-domains per processor. A parallel GMRES(m) method was implemented as an alternative to stationary iterations. Computational results show that the PGS method can improve on the PBJ method execution time by up to 10´ when eight sub-domains per processor are used. However, compared to traditional source iterations with diffusion synthetic acceleration, it is still approximately an order of magnitude slower. The best-performing cases are optically thick because sub-domains decouple, yielding faster convergence. Further tests revealed that 64 sub-domains per processor was the best performing level of sub-domain division. An acceleration technique that improves the convergence rate would greatly improve the ITMM. The GMRES(m) method with a diagonal block pre conditioner consumes approximately the same time as the PBJ solver but could be improved by an as yet undeveloped, more efficient pre conditioner. (author)

Improved parallel solution techniques for the integral transport matrix method

International Nuclear Information System (INIS)

Zerr, R. Joseph; Azmy, Yousry Y.

2011-01-01

Alternative solution strategies to the parallel block Jacobi (PBJ) method for the solution of the global problem with the integral transport matrix method operators have been designed and tested. The most straightforward improvement to the Jacobi iterative method is the Gauss-Seidel alternative. The parallel red-black Gauss-Seidel (PGS) algorithm can improve on the number of iterations and reduce work per iteration by applying an alternating red-black color-set to the subdomains and assigning multiple sub-domains per processor. A parallel GMRES(m) method was implemented as an alternative to stationary iterations. Computational results show that the PGS method can improve on the PBJ method execution time by up to 10´ when eight sub-domains per processor are used. However, compared to traditional source iterations with diffusion synthetic acceleration, it is still approximately an order of magnitude slower. The best-performing cases are optically thick because sub-domains decouple, yielding faster convergence. Further tests revealed that 64 sub-domains per processor was the best performing level of sub-domain division. An acceleration technique that improves the convergence rate would greatly improve the ITMM. The GMRES(m) method with a diagonal block pre conditioner consumes approximately the same time as the PBJ solver but could be improved by an as yet undeveloped, more efficient pre conditioner. (author)

Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications

Directory of Open Access Journals (Sweden)

Changyong Cao

2015-01-01

Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.

The generalized tanh method to obtain exact solutions of nonlinear partial differential equation

OpenAIRE

Gómez, César

2007-01-01

In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.

Solution identification and quantitative analysis of fiber-capacitive drop analyzer based on multivariate statistical methods

Science.gov (United States)

Chen, Zhe; Qiu, Zurong; Huo, Xinming; Fan, Yuming; Li, Xinghua

2017-03-01

A fiber-capacitive drop analyzer is an instrument which monitors a growing droplet to produce a capacitive opto-tensiotrace (COT). Each COT is an integration of fiber light intensity signals and capacitance signals and can reflect the unique physicochemical property of a liquid. In this study, we propose a solution analytical and concentration quantitative method based on multivariate statistical methods. Eight characteristic values are extracted from each COT. A series of COT characteristic values of training solutions at different concentrations compose a data library of this kind of solution. A two-stage linear discriminant analysis is applied to analyze different solution libraries and establish discriminant functions. Test solutions can be discriminated by these functions. After determining the variety of test solutions, Spearman correlation test and principal components analysis are used to filter and reduce dimensions of eight characteristic values, producing a new representative parameter. A cubic spline interpolation function is built between the parameters and concentrations, based on which we can calculate the concentration of the test solution. Methanol, ethanol, n-propanol, and saline solutions are taken as experimental subjects in this paper. For each solution, nine or ten different concentrations are chosen to be the standard library, and the other two concentrations compose the test group. By using the methods mentioned above, all eight test solutions are correctly identified and the average relative error of quantitative analysis is 1.11%. The method proposed is feasible which enlarges the applicable scope of recognizing liquids based on the COT and improves the concentration quantitative precision, as well.

Spectral methods and their implementation to solution of aerodynamic and fluid mechanic problems

Science.gov (United States)

Streett, C. L.

1987-01-01

Fundamental concepts underlying spectral collocation methods, especially pertaining to their use in the solution of partial differential equations, are outlined. Theoretical accuracy results are reviewed and compared with results from test problems. A number of practical aspects of the construction and use of spectral methods are detailed, along with several solution schemes which have found utility in applications of spectral methods to practical problems. Results from a few of the successful applications of spectral methods to problems of aerodynamic and fluid mechanic interest are then outlined, followed by a discussion of the problem areas in spectral methods and the current research under way to overcome these difficulties.

Saturated salt solution method: a useful cadaver embalming for surgical skills training.

Science.gov (United States)

Hayashi, Shogo; Homma, Hiroshi; Naito, Munekazu; Oda, Jun; Nishiyama, Takahisa; Kawamoto, Atsuo; Kawata, Shinichi; Sato, Norio; Fukuhara, Tomomi; Taguchi, Hirokazu; Mashiko, Kazuki; Azuhata, Takeo; Ito, Masayuki; Kawai, Kentaro; Suzuki, Tomoya; Nishizawa, Yuji; Araki, Jun; Matsuno, Naoto; Shirai, Takayuki; Qu, Ning; Hatayama, Naoyuki; Hirai, Shuichi; Fukui, Hidekimi; Ohseto, Kiyoshige; Yukioka, Tetsuo; Itoh, Masahiro

2014-12-01

This article evaluates the suitability of cadavers embalmed by the saturated salt solution (SSS) method for surgical skills training (SST). SST courses using cadavers have been performed to advance a surgeon's techniques without any risk to patients. One important factor for improving SST is the suitability of specimens, which depends on the embalming method. In addition, the infectious risk and cost involved in using cadavers are problems that need to be solved. Six cadavers were embalmed by 3 methods: formalin solution, Thiel solution (TS), and SSS methods. Bacterial and fungal culture tests and measurement of ranges of motion were conducted for each cadaver. Fourteen surgeons evaluated the 3 embalming methods and 9 SST instructors (7 trauma surgeons and 2 orthopedists) operated the cadavers by 21 procedures. In addition, ultrasonography, central venous catheterization, and incision with cauterization followed by autosuture stapling were performed in some cadavers. The SSS method had a sufficient antibiotic effect and produced cadavers with flexible joints and a high tissue quality suitable for SST. The surgeons evaluated the cadavers embalmed by the SSS method to be highly equal to those embalmed by the TS method. Ultrasound images were clear in the cadavers embalmed by both the methods. Central venous catheterization could be performed in a cadaver embalmed by the SSS method and then be affirmed by x-ray. Lungs and intestines could be incised with cauterization and autosuture stapling in the cadavers embalmed by TS and SSS methods. Cadavers embalmed by the SSS method are sufficiently useful for SST. This method is simple, carries a low infectious risk, and is relatively of low cost, enabling a wider use of cadavers for SST.

A Method for Generating Approximate Similarity Solutions of Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Mazhar Iqbal

2014-01-01

Full Text Available Standard application of similarity method to find solutions of PDEs mostly results in reduction to ODEs which are not easily integrable in terms of elementary or tabulated functions. Such situations usually demand solving reduced ODEs numerically. However, there are no systematic procedures available to utilize these numerical solutions of reduced ODE to obtain the solution of original PDE. A practical and tractable approach is proposed to deal with such situations and is applied to obtain approximate similarity solutions to different cases of an initial-boundary value problem of unsteady gas flow through a semi-infinite porous medium.

New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method

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L.K. Ravi

2017-03-01

Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.

Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method

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Mohammad Mehdi Mashinchi Joubari

2015-01-01

Full Text Available In this paper, we implemented the Modified Iteration Perturbation Method (MIPM for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need to complicated calculations. Comparing the results of the MIPM with the exact solution shows that this method is effective and convenient. Also, it is predicated that MIPM can be potentially used in the analysis of strongly nonlinear oscillation problems accurately.

History and future of human cadaver preservation for surgical training: from formalin to saturated salt solution method.

Science.gov (United States)

Hayashi, Shogo; Naito, Munekazu; Kawata, Shinichi; Qu, Ning; Hatayama, Naoyuki; Hirai, Shuichi; Itoh, Masahiro

2016-01-01

Traditionally, surgical training meant on-the-job training with live patients in an operating room. However, due to advancing surgical techniques, such as minimally invasive surgery, and increasing safety demands during procedures, human cadavers have been used for surgical training. When considering the use of human cadavers for surgical training, one of the most important factors is their preservation. In this review, we summarize four preservation methods: fresh-frozen cadaver, formalin, Thiel's, and saturated salt solution methods. Fresh-frozen cadaver is currently the model that is closest to reality, but it also presents myriad problems, including the requirement of freezers for storage, limited work time because of rapid putrefaction, and risk of infection. Formalin is still used ubiquitously due to its low cost and wide availability, but it is not ideal because formaldehyde has an adverse health effect and formalin-embalmed cadavers do not exhibit many of the qualities of living organs. Thiel's method results in soft and flexible cadavers with almost natural colors, and Thiel-embalmed cadavers have been appraised widely in various medical disciplines. However, Thiel's method is relatively expensive and technically complicated. In addition, Thiel-embalmed cadavers have a limited dissection time. The saturated salt solution method is simple, carries a low risk of infection, and is relatively low cost. Although more research is needed, this method seems to be sufficiently useful for surgical training and has noteworthy features that expand the capability of clinical training. The saturated salt solution method will contribute to a wider use of cadavers for surgical training.

An effective method for finding special solutions of nonlinear differential equations with variable coefficients

International Nuclear Information System (INIS)

Qin Maochang; Fan Guihong

2008-01-01

There are many interesting methods can be utilized to construct special solutions of nonlinear differential equations with constant coefficients. However, most of these methods are not applicable to nonlinear differential equations with variable coefficients. A new method is presented in this Letter, which can be used to find special solutions of nonlinear differential equations with variable coefficients. This method is based on seeking appropriate Bernoulli equation corresponding to the equation studied. Many well-known equations are chosen to illustrate the application of this method

Singular characteristic tracking algorithm for improved solution accuracy of the discrete ordinates method with isotropic scattering

International Nuclear Information System (INIS)

Duo, J. I.; Azmy, Y. Y.

2007-01-01

A new method, the Singular Characteristics Tracking algorithm, is developed to account for potential non-smoothness across the singular characteristics in the exact solution of the discrete ordinates approximation of the transport equation. Numerical results show improved rate of convergence of the solution to the discrete ordinates equations in two spatial dimensions with isotropic scattering using the proposed methodology. Unlike the standard Weighted Diamond Difference methods, the new algorithm achieves local convergence in the case of discontinuous angular flux along the singular characteristics. The method also significantly reduces the error for problems where the angular flux presents discontinuous spatial derivatives across these lines. For purposes of verifying the results, the Method of Manufactured Solutions is used to generate analytical reference solutions that permit estimating the local error in the numerical solution. (authors)

Improved Riccati Transfer Matrix Method for Free Vibration of Non-Cylindrical Helical Springs Including Warping

Directory of Open Access Journals (Sweden)

A.M. Yu

2012-01-01

Full Text Available Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types helical springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45 in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical helical springs than that of cylindrical helical springs, which should be taken into consideration in the free vibration analysis of such springs.

Determination of plutonium in pure plutonium nitrate solutions - Gravimetric method

International Nuclear Information System (INIS)

1987-01-01

This International Standard specifies a precise and accurate gravimetric method for determining the concentration of plutonium in pure plutonium nitrate solutions and reference solutions, containing between 100 and 300 g of plutonium per litre, in a nitric acid medium. The weighed portion of the plutonium nitrate is treated with sulfuric acid and evaporated to dryness. The plutonium sulfate is decomposed and formed to oxide by heating in air. The oxide is ignited in air at 1200 to 1250 deg. C and weighed as stoichiometric plutonium dioxide, which is stable and non-hygroscopic

Removal of plutonium from nitric acid-oxalic acid solutions using anion exchange method

International Nuclear Information System (INIS)

Kasar, U.M.; Pawar, S.M.; Joshi, A.R.

1999-01-01

An anion exchange method using Amberlyst A-26 (MP) resin was developed for removal of Pu from nitric acid-oxalic acid solutions without destroying oxalate. The method consists of sorption of Pu(IV) on Amberlyst A-26, a macroporous anion exchange resin, from nitric acid-oxalic acid medium in the presence of Al(NO 3 ) 3 . Pu(IV) breakthrough capacity of Amberlyst A-26 using synthetic feed solution was determined. (author)

The Teaching of General Solution Methods to Pattern Finding Problems through Focusing on an Evaluation and Improvement Process.

Science.gov (United States)

Ishida, Junichi

1997-01-01

Examines the effects of a teaching strategy in which fifth-grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems, including an experimental and control group each consisting of 34 elementary students, in Japan. The experimental group showed a significantly better performance on the retention test…

Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

Science.gov (United States)

Fulcher, Lewis P.

1979-01-01

Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method

International Nuclear Information System (INIS)

Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.

2007-01-01

In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple

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

International Nuclear Information System (INIS)

Biddlecombe, C.S.

1978-07-01

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

A method of fundamental solutions in poroelasticity to model the stress field in geothermal reservoirs

CERN Document Server

Augustin, Matthias Albert

2015-01-01

This monograph focuses on the numerical methods needed in the context of developing a reliable simulation tool to promote the use of renewable energy. One very promising source of energy is the heat stored in the Earth’s crust, which is harnessed by so-called geothermal facilities. Scientists from fields like geology, geo-engineering, geophysics and especially geomathematics are called upon to help make geothermics a reliable and safe energy production method. One of the challenges they face involves modeling the mechanical stresses at work in a reservoir. The aim of this thesis is to develop a numerical solution scheme by means of which the fluid pressure and rock stresses in a geothermal reservoir can be determined prior to well drilling and during production. For this purpose, the method should (i) include poroelastic effects, (ii) provide a means of including thermoelastic effects, (iii) be inexpensive in terms of memory and computational power, and (iv) be flexible with regard to the locations of data ...

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....

Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

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S. Balaji

2014-01-01

Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.

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

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

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

Numerical solution of the state-delayed optimal control problems by a fast and accurate finite difference θ-method

Science.gov (United States)

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.

Exact solutions of the population balance equation including particle transport, using group analysis

Science.gov (United States)

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

2018-06-01

The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.

The Train Driver Recovery Problem - Solution Method and Decision Support System Framework

DEFF Research Database (Denmark)

Rezanova, Natalia Jurjevna

2009-01-01

the proposed model and solution method is suitable for solving in real-time. Recovery duties are generated as resource constrained paths in duty networks, and the set partitioning problem is solved with a linear programming based branch-and-price algorithm. Dynamic column generation and problem space expansion...... driver decision support system in their operational environment. Besides solving a particular optimization problem, this thesis contributes with a description of the railway planning process, tactical crew scheduling and the real-time dispatching solutions, taking a starting point in DSB S....... Rezanova NJ, Ryan DM. The train driver recovery problem–A set partitioning based model and solution method. Computers and Operations Research, in press, 2009. doi: 10.1016/j.cor.2009.03.023. 2. Clausen J, Larsen A, Larsen J, Rezanova NJ. Disruption management in the airline industry–Concepts, models...

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

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

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

Comparison of four methods for determining aluminum in highly radioactive solutions

International Nuclear Information System (INIS)

Hanson, T.J.

1976-06-01

Four methods for the accurate determination of aluminum in highly alkaline nuclear waste solutions were developed and the results were compared to determine the strengths and weaknesses of each. The solutions of interest contain aluminum in concentrations of 0.5 to 3.5 M and the hydroxide (OH - ) concentrations were greater than 1.0 M. The normal atomic absorption determination was highly inaccurate for these samples so citrate was used as a complexant to improve the results. A fluoride titration was carried out in an ethanol-water matrix using a fluoride ion-selective electrode. A thermometric titration proved successful in determining both the OH - and aluminum concentrations of the samples. Finally, a titrimetric method using a pH electrode to determine OH - d aluminum was checked and compared with the other methods. Samples were analyzed using all four methods and the agreement of the results was very good. For all four methods the accuracy was around 100 percent and the precision varied from approximately +-2 percent for the fluoride electrode determination to approximately +-10 percent for the atomic absorption determination. On the basis of the work performed, conclusions were drawn about the strengths and weaknesses of each method and whether or not the method was suitable for routine use in analytical laboratories

Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

International Nuclear Information System (INIS)

Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

2009-01-01

A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

Soliton solution for nonlinear partial differential equations by cosine-function method

International Nuclear Information System (INIS)

Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

2007-01-01

In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

Rapid processing method for solution deposited YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} thin films

Energy Technology Data Exchange (ETDEWEB)

Dawley, J.T.; Clem, P.G.; Boyle, T.J.; Ottley, L.M.; Overmyer, D.L.; Siegal, M.P

2004-02-01

YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} (YBCO) films, deposited on buffered metal substrates, are the primary candidate for second-generation superconducting (SC) wires, with applications including expanded power grid transmission capability, compact motors, and enhanced sensitivity magnetic resonance imaging. Feasibility of manufacturing such superconducting wires is dependent on high processing speed, often a limitation of vapor and solution-based YBCO deposition processes. In this work, YBCO films were fabricated via a new diethanolamine-modified trifluoroacetic film solution deposition method. Modifying the copper chemistry of the YBCO precursor solution with diethanolamine enables a hundredfold decrease in the organic pyrolysis time required for MA/cm{sup 2} current density (J{sub c}) YBCO films, from multiple hours to {approx}20 s in atmospheric pressure air. High quality, {approx}0.2 {mu}m thick YBCO films with J{sub c} (77 K) values {>=}2 MA/cm{sup 2} at 77 K are routinely crystallized from these rapidly pyrolyzed films deposited on LaAlO{sub 3}. This process has also enabled J{sub c} (77 K)=1.1 MA/cm{sup 2} YBCO films via 90 m/h dip-coating on Oak Ridge National Laboratory RABiTS textured metal tape substrates. This new YBCO solution deposition method suggests a route toward inexpensive and commercializable {approx}$10/kA m solution deposited YBCO coated conductor wires.

Approximate analytical solution of diffusion equation with fractional time derivative using optimal homotopy analysis method

Directory of Open Access Journals (Sweden)

S. Das

2013-12-01

Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

Science.gov (United States)

Rahman, Nurhakimah Ab.; Abdullah, Lazim; Ghani, Ahmad Termimi Ab.; Ahmad, Noor'Ani

2015-10-01

A few years ago, a ranking method have been introduced in the fuzzy polynomial equations. Concept of the ranking method is proposed to find actual roots of fuzzy polynomials (if exists). Fuzzy polynomials are transformed to system of crisp polynomials, performed by using ranking method based on three parameters namely, Value, Ambiguity and Fuzziness. However, it was found that solutions based on these three parameters are quite inefficient to produce answers. Therefore in this study a new ranking method have been developed with the aim to overcome the inherent weakness. The new ranking method which have four parameters are then applied in the interval type-2 fuzzy polynomials, covering the interval type-2 of fuzzy polynomial equation, dual fuzzy polynomial equations and system of fuzzy polynomials. The efficiency of the new ranking method then numerically considered in the triangular fuzzy numbers and the trapezoidal fuzzy numbers. Finally, the approximate solutions produced from the numerical examples indicate that the new ranking method successfully produced actual roots for the interval type-2 fuzzy polynomials.

Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

Science.gov (United States)

Boronin, Ivan; Shevlyakov, Andrey

2018-03-01

Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.

Two Novel Methods and Multi-Mode Periodic Solutions for the Fermi-Pasta-Ulam Model

Science.gov (United States)

Arioli, Gianni; Koch, Hans; Terracini, Susanna

2005-04-01

We introduce two novel methods for studying periodic solutions of the FPU β-model, both numerically and rigorously. One is a variational approach, based on the dual formulation of the problem, and the other involves computer-assisted proofs. These methods are used e.g. to construct a new type of solutions, whose energy is spread among several modes, associated with closely spaced resonances.

Generation of new solutions of the stationary axisymmetric Einstein equations by a double complex function method

International Nuclear Information System (INIS)

Zhong, Z.

1985-01-01

A new approach to the solution of certain differential equations, the double complex function method, is developed, combining ordinary complex numbers and hyperbolic complex numbers. This method is applied to the theory of stationary axisymmetric Einstein equations in general relativity. A family of exact double solutions, double transformation groups, and n-soliton double solutions are obtained

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

Science.gov (United States)

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

A Three Step Explicit Method for Direct Solution of Third Order ...

African Journals Online (AJOL)

This study produces a three step discrete Linear Multistep Method for Direct solution of third order initial value problems of ordinary differential equations of the form y'''= f(x,y,y',y''). Taylor series expansion technique was adopted in the development of the method. The differential system from the basis polynomial function to ...

Variable separation solutions for the Nizhnik-Novikov-Veselov equation via the extended tanh-function method

International Nuclear Information System (INIS)

Zhang Jiefang; Dai Chaoqing; Zong Fengde

2007-01-01

In this paper, with the variable separation approach and based on the general reduction theory, we successfully generalize this extended tanh-function method to obtain new types of variable separation solutions for the following Nizhnik-Novikov-Veselov (NNV) equation. Among the solutions, two solutions are new types of variable separation solutions, while the last solution is similar to the solution given by Darboux transformation in Hu et al 2003 Chin. Phys. Lett. 20 1413

The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval

Directory of Open Access Journals (Sweden)

Majid Tavassoli Kajani

2013-01-01

Full Text Available We propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on the rational third-kind Chebyshev pseudospectral method that is indeed a combination of Tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate.

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

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

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

Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

International Nuclear Information System (INIS)

Franke, H.P.

1976-05-01

The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

Solution of neutron slowing down equation including multiple inelastic scattering

International Nuclear Information System (INIS)

El-Wakil, S.A.; Saad, A.E.

1977-01-01

The present work is devoted the presentation of an analytical method for the calculation of elastically and inelastically slowed down neutrons in an infinite non absorbing homogeneous medium. On the basis of the Central limit theory (CLT) and the integral transform technique the slowing down equation including inelastic scattering in terms of the Green function of elastic scattering is solved. The Green function is decomposed according to the number of collisions. A formula for the flux at any lethargy O (u) after any number of collisions is derived. An equation for the asymptotic flux is also obtained

Solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

International Nuclear Information System (INIS)

Rosenfeld, M.; Kwak, D.; Vinokur, M.

1988-01-01

A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references

Membrane for distillation including nanostructures, methods of making membranes, and methods of desalination and separation

KAUST Repository

Lai, Zhiping; Huang, Kuo-Wei; Chen, Wei

2016-01-01

In accordance with the purpose(s) of the present disclosure, as embodied and broadly described herein, embodiments of the present disclosure provide membranes, methods of making the membrane, systems including the membrane, methods of separation, methods of desalination, and the like.

Membrane for distillation including nanostructures, methods of making membranes, and methods of desalination and separation

KAUST Repository

Lai, Zhiping

2016-01-21

In accordance with the purpose(s) of the present disclosure, as embodied and broadly described herein, embodiments of the present disclosure provide membranes, methods of making the membrane, systems including the membrane, methods of separation, methods of desalination, and the like.

Analytic method for solitary solutions of some partial differential equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2007-01-01

In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation

Parallel shooting methods for finding steady state solutions to engine simulation models

DEFF Research Database (Denmark)

Andersen, Stig Kildegård; Thomsen, Per Grove; Carlsen, Henrik

2007-01-01

Parallel single- and multiple shooting methods were tested for finding periodic steady state solutions to a Stirling engine model. The model was used to illustrate features of the methods and possibilities for optimisations. Performance was measured using simulation of an experimental data set...

Evaluation of the Ross fast solution of Richards' equation in unfavourable conditions for standard finite element methods

International Nuclear Information System (INIS)

Crevoisier, D.; Voltz, M.; Chanzy, A.

2009-01-01

Ross [Ross PJ. Modeling soil water and solute transport - fast, simplified numerical solutions. Agron J 2003;95:1352-61] developed a fast, simplified method for solving Richards' equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins: 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions. The Ross method is compared with the standard finite element model, Hydrus-1D [Simunek J, Sejna M, Van Genuchten MTh. The HYDRUS-1D and HYDRUS-2D codes for estimating unsaturated soil hydraulic and solutes transport parameters. Agron Abstr 357; 1999]. Computing time, accuracy of results and robustness of numerical schemes are monitored in 1D simulations involving different types of homogeneous soils, grids and hydrological conditions. The Ross method associated with modified Van Genuchten hydraulic functions [Vogel T, Cislerova M. On the reliability of unsaturated hydraulic conductivity calculated from the moisture retention curve. Transport Porous Media 1988:3:1-15] proves in every tested scenario to be more robust numerically, and the compromise of computing time/accuracy is seen to be particularly improved on coarse grids. Ross method run from 1.25 to 14 times faster than Hydrus-1D. (authors)

Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

Directory of Open Access Journals (Sweden)

Özkan Güner

2014-01-01

Full Text Available We apply the functional variable method, exp-function method, and (G′/G-expansion method to establish the exact solutions of the nonlinear fractional partial differential equation (NLFPDE in the sense of the modified Riemann-Liouville derivative. As a result, some new exact solutions for them are obtained. The results show that these methods are very effective and powerful mathematical tools for solving nonlinear fractional equations arising in mathematical physics. As a result, these methods can also be applied to other nonlinear fractional differential equations.

New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

Directory of Open Access Journals (Sweden)

Hasibun Naher

2012-01-01

Full Text Available We construct new analytical solutions of the (3+1-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

Science.gov (United States)

Hano, Mitsuo; Hotta, Masashi

A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.

Dynamic nuclear polarization methods in solids and solutions to explore membrane proteins and membrane systems.

Science.gov (United States)

Cheng, Chi-Yuan; Han, Songi

2013-01-01

Membrane proteins regulate vital cellular processes, including signaling, ion transport, and vesicular trafficking. Obtaining experimental access to their structures, conformational fluctuations, orientations, locations, and hydration in membrane environments, as well as the lipid membrane properties, is critical to understanding their functions. Dynamic nuclear polarization (DNP) of frozen solids can dramatically boost the sensitivity of current solid-state nuclear magnetic resonance tools to enhance access to membrane protein structures in native membrane environments. Overhauser DNP in the solution state can map out the local and site-specific hydration dynamics landscape of membrane proteins and lipid membranes, critically complementing the structural and dynamics information obtained by electron paramagnetic resonance spectroscopy. Here, we provide an overview of how DNP methods in solids and solutions can significantly increase our understanding of membrane protein structures, dynamics, functions, and hydration in complex biological membrane environments.

Analytic method for solitary solutions of some partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya@firat.edu.tr

2007-10-22

In this Letter by considering an improved tanh function method, we found some exact solutions of the clannish random walker's parabolic equation, the modified Korteweg-de Vries (KdV) equation, and the Sharma-Tasso-Olver (STO) equation with its fission and fusion, the Jaulent-Miodek equation.

Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method.

Science.gov (United States)

Akbar, M Ali; Hj Mohd Ali, Norhashidah

2014-01-01

The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.

Predictive Sampling of Rare Conformational Events in Aqueous Solution: Designing a Generalized Orthogonal Space Tempering Method.

Science.gov (United States)

Lu, Chao; Li, Xubin; Wu, Dongsheng; Zheng, Lianqing; Yang, Wei

2016-01-12

In aqueous solution, solute conformational transitions are governed by intimate interplays of the fluctuations of solute-solute, solute-water, and water-water interactions. To promote molecular fluctuations to enhance sampling of essential conformational changes, a common strategy is to construct an expanded Hamiltonian through a series of Hamiltonian perturbations and thereby broaden the distribution of certain interactions of focus. Due to a lack of active sampling of configuration response to Hamiltonian transitions, it is challenging for common expanded Hamiltonian methods to robustly explore solvent mediated rare conformational events. The orthogonal space sampling (OSS) scheme, as exemplified by the orthogonal space random walk and orthogonal space tempering methods, provides a general framework for synchronous acceleration of slow configuration responses. To more effectively sample conformational transitions in aqueous solution, in this work, we devised a generalized orthogonal space tempering (gOST) algorithm. Specifically, in the Hamiltonian perturbation part, a solvent-accessible-surface-area-dependent term is introduced to implicitly perturb near-solute water-water fluctuations; more importantly in the orthogonal space response part, the generalized force order parameter is generalized as a two-dimension order parameter set, in which essential solute-solvent and solute-solute components are separately treated. The gOST algorithm is evaluated through a molecular dynamics simulation study on the explicitly solvated deca-alanine (Ala10) peptide. On the basis of a fully automated sampling protocol, the gOST simulation enabled repetitive folding and unfolding of the solvated peptide within a single continuous trajectory and allowed for detailed constructions of Ala10 folding/unfolding free energy surfaces. The gOST result reveals that solvent cooperative fluctuations play a pivotal role in Ala10 folding/unfolding transitions. In addition, our assessment

Methods for removing transuranic elements from waste solutions

International Nuclear Information System (INIS)

Slater, S.A.; Chamberlain, D.B.; Connor, C.; Sedlet, J.; Srinivasan, B.; Vandegrift, G.F.

1994-11-01

This report outlines a treatment scheme for separating and concentrating the transuranic (TRU) elements present in aqueous waste solutions stored at Argonne National Laboratory (ANL). The treatment method selected is carrier precipitation. Potential carriers will be evaluated in future laboratory work, beginning with ferric hydroxide and magnetite. The process will result in a supernatant with alpha activity low enough that it can be treated in the existing evaporator/concentrator at ANL. The separated TRU waste will be packaged for shipment to the Waste Isolation Pilot Plant

New exact solutions of the KdV-Burgers-Kuramoto equation

International Nuclear Information System (INIS)

Zhang Sheng

2006-01-01

A generalized F-expansion method is proposed and applied to the KdV-Burgers-Kuramoto equation. As a result, many new and more general exact travelling wave solutions are obtained including combined non-degenerate Jacobi elliptic function solutions, solitary wave solutions and trigonometric function solutions. The method can be applied to other nonlinear partial differential equations in mathematical physics

Inverse Scattering Method and Soliton Solution Family for String Effective Action

International Nuclear Information System (INIS)

Ya-Jun, Gao

2009-01-01

A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained

Numerical method for solution of transient, homogeneous, equilibrium, two-phase flows in one space dimension

International Nuclear Information System (INIS)

Shin, Y.W.; Wiedermann, A.H.

1979-10-01

A solution method is presented for transient, homogeneous, equilibrium, two-phase flows of a single-component fluid in one space dimension. The method combines a direct finite-difference procedure and the method of characteristics. The finite-difference procedure solves the interior points of the computing domain; the boundary information is provided by a separate procedure based on the characteristics theory. The solution procedure for boundary points requires information in addition to the physical boundary conditions. This additional information is obtained by a new procedure involving integration of characteristics in the hodograph plane. Sample problems involving various combinations of basic boundary types are calculated for two-phase water/steam mixtures and single-phase nitrogen gas, and compared with independent method-of-characteristics solutions using very fine characteristic mesh. In all cases, excellent agreement is demonstrated

Solution of linear ordinary differential equations by means of the method of variation of arbitrary constants

DEFF Research Database (Denmark)

Mejlbro, Leif

1997-01-01

An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians.......An alternative formula for the solution of linear differential equations of order n is suggested. When applicable, the suggested method requires fewer and simpler computations than the well-known method using Wronskians....

Approximate solution methods in engineering mechanics

International Nuclear Information System (INIS)

Boresi, A.P.; Cong, K.P.

1991-01-01

This is a short book of 147 pages including references and sometimes bibliographies at the end of each chapter, and subject and author indices at the end of the book. The test includes an introduction of 3 pages, 29 pages explaining approximate analysis, 41 pages on finite differences, 36 pages on finite elements, and 17 pages on specialized methods

Volume-weighted particle-tracking method for solute-transport modeling; Implementation in MODFLOW–GWT

Science.gov (United States)

Winston, Richard B.; Konikow, Leonard F.; Hornberger, George Z.

2018-02-16

In the traditional method of characteristics for groundwater solute-transport models, advective transport is represented by moving particles that track concentration. This approach can lead to global mass-balance problems because in models of aquifers having complex boundary conditions and heterogeneous properties, particles can originate in cells having different pore volumes and (or) be introduced (or removed) at cells representing fluid sources (or sinks) of varying strengths. Use of volume-weighted particles means that each particle tracks solute mass. In source or sink cells, the changes in particle weights will match the volume of water added or removed through external fluxes. This enables the new method to conserve mass in source or sink cells as well as globally. This approach also leads to potential efficiencies by allowing the number of particles per cell to vary spatially—using more particles where concentration gradients are high and fewer where gradients are low. The approach also eliminates the need for the model user to have to distinguish between “weak” and “strong” fluid source (or sink) cells. The new model determines whether solute mass added by fluid sources in a cell should be represented by (1) new particles having weights representing appropriate fractions of the volume of water added by the source, or (2) distributing the solute mass added over all particles already in the source cell. The first option is more appropriate for the condition of a strong source; the latter option is more appropriate for a weak source. At sinks, decisions whether or not to remove a particle are replaced by a reduction in particle weight in proportion to the volume of water removed. A number of test cases demonstrate that the new method works well and conserves mass. The method is incorporated into a new version of the U.S. Geological Survey’s MODFLOW–GWT solute-transport model.

Higher order methods for burnup calculations with Bateman solutions

International Nuclear Information System (INIS)

Isotalo, A.E.; Aarnio, P.A.

2011-01-01

Highlights: → Average microscopic reaction rates need to be estimated at each step. → Traditional predictor-corrector methods use zeroth and first order predictions. → Increasing predictor order greatly improves results. → Increasing corrector order does not improve results. - Abstract: A group of methods for burnup calculations solves the changes in material compositions by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates. This requires predicting representative averages for the one-group cross-sections and flux during each step, which is usually done using zeroth and first order predictions for their time development in a predictor-corrector calculation. In this paper we present the results of using linear, rather than constant, extrapolation on the predictor and quadratic, rather than linear, interpolation on the corrector. Both of these are done by using data from the previous step, and thus do not affect the stepwise running time. The methods were tested by implementing them into the reactor physics code Serpent and comparing the results from four test cases to accurate reference results obtained with very short steps. Linear extrapolation greatly improved results for thermal spectra and should be preferred over the constant one currently used in all Bateman solution based burnup calculations. The effects of using quadratic interpolation on the corrector were, on the other hand, predominantly negative, although not enough so to conclusively decide between the linear and quadratic variants.

A New Method for Constructing Travelling Wave Solutions to the modified Benjamin–Bona–Mahoney Equation

International Nuclear Information System (INIS)

Jun-Mao, Wang; Miao, Zhang; Wen-Liang, Zhang; Rui, Zhang; Jia-Hua, Han

2008-01-01

We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified Benjamin–Bona–Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. (general)

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

A New Method to Solve Numeric Solution of Nonlinear Dynamic System

Directory of Open Access Journals (Sweden)

Min Hu

2016-01-01

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

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

Science.gov (United States)

Ghosh, Pradipto

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

Standard test method for evaluating stress-corrosion cracking of stainless alloys with different nickel content in boiling acidified sodium chloride solution

CERN Document Server

American Society for Testing and Materials. Philadelphia

2000-01-01

1.1 This test method describes a procedure for conducting stress-corrosion cracking tests in an acidified boiling sodium chloride solution. This test method is performed in 25% (by mass ) sodium chloride acidified to pH 1.5 with phosphoric acid. This test method is concerned primarily with the test solution and glassware, although a specific style of U-bend test specimen is suggested. 1.2 This test method is designed to provide better correlation with chemical process industry experience for stainless steels than the more severe boiling magnesium chloride test of Practice G36. Some stainless steels which have provided satisfactory service in many environments readily crack in Practice G36, but have not cracked during interlaboratory testing using this sodium chloride test method. 1.3 This boiling sodium chloride test method was used in an interlaboratory test program to evaluate wrought stainless steels, including duplex (ferrite-austenite) stainless and an alloy with up to about 33% nickel. It may also b...

Verification of the coupled space-angle adaptivity algorithm for the finite element-spherical harmonics method via the method of manufactured solutions

International Nuclear Information System (INIS)

Park, H.; De Oliveira, C. R. E.

2007-01-01

This paper describes the verification of the recently developed space-angle self-adaptive algorithm for the finite element-spherical harmonics method via the Method of Manufactured Solutions. This method provides a simple, yet robust way for verifying the theoretical properties of the adaptive algorithm and interfaces very well with the underlying second-order, even-parity transport formulation. Simple analytic solutions in both spatial and angular variables are manufactured to assess the theoretical performance of the a posteriori error estimates. The numerical results confirm reliability of the developed space-angle error indicators. (authors)

New exact solutions of the generalized Zakharov–Kuznetsov ...

Indian Academy of Sciences (India)

In this paper, new exact solutions, including soliton, rational and elliptic integral function solutions, for the generalized Zakharov–Kuznetsov modified equal-width equation are obtained using a new approach called the extended trial equation method. In this discussion, a new version of the trial equation method for the ...

Uranium in aqueous solutions by colorimetry

International Nuclear Information System (INIS)

Anon.

1981-01-01

The method covers the quantitative determination of uranium in known volumes of aqueous solutions that contain radioactive nuclides. These solutions arise from processing of irradiated nuclear fuel and from laboratory studies on irradiated uranium. The method is applicable to solutions containing a minimum of 30 μg of uranium per sample although as little as 0.5 μg can be detected but with lower precision. Highest precision is obtained with 50 to 75 μg of uranium in the test sample. Dilutions must be made at concentrations above 750 μg/ml. The method includes a discussion of photometers and photometric practice, apparatus, reagents, cell matching, preparation of standard curves, calibration by the method of internal standards, procedure, calculation, and precision

Operational method of solution of linear non-integer ordinary and partial differential equations.

Science.gov (United States)

Zhukovsky, K V

2016-01-01

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

The Train Driver Recovery Problem - a Set Partitioning Based Model and Solution Method

DEFF Research Database (Denmark)

Rezanova, Natalia Jurjevna; Ryan, David

The need to recover a train driver schedule occurs during major disruptions in the daily railway operations. Using data from the train driver schedule of the Danish passenger railway operator DSB S-tog A/S, a solution method to the Train Driver Recovery Problem (TDRP) is developed. The TDRP...... the depth-first search of the Branch & Bound tree. Preliminarily results are encouraging, showing that nearly all tested real-life instances produce integer solutions to the LP relaxation and solutions are found within a few seconds....

On the economical solution method for a system of linear algebraic equations

Directory of Open Access Journals (Sweden)

Jan Awrejcewicz

2004-01-01

Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

An online interactive geometric database including exact solutions of Einstein's field equations

International Nuclear Information System (INIS)

Ishak, Mustapha; Lake, Kayll

2002-01-01

We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed for the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII, used to perform online coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows systematic internal self-checking and minimization of the required internal records. This new database is now available online at http://grdb.org

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method

International Nuclear Information System (INIS)

Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de

2003-01-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

The Method of Subsuper Solutions for Weighted p(r-Laplacian Equation Boundary Value Problems

Directory of Open Access Journals (Sweden)

Zhimei Qiu

2008-10-01

Full Text Available This paper investigates the existence of solutions for weighted p(r-Laplacian ordinary boundary value problems. Our method is based on Leray-Schauder degree. As an application, we give the existence of weak solutions for p(x-Laplacian partial differential equations.

Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy

International Nuclear Information System (INIS)

Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos

2008-01-01

Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events

Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

Science.gov (United States)

Zhao, Zhonglong; Han, Bo

2018-04-01

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

Exact solutions for the cubic-quintic nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Zhu Jiamin; Ma Zhengyi

2007-01-01

In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

International Nuclear Information System (INIS)

Ebaid, A.

2007-01-01

Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method

Evaluation and comparison of two complexometric titration methods for determining of lanthanum in cloridric solutions

International Nuclear Information System (INIS)

Menezes, M.F.; Santos, R.L.C. dos; Goes, M.A.C. de

1994-01-01

The fast determination of total rare earth concentration in aqueous solutions is based on titrimetric methods using EDTA as complexing agent. This paper evaluates two among several others titrimetric methods used in the determination of lanthanum in hydrochloric acid solutions, using xylenol orange and a mixture of methyl orange and xylenol orange as indicators. The applied statistical evaluation allowed the determination of the stability, accuracy and adequacy of these methods on a given technical specification. (author). 12 refs., 03 tabs., 01 fig

EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

Methods of making metal oxide nanostructures and methods of controlling morphology of same

Science.gov (United States)

Wong, Stanislaus S; Hongjun, Zhou

2012-11-27

The present invention includes a method of producing a crystalline metal oxide nanostructure. The method comprises providing a metal salt solution and providing a basic solution; placing a porous membrane between the metal salt solution and the basic solution, wherein metal cations of the metal salt solution and hydroxide ions of the basic solution react, thereby producing a crystalline metal oxide nanostructure.

A new method to assess the statistical convergence of monte carlo solutions

International Nuclear Information System (INIS)

Forster, R.A.

1991-01-01

Accurate Monte Carlo confidence intervals (CIs), which are formed with an estimated mean and an estimated standard deviation, can only be created when the number of particle histories N becomes large enough so that the central limit theorem can be applied. The Monte Carlo user has a limited number of marginal methods to assess the fulfillment of this condition, such as statistical error reduction proportional to 1/√N with error magnitude guidelines and third and fourth moment estimators. A new method is presented here to assess the statistical convergence of Monte Carlo solutions by analyzing the shape of the empirical probability density function (PDF) of history scores. Related work in this area includes the derivation of analytic score distributions for a two-state Monte Carlo problem. Score distribution histograms have been generated to determine when a small number of histories accounts for a large fraction of the result. This summary describes initial studies of empirical Monte Carlo history score PDFs created from score histograms of particle transport simulations. 7 refs., 1 fig

A coupling method for a cardiovascular simulation model which includes the Kalman filter.

Science.gov (United States)

Hasegawa, Yuki; Shimayoshi, Takao; Amano, Akira; Matsuda, Tetsuya

2012-01-01

Multi-scale models of the cardiovascular system provide new insight that was unavailable with in vivo and in vitro experiments. For the cardiovascular system, multi-scale simulations provide a valuable perspective in analyzing the interaction of three phenomenons occurring at different spatial scales: circulatory hemodynamics, ventricular structural dynamics, and myocardial excitation-contraction. In order to simulate these interactions, multiscale cardiovascular simulation systems couple models that simulate different phenomena. However, coupling methods require a significant amount of calculation, since a system of non-linear equations must be solved for each timestep. Therefore, we proposed a coupling method which decreases the amount of calculation by using the Kalman filter. In our method, the Kalman filter calculates approximations for the solution to the system of non-linear equations at each timestep. The approximations are then used as initial values for solving the system of non-linear equations. The proposed method decreases the number of iterations required by 94.0% compared to the conventional strong coupling method. When compared with a smoothing spline predictor, the proposed method required 49.4% fewer iterations.

Multigroup adjoint transport solution using the method of cyclic characteristics

International Nuclear Information System (INIS)

Assawaroongruengchot, M.; Marleau, G.

2005-01-01

The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2-dimensional geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 17*17 PWR and Watanabe-Maynard benchmark problems. Comparisons of adjoint flux and k eff results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. It appears that the pseudo-adjoint flux by CP method is equivalent to the adjoint flux by MOCC method and that the MOCC method requires lower computing time than the CP method for a single adjoint flux calculation

Multigroup adjoint transport solution using the method of cyclic characteristics

Energy Technology Data Exchange (ETDEWEB)

Assawaroongruengchot, M.; Marleau, G. [Ecole Polytechnique de Montreal, Institut de Genie Nucleaire, Montreal, Quebec (Canada)

2005-07-01

The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2-dimensional geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 17*17 PWR and Watanabe-Maynard benchmark problems. Comparisons of adjoint flux and k{sub eff} results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. It appears that the pseudo-adjoint flux by CP method is equivalent to the adjoint flux by MOCC method and that the MOCC method requires lower computing time than the CP method for a single adjoint flux calculation.

Numerical solution of stiff burnup equation with short half lived nuclides by the Krylov subspace method

International Nuclear Information System (INIS)

Yamamoto, Akio; Tatsumi, Masahiro; Sugimura, Naoki

2007-01-01

The Krylov subspace method is applied to solve nuclide burnup equations used for lattice physics calculations. The Krylov method is an efficient approach for solving ordinary differential equations with stiff nature such as the nuclide burnup with short lived nuclides. Some mathematical fundamentals of the Krylov subspace method and its application to burnup equations are discussed. Verification calculations are carried out in a PWR pin-cell geometry with UO 2 fuel. A detailed burnup chain that includes 193 fission products and 28 heavy nuclides is used in the verification calculations. Shortest half life found in the present burnup chain is approximately 30 s ( 106 Rh). Therefore, conventional methods (e.g., the Taylor series expansion with scaling and squaring) tend to require longer computation time due to numerical stiffness. Comparison with other numerical methods (e.g., the 4-th order Runge-Kutta-Gill) reveals that the Krylov subspace method can provide accurate solution for a detailed burnup chain used in the present study with short computation time. (author)

Development and evaluation of methods for safeguards use of solution monitoring data

International Nuclear Information System (INIS)

Burr, T.; Wangen, L.

1996-09-01

This report describes the effort to develop, implement, and evaluate data analysis methods for solution-monitoring measurements in the plutonium nitrate storage at the Tokai Reprocessing Plant (TRP). The intent is to address TRP-specific issues to some extent, as well as to anticipate the data analysis needs at future reprocessing plants (especially the new Rokkasho reprocessing plant (RRP)) in Japan. The essential difference between a plant like TRP and a more modern plant like RRP is that one expects more and better instrumentation in the tanks in a modern plant. Because the TRP solution monitoring hardware is scheduled to be upgraded, the authors de-emphasized the effort to handle information-poor plants like TRP. This report mostly describes the analysis methods and software for finding and identifying all key tank events. To a large extent they have to experiment with several candidate methods for implementing their analysis objectives. Therefore, they chose to use a prototyping software system called S-PLUS, which is an object-oriented statistical programming and graphics package. The intent is to eventually implement selected portions of their current solution-monitoring toolkit in a more robust and user-friendly system. The authors describe their current software system as being far more than they needed for their own in-house use (menus are provided for the user who doesn't want to type any S-PLUS commands), but less than is needed for a fieldable system. Mostly as a result of working on this project, they have come to conclude that solution monitoring is a potentially very valuable asset to nuclear safeguards at a modern reprocessing plant

An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2017-11-01

Full Text Available In this article, a variety of solitary wave solutions are observed for microtubules (MTs. We approach the problem by treating the solutions as nonlinear RLC transmission lines and then find exact solutions of Nonlinear Evolution Equations (NLEEs involving parameters of special interest in nanobiosciences and biophysics. We determine hyperbolic, trigonometric, rational and exponential function solutions and obtain soliton-like pulse solutions for these equations. A comparative study against other methods demonstrates the validity of the technique that we developed and demonstrates that our method provides additional solutions. Finally, using suitable parameter values, we plot 2D and 3D graphics of the exact solutions that we observed using our method. Keywords: Analytical method, Exact solutions, Nonlinear evolution equations (NLEEs of microtubules, Nonlinear RLC transmission lines

78 FR 70584 - ATOS IT Solutions & Services, Inc., Billing and Collections Department, Including Workers Whose...

Science.gov (United States)

2013-11-26

...) Wages are Reported Through Siemens IT Solutions and Services, Mason, Ohio; Amended Certification... Solutions & Services, Inc., Billing and Collections Department, Mason, Ohio. The workers are engaged in... workers separated from employment at the Mason, Ohio location of ATOS IT Solutions & Services, Inc...

Unsteady panel method for complex configurations including wake modeling

CSIR Research Space (South Africa)

Van Zyl, Lourens H

2008-01-01

Full Text Available implementations of the DLM are however not very versatile in terms of geometries that can be modeled. The ZONA6 code offers a versatile surface panel body model including a separated wake model, but uses a pressure panel method for lifting surfaces. This paper...

Solution Methods for the Periodic Petrol Station Replenishment Problem

OpenAIRE

C Triki

2013-01-01

In this paper we introduce the Periodic Petrol Station Replenishment Problem (PPSRP) over a T-day planning horizon and describe four heuristic methods for its solution. Even though all the proposed heuristics belong to the common partitioning-then-routing paradigm, they differ in assigning the stations to each day of the horizon. The resulting daily routing problems are then solved exactly until achieving optimalization. Moreover, an improvement procedure is also developed with the aim of ens...

Conductometry of electrolyte solutions

Science.gov (United States)

Safonova, Lyubov P.; Kolker, Arkadii M.

1992-09-01

A review is given of the theories of the electrical conductance of electrolyte solutions of different ionic strengths and concentrations, and of the models of ion association. An analysis is made of the methods for mathematical processing of experimental conductometric data. An account is provided of various theories describing the dependence of the limiting value of the ionic electrical conductance on the properties of the solute and solvent. The bibliography includes 115 references.

Determination of hexamethylene tetramine in the process solution of sol-gel method for nuclear fuel fabrication

International Nuclear Information System (INIS)

Ganatra, V.R.; Sawant, R.M.; Chaudhuri, N.K.; Vaidya, V.N.

1998-01-01

Hexamethylene tetramine (HMTA) was determined in the presence of large quantities of urea, formaldehyde and ammonium hydroxide by potentiometric titration with perchloric acid solution using an autotitrator coupled to a personal computer. This analysis is required for the process control of the sol-gel method in the production of ceramic metal oxide (e.g., oxides and mixed oxides of Th, U and Pu) microspheres using the internal gelation route. Feed solution used for preparation of microspheres contains large quantities of urea. The washings of gel microspheres produced after the internal gelation process contain urea, formaldehyde, urea-formaldehyde complex and ammonium hydroxide. The presence of these constituents in the feed solution and washings seriously interfere in the commonly used methods for the determination of HMTA. Using this method the relative standard deviation was found to be 0.27% in eleven determinations of a typical feed solution (3.0M HMTA) when the aliquots contained 75 to 125 mg of HMTA. Time required for each titration was 5-7 minutes. Feed and effluent solutions of sol-gel process were analysed. (author)

Application of Homotopy-Perturbation Method to Nonlinear Ozone Decomposition of the Second Order in Aqueous Solutions Equations

DEFF Research Database (Denmark)

Ganji, D.D; Miansari, Mo; B, Ganjavi

2008-01-01

In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...

A new method for the solution of the Schroedinger equation

International Nuclear Information System (INIS)

Amore, Paolo; Aranda, Alfredo; De Pace, Arturo

2004-01-01

We present a new method for the solution of the Schroedinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings

He's variational iteration method applied to the solution of the prey and predator problem with variable coefficients

International Nuclear Information System (INIS)

Yusufoglu, Elcin; Erbas, Baris

2008-01-01

In this Letter, a mathematical model of the problem of prey and predator is presented and He's variational iteration method is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Comparison of the methods show that He's variational iteration method is a powerful method for obtaining approximate solutions to nonlinear equations and their systems

White noise solutions to the stochastic mKdV equation

International Nuclear Information System (INIS)

Zhang Zhongjun; Wei Caimin

2009-01-01

In this paper, we present the white noise solutions of the stochastic mKdV equation via the Hermite transformation and variable-coefficient generalized projected Ricatti equation expansion method. These solutions include white noise solitary wave solutions, white noise soliton-like solutions and white noise trigonometric function solutions.

Solution of the neutron transport problem with anisotropic scattering in cylindrical geometry by the decomposition method

International Nuclear Information System (INIS)

Goncalves, G.A.; Bogado Leite, S.Q.; Vilhena, M.T. de

2009-01-01

An analytical solution has been obtained for the one-speed stationary neutron transport problem, in an infinitely long cylinder with anisotropic scattering by the decomposition method. Series expansions of the angular flux distribution are proposed in terms of suitably constructed functions, recursively obtainable from the isotropic solution, to take into account anisotropy. As for the isotropic problem, an accurate closed-form solution was chosen for the problem with internal source and constant incident radiation, obtained from an integral transformation technique and the F N method

Perturbational blowup solutions to the compressible Euler equations with damping.

Science.gov (United States)

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Cementation of the solid radioactive waste with polymer-cement solutions using the method of impregnation

International Nuclear Information System (INIS)

Gorbunova, O.

2015-01-01

Cementation of solid radioactive waste (SRW), i.e. inclusion of solid radioactive waste into cement matrix without cavities - is one of the main technological processes used for conditioning low and intermediate level radioactive waste. At FSUE 'Radon' the industrialized method of impregnation has been developed and since 2003 has been using for cementation of solid radioactive waste. The technology is that the polymer-cement solution, having high penetrating properties, is supplied under pressure through a tube to the bottom of the container in which solid radioactive waste has preliminarily been placed. The polymer-cement solution is evenly moving upwards through the channels between the particles of solid radioactive waste, fills the voids in the bulk volume of the waste and hardens, forming a cement compound, the amount of which is equal to the original volume. The aim of the investigation was a selection of a cement solution suitable for SRW impregnation (including fine particles) without solution depletion and bottom layers stuffing. It has been chosen a polymer: PHMG (polyhexamethylene-guanidine), which is a stabilizing and water-retaining component of the cement solution. The experiments confirm that the polymer increases the permeability of the cement solution by a 2-2.5 factor, the viscosity by a 1.2 factor, the stability of the consistency by a 1.5-1.7 factor, and extends the operating range of the W/C ratio to 0.5-1.1. So it is possible to penetrate a volume of SRW bigger by a 1.5-2.0 factor. It has been proved, that PHMG polymer increases strength and frost-resistance of the final compounds by a 1.8-2.7 factor, and contributes to fast strength development at the beginning of hardening and it decreases Cs-137 leashing rate by a 1.5-2 factor

Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method

International Nuclear Information System (INIS)

Yusufoglu, E.; Bekir, A.; Alp, M.

2008-01-01

In this paper, we establish exact solutions for nonlinear evolution equations. The sine-cosine method is used to construct periodic and solitary wave solutions of the Kawahara and modified Kawahara equations. These solutions may be important of significance for the explanation of some practical physical problems

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

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

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

Method for regeneration of electroless nickel plating solution

Science.gov (United States)

Eisenmann, E.T.

1997-03-11

An electroless nickel(EN)/hypophosphite plating bath is provided employing acetic acid/acetate as a buffer and which is, as a result, capable of perpetual regeneration while avoiding the production of hazardous waste. A regeneration process is provided to process the spent EN plating bath solution. A concentrated starter and replenishment solution is provided for ease of operation of the plating bath. The regeneration process employs a chelating ion exchange system to remove nickel cations from spent EN plating solution. Phosphites are then removed from the solution by precipitation. The nickel cations are removed from the ion exchange system by elution with hypophosphorus acid and the nickel concentration of the eluate adjusted by addition of nickel salt. The treated solution and adjusted eluate are combined, stabilizer added, and the volume of resulting solution reduced by evaporation to form the bath starter and replenishing solution. 1 fig.

Method for regeneration of electroless nickel plating solution

Science.gov (United States)

Eisenmann, Erhard T.

1997-01-01

An electroless nickel(EN)/hypophosphite plating bath is provided employing acetic acid/acetate as a buffer and which is, as a result, capable of perpetual regeneration while avoiding the production of hazardous waste. A regeneration process is provided to process the spent EN plating bath solution. A concentrated starter and replenishment solution is provided for ease of operation of the plating bath. The regeneration process employs a chelating ion exchange system to remove nickel cations from spent EN plating solution. Phosphites are then removed from the solution by precipitation. The nickel cations are removed from the ion exchange system by elution with hypophosphorous acid and the nickel concentration of the eluate adjusted by addition of nickel salt. The treated solution and adjusted eluate are combined, stabilizer added, and the volume of resulting solution reduced by evaporation to form the bath starter and replenishing solution.

Novel geochemistry-inspired method for the deep removal of vanadium from molybdate solution

Energy Technology Data Exchange (ETDEWEB)

Zhang, Jialiang [School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 (China); Beijing Key Laboratory of Green Recycling and Extraction of Metals, Beijing, 100083 (China); Deng, Yuping; Zhou, Qiuyue; Qin, Peixin; Liu, Yubo [School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 (China); Wang, Chengyan, E-mail: chywang@yeah.net [School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing, 100083 (China)

2017-06-05

Highlights: • A geochemistry-inspired method was developed for removal of V from molybdates. • Magnetic separation of the Fe{sub 3}O{sub 4} adsorbent took 10 s. • Vanadium can be deeply removed in 5 min at pH of 7.0–11.0. • Fe{sub 3}O{sub 4} adsorbent has excellent V selectivity and reusability. • A flowchart is presented for Mo/V separation in the leachate of spent HDS catalyst. - Abstract: Separation of vanadium from molybdates is an essential task for processing the leaching solution of hazardous spent hydrodesulphurization (HDS) catalyst. In this study, the difference in the main naturally occurring mineral forms of Mo and V inspired us to develop a method for the deep removal of V from molybdate solution using Fe{sub 3}O{sub 4} as an adsorbent. First, the adsorbent was synthesized with coprecipitation method, and then it was characterized by XRD, TEM, and VSM. The synthesized material consisted of pure Fe{sub 3}O{sub 4} nanoparticles that exhibited paramagnetic property, with a saturated magnetization of 68.6 emu g{sup −1}. The V removal efficiency was investigated using batch adsorption experiments in varying conditions. Results indicated that V could be deeply removed from various concentrations of molybdate solution at pH of 7.0–11.0 within 5 min. A slight decrease was found in the adsorption ratio after the adsorbent had been reused for 4 cycles. The resulting molybdate solution contained less than 0.02 g L{sup −1} of V, which satisfies the requirement for preparing high-quality products. Finally, a process flowchart is presented for the separation of Mo and V from the leaching solution of spent HDS catalyst, based on the excellent V removal performance and rapid separation rate of the Fe{sub 3}O{sub 4} adsorbent.

Catalyst support structure, catalyst including the structure, reactor including a catalyst, and methods of forming same

Science.gov (United States)

Van Norman, Staci A.; Aston, Victoria J.; Weimer, Alan W.

2017-05-09

Structures, catalysts, and reactors suitable for use for a variety of applications, including gas-to-liquid and coal-to-liquid processes and methods of forming the structures, catalysts, and reactors are disclosed. The catalyst material can be deposited onto an inner wall of a microtubular reactor and/or onto porous tungsten support structures using atomic layer deposition techniques.

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

Directory of Open Access Journals (Sweden)

Won-Tak Hong

2016-01-01

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

Factors influencing hydroquinone degradation in aqueous solution using a modified microelectrolysis method.

Science.gov (United States)

Li, Tong; Li, Tingting; Xiong, Houfeng; Zou, Donglei

2015-01-01

The discharge of hydroquinone (HQ), an important chemical raw material, to natural waters poses different ecological threats to aquatic organisms. In this study, we investigated the removal performance of traditional and modified microelectrolysis methods in aqueous solutions. The traditional microelectrolysis packing was modified by adding manganese (Mn), zinc (Zn), and copper (Cu) powder as additives. The factors affecting the removal performance of HQ, such as catalytic metal type, mass fraction of additive, reaction time, and initial pH, were examined. The results showed that the Mn modified packing exhibited the best performance compared to Zn and Cu powder. The removal rate of HQ using Mn modified packing can reach 94% after 4 h. In addition, 9% of Mn packing has a higher removal rate than other mass fractions. The acidic solution pH shows a more favorable degradation than a neutral and alkaline solution. The intermediates of HQ degradation by modified microelectrolysis were identified and then the pathway of HQ degradation was proposed. Our result indicates that Mn as catalytic metal holds promising potential to enhance HQ removal in water using the microelectrolysis method.

Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations

International Nuclear Information System (INIS)

Zhou Yubin; Li Chao

2009-01-01

A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. (general)

New exact solutions of (2 + 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method

International Nuclear Information System (INIS)

Chen Yong; Yan Zhenya

2005-01-01

In this paper (2 + 1)-dimensional Gardner equation is investigated using a sine-Gordon equation expansion method, which was presented via a generalized sine-Gordon reduction equation and a new transformation. As a consequence, it is shown that the method is more powerful to obtain many types of new doubly periodic solutions of (2 + 1)-dimensional Gardner equation. In particular, solitary wave solutions are also given as simple limits of doubly periodic solutions

Method of solution mining subsurface orebodies to reduce restoration activities

Energy Technology Data Exchange (ETDEWEB)

Hartman, G.J.

1984-01-24

A method of solution mining is claimed wherein a lixiviant containing both leaching and oxidizing agents is injected into the subsurface orebody. The composition of the lixiviant is changed by reducing the level of oxidizing agent to zero so that soluble species continue to be removed from the subsurface environment. This reduces the uranium level of the ground water aquifer after termination of the lixiviant injection.

Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method

Directory of Open Access Journals (Sweden)

Reza Ezzati

2014-08-01

Full Text Available In this paper, we propose the least square method for computing the positive solution of a non-square fully fuzzy linear system. To this end, we use Kaffman' arithmetic operations on fuzzy numbers \\cite{17}. Here, considered existence of exact solution using pseudoinverse, if they are not satisfy in positive solution condition, we will compute fuzzy vector core and then we will obtain right and left spreads of positive fuzzy vector by introducing constrained least squares problem. Using our proposed method, non-square fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.

Solution of continuous nonlinear PDEs through order completion

CERN Document Server

Oberguggenberger, MB

1994-01-01

This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method

Directory of Open Access Journals (Sweden)

Eman M. A. Hilal

2014-01-01

Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.

A Summary of the Space-Time Conservation Element and Solution Element (CESE) Method

Science.gov (United States)

Wang, Xiao-Yen J.

2015-01-01

The space-time Conservation Element and Solution Element (CESE) method for solving conservation laws is examined for its development motivation and design requirements. The characteristics of the resulting scheme are discussed. The discretization of the Euler equations is presented to show readers how to construct a scheme based on the CESE method. The differences and similarities between the CESE method and other traditional methods are discussed. The strengths and weaknesses of the method are also addressed.

Method of processing plutonium and uranium solution

International Nuclear Information System (INIS)

Otsuka, Katsuyuki; Kondo, Isao; Suzuki, Toru.

1989-01-01

Solutions of plutonium nitrate solutions and uranyl nitrate recovered in the solvent extraction step in reprocessing plants and nuclear fuel production plants are applied with low temperature treatment by means of freeze-drying under vacuum into residues containing nitrates, which are denitrated under heating and calcined under reduction into powders. That is, since complicate processes of heating, concentration and dinitration conducted so far for the plutonium solution and uranyl solution are replaced with one step of freeze-drying under vacuum, the process can be simplified significantly. In addition, since the treatment is applied at low temperature, occurrence of corrosion for the material of evaporation, etc. can be prevented. Further, the number of operators can be saved by dividing the operations into recovery of solidification products, supply and sintering of the solutions and vacuum sublimation. Further, since nitrates processed at a low temperature are powderized by heating dinitration, the powderization step can be simplified. The specific surface area and the grain size distribution of the powder is made appropriate and it is possible to obtain oxide powders of physical property easily to be prepared into pellets. (N.H.)

On Solution of a Fractional Diffusion Equation by Homotopy Transform Method

International Nuclear Information System (INIS)

Salah, A.; Hassan, S.S.A.

2012-01-01

The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.

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

Science.gov (United States)

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

2017-11-01

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

Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

Science.gov (United States)

Grolet, Aurelien; Thouverez, Fabrice

2015-02-01

This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

Exp-function method for constructing exact solutions of Sharma-Tasso-Olver equation

International Nuclear Information System (INIS)

Erbas, Baris; Yusufoglu, Elcin

2009-01-01

In this paper we use the Exp-function method for the analytic treatment of Sharma-Tasso-Olver equation. New solitonary solutions are formally derived. Change of parameters, which drastically changes the characteristics of the equations, is examined. It is shown that the Exp-function method provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics. The proposed schemes are reliable and manageable.

Solution of Moving Boundary Space-Time Fractional Burger’s Equation

Directory of Open Access Journals (Sweden)

E. A.-B. Abdel-Salam

2014-01-01

Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.

Numerical solution of sixth-order boundary-value problems using Legendre wavelet collocation method

Science.gov (United States)

Sohaib, Muhammad; Haq, Sirajul; Mukhtar, Safyan; Khan, Imad

2018-03-01

An efficient method is proposed to approximate sixth order boundary value problems. The proposed method is based on Legendre wavelet in which Legendre polynomial is used. The mechanism of the method is to use collocation points that converts the differential equation into a system of algebraic equations. For validation two test problems are discussed. The results obtained from proposed method are quite accurate, also close to exact solution, and other different methods. The proposed method is computationally more effective and leads to more accurate results as compared to other methods from literature.

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

International Nuclear Information System (INIS)

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

2010-01-01

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

A solution of the Schrodinger equation with two-body correlations included

International Nuclear Information System (INIS)

Fabre de la Ripelle, M.

1984-01-01

A procedure for introducing the two-body correlations in the solution of the Schrodinger equation is described. The N-body Schrodinger equation for nucleons subject to two-(or many)-body N-N interaction has never been solved with accuracy except for few-body systems. Indeed it is difficult to take the two-body correlations generated by the interaction into account in the wave function

Replica exchange with solute tempering: A method for sampling biological systems in explicit water

Science.gov (United States)

Liu, Pu; Kim, Byungchan; Friesner, Richard A.; Berne, B. J.

2005-09-01

An innovative replica exchange (parallel tempering) method called replica exchange with solute tempering (REST) for the efficient sampling of aqueous protein solutions is presented here. The method bypasses the poor scaling with system size of standard replica exchange and thus reduces the number of replicas (parallel processes) that must be used. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST is compared with standard replica exchange for an alanine dipeptide molecule in water. The comparisons confirm that REST greatly reduces the number of CPUs required by regular replica exchange and increases the sampling efficiency. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water. Author contributions: B.J.B. designed research; P.L. and B.K. performed research; P.L. and B.K. analyzed data; and P.L., B.K., R.A.F., and B.J.B. wrote the paper.Abbreviations: REST, replica exchange with solute tempering; REM, replica exchange method; MD, molecular dynamics.*P.L. and B.K. contributed equally to this work.

A generalized trial solution method for solving the aerosol equation

International Nuclear Information System (INIS)

Simons, S.; Simpson, D.R.

1988-01-01

It is shown how the introduction of orthogonal functions together with a time-dependent scaling factor may be used to develop a generalized trial solution method for tackling the aerosol equation. The approach is worked out in detail for the case where the initial particle size spectrum follows a γ-distribution, and it is shown to be a viable technique as long as the initial volume fraction of particulate material is not too large. The method is applied to several situations of interest, and is shown to give more accurate results (with marginally shorter computing times) than are given by the three-parameter log-normal or γ distribution trial functions. (author)

Solution combustion method for synthesis of nanostructured hydroxyapatite, fluorapatite and chlorapatite

Energy Technology Data Exchange (ETDEWEB)

Zhao, Junjie; Dong, Xiaochen; Bian, Mengmeng [School of Chemistry and Materials Engineering, Changshu Institute of Technology, Changshu (China); Zhao, Junfeng, E-mail: daidai02304@163.com [School of Chemistry and Materials Engineering, Changshu Institute of Technology, Changshu (China); Jiangsu Laboratory of Advanced Functional Materials, Changshu Institute of Technology, Changshu (China); Zhang, Yao; Sun, Yue [School of Chemistry and Materials Engineering, Changshu Institute of Technology, Changshu (China); Chen, JianHua; Wang, XuHong [School of Chemistry and Materials Engineering, Changshu Institute of Technology, Changshu (China); Jiangsu Laboratory of Advanced Functional Materials, Changshu Institute of Technology, Changshu (China)

2014-09-30

Highlights: • We report a synthesis of HA, Fap and Clap vio a modified solution combustion method. The nucleation of β-TCP was inhibited in the abundant-calcium system (Ca/P = 2.3>>1.67) in this study. F{sup −} brushed into the structure of HA and replace the position of OH{sup −} is easier than that of Cl{sup −}. - Abstract: Hydroxyapatite (HAP), fluorapatite (Fap) and chlorapatite (Clap) were prepared by solution combustion method with further annealing at 800 °C. The characterization and structural features of the synthesized powders were evaluated by the powder X-ray diffraction (XRD, Fourier transform infrared spectroscopy (FT-IR), scanning electron microscope (SEM) and transmission electron microscopy (TEM) techniques. Characterization results from XRD and Rietveld analysis revealed that OH{sup −} in the HAP lattice were gradually substituted with the increase of F{sup −} and Cl{sup −} content and totally substituted at the molar concentration of 0.28 and 0.6, respectively. The results from FI-IR have also confirmed the incorporation of substituted anions in the apatite structure.

The core spline method for solution of quantum-mechanical systems of differential equations for bound states

International Nuclear Information System (INIS)

Aleksandrov, L.; Drenska, M.; Karadzhov, D.

1986-01-01

A generalization of the core spline method is given in the case of solution of the general bound state problem for a system of M linear differential equations with coefficients depending on the spectral parameter. The recursion scheme for construction of basic splines is described. The wave functions are expressed as linear combinations of basic splines, which are approximate partial solutions of the system. The spectral parameter (the eigenvalue) is determined from the condition for existence of a nontrivial solution of a (MxM) linear algebraic system at the last collocation point. The nontrivial solutions of this system determine (M - 1) coefficients of the linear spans, expressing the wave functions. The last unknown coefficient is determined from a boundary (or normalization) condition for the system. The computational aspects of the method are discussed, in particular, its concrete algorithmic realization used in the RODSOL program. The numerical solution of the Dirac system for the bound states of a hydrogen atom is given is an example

Analytical approximate solutions for a general class of nonlinear delay differential equations.

Science.gov (United States)

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

A new method to measure effective soil solution concentration predicts copper availability to plants.

Science.gov (United States)

Zhang, H; Zhao, F J; Sun, B; Davison, W; McGrath, S P

2001-06-15

Risk assessments of metal contaminated soils need to address metal bioavailability. To predict the bioavailability of metals to plants, it is necessary to understand both solution and solid phase supply processes in soils. In striving to find surrogate chemical measurements, scientists have focused either on soil solution chemistry, including free ion activities, or operationally defined fractions of metals. Here we introduce the new concept of effective concentration, CE, which includes both the soil solution concentration and an additional term, expressed as a concentration, that represents metal supplied from the solid phase. CE was measured using the technique of diffusive gradients in thin films (DGT) which, like a plant, locally lowers soil solution concentrations, inducing metal supply from the solid phase, as shown by a dynamic model of the DGT-soil system. Measurements of Cu as CE, soil solution concentration, by EDTA extraction and as free Cu2+ activity in soil solution were made on 29 different soils covering a large range of copper concentrations. Theywere compared to Cu concentrations in the plant material of Lepidium heterophyllum grown on the same soils. Plant concentrations were linearly related and highly correlated with CE but were more scattered and nonlinear with respect to free Cu2+ activity, EDTA extraction, or soil solution concentrations. These results demonstrate that the dominant supply processes in these soils are diffusion and labile metal release, which the DGT-soil system mimics. The quantity CE is shown to have promise as a quantitative measure of the bioavailable metal in soils.

Formation of H2O2 at UV-photolysis of water solutions of phenol

International Nuclear Information System (INIS)

Guliyeva, U.A.; Gurbanov, M.A.; Mahmudov, H.M.

2013-01-01

Non-traditional methods, based on application of ionizing and UV-radiation widely used for cleaning of water solutions from toxic substances, including phenols. These methods have simultaneously effect including of disinfection and chemical cleaning of water solutions from various industrial processes

Investigation into state of phosphomolybdovanadic heteropolyacids in aqueous solutions by the NMR method

International Nuclear Information System (INIS)

Maksimovskaya, R.I.; Fedotov, M.A.; Mastikhin, V.M.; Kuznetsova, L.I.; Matveev, K.I.

1978-01-01

The methods of 31 P, 51 V, and 17 O NMR have been used for studying the solutions of phospho-molybdenum-vanadium heteropolyacids (HPA) with x=0,1,2,3 (HPA-x) and their mixture with changing concentration, acidity, temperature, and upon partial reduction for separating the lines corresponding to HPA with a certain x. It has been found that in aqueous solutions HPA is present as a mixture of HPA of different compositions; the relationship has been observed between chemical shifts of the lines and the solution acidity which is of a different character for HPA with different x. This allows to make a conclusion about the mechanism of HPA protonation

Extending the charge-flipping method towards structure solution from incomplete data sets

Czech Academy of Sciences Publication Activity Database

Palatinus, Lukáš; Steurer, W.; Chapuis, G.

2007-01-01

Roč. 40, - (2007), s. 456-462 ISSN 0021-8898 Institutional research plan: CEZ:AV0Z10100521 Keywords : ab initio structure solution * density modification * maximum entropy method * intensity extrapolation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.629, year: 2007

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

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

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

Application of finite element method in the solution of transport equation

International Nuclear Information System (INIS)

Maiorino, J.R.; Vieira, W.J.

1985-01-01

It is presented the application of finite element method in the solution of second order transport equation (self-adjoint) for the even parity flux. The angular component is treated by expansion in Legendre polinomials uncoupled of the spatial component, which is approached by an expansion in base functions, interpolated in each spatial element. (M.C.K.) [pt

A two-dimensional method of manufactured solutions benchmark suite based on variations of Larsen's benchmark with escalating order of smoothness of the exact solution

International Nuclear Information System (INIS)

Schunert, Sebastian; Azmy, Yousry Y.

2011-01-01

The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally ne mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite rst eliminates the aforementioned limitation of ne mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme. (author)

A Green's function method for simulation of time-dependent solute transport and reaction in realistic microvascular geometries.

Science.gov (United States)

Secomb, Timothy W

2016-12-01

A novel theoretical method is presented for simulating the spatially resolved convective and diffusive transport of reacting solutes between microvascular networks and the surrounding tissues. The method allows for efficient computational solution of problems involving convection and non-linear binding of solutes in blood flowing through microvascular networks with realistic 3D geometries, coupled with transvascular exchange and diffusion and reaction in the surrounding tissue space. The method is based on a Green's function approach, in which the solute concentration distribution in the tissue is expressed as a sum of fields generated by time-varying distributions of discrete sources and sinks. As an example of the application of the method, the washout of an inert diffusible tracer substance from a tissue region perfused by a network of microvessels is simulated, showing its dependence on the solute's transvascular permeability and tissue diffusivity. Exponential decay of the washout concentration is predicted, with rate constants that are about 10-30% lower than the rate constants for a tissue cylinder model with the same vessel length, vessel surface area and blood flow rate per tissue volume. © The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

International Nuclear Information System (INIS)

Sabry, R.; Zahran, M.A.; Fan Engui

2004-01-01

A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found

A perturbation method for dark solitons based on a complete set of the squared Jost solutions

International Nuclear Information System (INIS)

Ao Shengmei; Yan Jiaren

2005-01-01

A perturbation method for dark solitons is developed, which is based on the construction and the rigorous proof of the complete set of squared Jost solutions. The general procedure solving the adiabatic solution of perturbed nonlinear Schroedinger + equation, the time-evolution equation of dark soliton parameters and a formula for calculating the first-order correction are given. The method can also overcome the difficulties resulting from the non-vanishing boundary condition

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

International Nuclear Information System (INIS)

Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

2017-01-01

In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)

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

Science.gov (United States)

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

2017-09-01

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

Development of rupture process analysis method for great earthquakes using Direct Solution Method

Science.gov (United States)

Yoshimoto, M.; Yamanaka, Y.; Takeuchi, N.

2010-12-01

Conventional rupture process analysis methods using teleseismic body waves were based on ray theory. Therefore, these methods have the following problems in applying to great earthquakes such as 2004 Sumatra earthquake: (1) difficulty in computing all later phases such as the PP reflection phase, (2) impossibility of computing called “W phase”, the long period phase arriving before S wave, (3) implausibility of hypothesis that the distance is far enough from the observation points to the hypocenter compared to the fault length. To solve above mentioned problems, we have developed a new method which uses the synthetic seismograms computed by the Direct Solution Method (DSM, e.g. Kawai et al. 2006) as Green’s functions. We used the DSM software (http://www.eri.u-tokyo.ac.jp/takeuchi/software/) for computing the Green’s functions up to 1 Hz for the IASP91 (Kennett and Engdahl, 1991) model, and determined the final slip distributions using the waveform inversion method (Kikuchi et al. 2003). First we confirmed whether the Green’s functions computed by DSM were accurate in higher frequencies up to 1 Hz. Next we performed the rupture process analysis of this new method for Mw8.0 (GCMT) large Solomon Islands earthquake on April 1, 2007. We found that this earthquake consisted of two asperities and the rupture propagated across the subducting Sinbo ridge. The obtained slip distribution better correlates to the aftershock distributions than existing method. Furthermore, this new method keep same accuracy of existing method (which has the advantage of calculating) with respect to direct P-wave and reflection phases near the source, and also accurately calculate the later phases such a PP-wave.

A new force field including charge directionality for TMAO in aqueous solution

Energy Technology Data Exchange (ETDEWEB)

Usui, Kota; Nagata, Yuki, E-mail: sulpizi@uni-mainz.de, E-mail: nagata@mpip-mainz.mpg.de; Hunger, Johannes; Bonn, Mischa [Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany); Sulpizi, Marialore, E-mail: sulpizi@uni-mainz.de, E-mail: nagata@mpip-mainz.mpg.de [Johannes Gutenberg University Mainz, Staudingerweg 7, 55099 Mainz (Germany)

2016-08-14

We propose a new force field for trimethylamine N-oxide (TMAO), which is designed to reproduce the long-lived and highly directional hydrogen bond between the TMAO oxygen (O{sub TMAO}) atom and surrounding water molecules. Based on the data obtained by ab initio molecular dynamics simulations, we introduce three dummy sites around O{sub TMAO} to mimic the O{sub TMAO} lone pairs and we migrate the negative charge on the O{sub TMAO} to the dummy sites. The force field model developed here improves both structural and dynamical properties of aqueous TMAO solutions. Moreover, it reproduces the experimentally observed dependence of viscosity upon increasing TMAO concentration quantitatively. The simple procedure of the force field construction makes it easy to implement in molecular dynamics simulation packages and makes it compatible with the existing biomolecular force fields. This paves the path for further investigation of protein-TMAO interaction in aqueous solutions.

A new force field including charge directionality for TMAO in aqueous solution

International Nuclear Information System (INIS)

Usui, Kota; Nagata, Yuki; Hunger, Johannes; Bonn, Mischa; Sulpizi, Marialore

2016-01-01

We propose a new force field for trimethylamine N-oxide (TMAO), which is designed to reproduce the long-lived and highly directional hydrogen bond between the TMAO oxygen (O TMAO ) atom and surrounding water molecules. Based on the data obtained by ab initio molecular dynamics simulations, we introduce three dummy sites around O TMAO to mimic the O TMAO lone pairs and we migrate the negative charge on the O TMAO to the dummy sites. The force field model developed here improves both structural and dynamical properties of aqueous TMAO solutions. Moreover, it reproduces the experimentally observed dependence of viscosity upon increasing TMAO concentration quantitatively. The simple procedure of the force field construction makes it easy to implement in molecular dynamics simulation packages and makes it compatible with the existing biomolecular force fields. This paves the path for further investigation of protein-TMAO interaction in aqueous solutions.

Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

Science.gov (United States)

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

The Linear Quadratic Gaussian Multistage Game with Nonclassical Information Pattern Using a Direct Solution Method

Science.gov (United States)

Clemens, Joshua William

Game theory has application across multiple fields, spanning from economic strategy to optimal control of an aircraft and missile on an intercept trajectory. The idea of game theory is fascinating in that we can actually mathematically model real-world scenarios and determine optimal decision making. It may not always be easy to mathematically model certain real-world scenarios, nonetheless, game theory gives us an appreciation for the complexity involved in decision making. This complexity is especially apparent when the players involved have access to different information upon which to base their decision making (a nonclassical information pattern). Here we will focus on the class of adversarial two-player games (sometimes referred to as pursuit-evasion games) with nonclassical information pattern. We present a two-sided (simultaneous) optimization solution method for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of each player's decision making (strategy) as compared to previously used formal solution methods. In addition to the optimal control strategies, we present a saddle point proof and we derive an expression for the optimal performance index value. We provide some numerical results in order to further interpret the optimal control strategies and to highlight real-world application of this game-theoretic optimal solution.

Determination of total fluoride in HF/HNO3/H2SiF6 etch solutions by new potentiometric titration methods.

Science.gov (United States)

Weinreich, Wenke; Acker, Jörg; Gräber, Iris

2007-03-30

In the photovoltaic industry the etching of silicon in HF/HNO(3) solutions is a decisive process for cleaning wafer surfaces or to produce certain surface morphologies like polishing or texturization. With regard to cost efficiency, a maximal utilisation of etch baths in combination with highest quality and accuracy is strived. To provide an etch bath control realised by a replenishment with concentrated acids the main constituents of these HF/HNO(3) etch solutions including the reaction product H(2)SiF(6) have to be analysed. Two new methods for the determination of the total fluoride content in an acidic etch solution based on the precipitation titration with La(NO(3))(3) are presented within this paper. The first method bases on the proper choice of the reaction conditions, since free fluoride ions have to be liberated from HF and H(2)SiF(6) at the same time to be detected by a fluoride ion-selective electrode (F-ISE). Therefore, the sample is adjusted to a pH of 8 for total cleavage of the SiF(6)(2-) anion and titrated in absence of buffers. In a second method, the titration with La(NO(3))(3) is followed by a change of the pH-value using a HF resistant glass-electrode. Both methods provide consistent values, whereas the analysis is fast and accurate, and thus, applicable for industrial process control.

Methods for the solution of the two-dimensional radiation-transfer equation

International Nuclear Information System (INIS)

Weaver, R.; Mihalas, D.; Olson, G.

1982-01-01

We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed

The solution of a coupled system of nonlinear physical problems using the homotopy analysis method

International Nuclear Information System (INIS)

El-Wakil, S A; Abdou, M A

2010-01-01

In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.

Solution of the multilayer multigroup neutron diffusion equation in cartesian geometry by fictitious borders power method

Energy Technology Data Exchange (ETDEWEB)

Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)

2017-05-15

In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.

Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

CERN Document Server

Meleshko, Sergey V

2005-01-01

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

An overview of solution methods for multi-objective mixed integer linear programming programs

DEFF Research Database (Denmark)

Andersen, Kim Allan; Stidsen, Thomas Riis

Multiple objective mixed integer linear programming (MOMIP) problems are notoriously hard to solve to optimality, i.e. finding the complete set of non-dominated solutions. We will give an overview of existing methods. Among those are interactive methods, the two phases method and enumeration...... methods. In particular we will discuss the existing branch and bound approaches for solving multiple objective integer programming problems. Despite the fact that branch and bound methods has been applied successfully to integer programming problems with one criterion only a few attempts has been made...

A finite element solution method for quadrics parallel computer

International Nuclear Information System (INIS)

Zucchini, A.

1996-08-01

A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of n p finite elements and each cell element is assigned to a different node of an n p -processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem

Solitary wave solutions to the modified form of Camassa-Holm equation by means of the homotopy analysis method

International Nuclear Information System (INIS)

Abbasbandy, S.

2009-01-01

Solitary wave solutions to the modified form of Camassa-Holm (CH) equation are sought. In this work, the homotopy analysis method (HAM), one of the most effective method, is applied to obtain the soliton wave solutions with and without continuity of first derivatives at crest

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

Science.gov (United States)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

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

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

International Nuclear Information System (INIS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes–Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently. -- Highlights: • We derived the radiative transfer equation accounting for rotational Raman scattering. • Different approximate radiative transfer approaches with first order scattering were used. • Rigorous and approximate approaches are shown to derive particular integrals. • An alternative forward-adjoint technique is suggested as well. • An additional spectral binning scheme which speeds up the calculations is presented

Methods of using the quadratic assignment problem solution

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Izabela Kudelska

2012-09-01

Full Text Available Background: Quadratic assignment problem (QAP is one of the most interesting of combinatorial optimization. Was presented by Koopman and Beckamanna in 1957, as a mathematical model of the location of indivisible tasks. This problem belongs to the class NP-hard issues. This forces the application to the solution already approximate methods for tasks with a small size (over 30. Even though it is much harder than other combinatorial optimization problems, it enjoys wide interest because it models the important class of decision problems. Material and methods: The discussion was an artificial intelligence tool that allowed to solve the problem QAP, among others are: genetic algorithms, Tabu Search, Branch and Bound. Results and conclusions: QAP did not arise directly as a model for certain actions, but he found its application in many areas. Examples of applications of the problem is: arrangement of buildings on the campus of the university, layout design of electronic components in systems with large scale integration (VLSI, design a hospital, arrangement of keys on the keyboard.

Linear facility location in three dimensions - Models and solution methods

DEFF Research Database (Denmark)

Brimberg, Jack; Juel, Henrik; Schöbel, Anita

2002-01-01

We consider the problem of locating a line or a line segment in three-dimensional space, such that the sum of distances from the facility represented by the line (segment) to a given set of points is minimized. An example is planning the drilling of a mine shaft, with access to ore deposits through...... horizontal tunnels connecting the deposits and the shaft. Various models of the problem are developed and analyzed, and efficient solution methods are given....

Solution of the linearly anisotropic neutron transport problem in a infinite cylinder combining the decomposition and HTSN methods

International Nuclear Information System (INIS)

Goncalves, Glenio A.; Bodmann, Bardo; Bogado, Sergio; Vilhena, Marco T.

2008-01-01

Analytical solutions for neutron transport in cylindrical geometry is available for isotropic problems, but to the best of our knowledge for anisotropic problems are not available, yet. In this work, an analytical solution for the neutron transport equation in an infinite cylinder assuming anisotropic scattering is reported. Here we specialize the solution, without loss of generality, for the linearly anisotropic problem using the combined decomposition and HTS N methods. The key feature of this method consists in the application of the decomposition method to the anisotropic problem by virtue of the fact that the inverse of the operator associated to isotropic problem is well know and determined by the HTS N approach. So far, following the idea of the decomposition method, we apply this operator to the integral term, assuming that the angular flux appearing in the integrand is considered to be equal to the HTS N solution interpolated by polynomial considering only even powers. This leads to the first approximation for an anisotropic solution. Proceeding further, we replace this solution for the angular flux in the integral and apply again the inverse operator for the isotropic problem in the integral term and obtain a new approximation for the angular flux. This iterative procedure yields a closed form solution for the angular flux. This methodology can be generalized, in a straightforward manner, for transport problems with any degree of anisotropy. For the sake of illustration, we report numerical simulations for linearly anisotropic transport problems. (author)

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

Directory of Open Access Journals (Sweden)

Tarikul Islam

2018-03-01

Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

The Shortlist Method for fast computation of the Earth Mover's Distance and finding optimal solutions to transportation problems.

Science.gov (United States)

Gottschlich, Carsten; Schuhmacher, Dominic

2014-01-01

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.

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

International Nuclear Information System (INIS)

Jo, Jong Chull; Shin, Won Ky

1997-01-01

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

Development of Extended Ray-tracing method including diffraction, polarization and wave decay effects

Science.gov (United States)

Yanagihara, Kota; Kubo, Shin; Dodin, Ilya; Nakamura, Hiroaki; Tsujimura, Toru

2017-10-01

Geometrical Optics Ray-tracing is a reasonable numerical analytic approach for describing the Electron Cyclotron resonance Wave (ECW) in slowly varying spatially inhomogeneous plasma. It is well known that the result with this conventional method is adequate in most cases. However, in the case of Helical fusion plasma which has complicated magnetic structure, strong magnetic shear with a large scale length of density can cause a mode coupling of waves outside the last closed flux surface, and complicated absorption structure requires a strong focused wave for ECH. Since conventional Ray Equations to describe ECW do not have any terms to describe the diffraction, polarization and wave decay effects, we can not describe accurately a mode coupling of waves, strong focus waves, behavior of waves in inhomogeneous absorption region and so on. For fundamental solution of these problems, we consider the extension of the Ray-tracing method. Specific process is planned as follows. First, calculate the reference ray by conventional method, and define the local ray-base coordinate system along the reference ray. Then, calculate the evolution of the distributions of amplitude and phase on ray-base coordinate step by step. The progress of our extended method will be presented.

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...... parameters of the model and suggest the use of projection methods when a high degree of accuracy is required....

CO2 capture in amine solutions: modelling and simulations with non-empirical methods

Science.gov (United States)

Andreoni, Wanda; Pietrucci, Fabio

2016-12-01

Absorption in aqueous amine solutions is the most advanced technology for the capture of CO2, although suffering from drawbacks that do not allow exploitation on large scale. The search for optimum solvents has been pursued with empirical methods and has also motivated a number of computational approaches over the last decade. However, a deeper level of understanding of the relevant chemical reactions in solution is required so as to contribute to this effort. We present here a brief critical overview of the most recent applications of computer simulations using ab initio methods. Comparison of their outcome shows a strong dependence on the structural models employed to represent the molecular systems in solution and on the strategy used to simulate the reactions. In particular, the results of very recent ab initio molecular dynamics augmented with metadynamics are summarized, showing the crucial role of water, which has been so far strongly underestimated both in the calculations and in the interpretation of experimental data. Indications are given for advances in computational approaches that are necessary if meant to contribute to the rational design of new solvents.

CO2 capture in amine solutions: modelling and simulations with non-empirical methods

International Nuclear Information System (INIS)

Andreoni, Wanda; Pietrucci, Fabio

2016-01-01

Absorption in aqueous amine solutions is the most advanced technology for the capture of CO 2 , although suffering from drawbacks that do not allow exploitation on large scale. The search for optimum solvents has been pursued with empirical methods and has also motivated a number of computational approaches over the last decade. However, a deeper level of understanding of the relevant chemical reactions in solution is required so as to contribute to this effort. We present here a brief critical overview of the most recent applications of computer simulations using ab initio methods. Comparison of their outcome shows a strong dependence on the structural models employed to represent the molecular systems in solution and on the strategy used to simulate the reactions. In particular, the results of very recent ab initio molecular dynamics augmented with metadynamics are summarized, showing the crucial role of water, which has been so far strongly underestimated both in the calculations and in the interpretation of experimental data. Indications are given for advances in computational approaches that are necessary if meant to contribute to the rational design of new solvents. (topical review)

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

International Nuclear Information System (INIS)

Bekir Ahmet; Güner Özkan

2013-01-01

In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

Triangular dislocation: an analytical, artefact-free solution

Science.gov (United States)

Nikkhoo, Mehdi; Walter, Thomas R.

2015-05-01

Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space {R}3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

Force measuring valve assemblies, systems including such valve assemblies and related methods

Science.gov (United States)

DeWall, Kevin George [Pocatello, ID; Garcia, Humberto Enrique [Idaho Falls, ID; McKellar, Michael George [Idaho Falls, ID

2012-04-17

Methods of evaluating a fluid condition may include stroking a valve member and measuring a force acting on the valve member during the stroke. Methods of evaluating a fluid condition may include measuring a force acting on a valve member in the presence of fluid flow over a period of time and evaluating at least one of the frequency of changes in the measured force over the period of time and the magnitude of the changes in the measured force over the period of time to identify the presence of an anomaly in a fluid flow and, optionally, its estimated location. Methods of evaluating a valve condition may include directing a fluid flow through a valve while stroking a valve member, measuring a force acting on the valve member during the stroke, and comparing the measured force to a reference force. Valve assemblies and related systems are also disclosed.

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

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

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

Slideline verification for multilayer pressure vessel and piping analysis including tangential motion

International Nuclear Information System (INIS)

Van Gulick, L.A.

1984-01-01

Nonlinear finite element method (FEM) computer codes with slideline algorithm implementations should be useful for the analysis of prestressed multilayer pressure vessels and piping. This paper presents closed form solutions including the effects of tangential motion useful for verifying slideline implementations for this purpose. The solutions describe stresses and displacements of a long internally pressurized elastic-plastic cylinder initially separated from an elastic outer cylinder by a uniform gap. Comparison of closed form and FEM results evaluates the usefulness of the closed form solution and the validity of the sideline implementation used

Calculating solution redox free energies with ab initio quantum mechanical/molecular mechanical minimum free energy path method

International Nuclear Information System (INIS)

Zeng Xiancheng; Hu Hao; Hu Xiangqian; Yang Weitao

2009-01-01

A quantum mechanical/molecular mechanical minimum free energy path (QM/MM-MFEP) method was developed to calculate the redox free energies of large systems in solution with greatly enhanced efficiency for conformation sampling. The QM/MM-MFEP method describes the thermodynamics of a system on the potential of mean force surface of the solute degrees of freedom. The molecular dynamics (MD) sampling is only carried out with the QM subsystem fixed. It thus avoids 'on-the-fly' QM calculations and thus overcomes the high computational cost in the direct QM/MM MD sampling. In the applications to two metal complexes in aqueous solution, the new QM/MM-MFEP method yielded redox free energies in good agreement with those calculated from the direct QM/MM MD method. Two larger biologically important redox molecules, lumichrome and riboflavin, were further investigated to demonstrate the efficiency of the method. The enhanced efficiency and uncompromised accuracy are especially significant for biochemical systems. The QM/MM-MFEP method thus provides an efficient approach to free energy simulation of complex electron transfer reactions.

Solution and study of nodal neutron transport equation applying the LTS{sub N}-DiagExp method

Energy Technology Data Exchange (ETDEWEB)

Hauser, Eliete Biasotto; Pazos, Ruben Panta [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil). Faculdade de Matematica]. E-mail: eliete@pucrs.br; rpp@mat.pucrs.br; Vilhena, Marco Tullio de [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil). Instituto de Matematica]. E-mail: vilhena@mat.ufrgs.br; Barros, Ricardo Carvalho de [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico]. E-mail: ricardo@iprj.uerj.br

2003-07-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S{sub N} equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS{sub N} method, first applying the Laplace transform to the set of the nodal S{sub N} equations and then obtained the solution by symbolic computation. We include the LTS{sub N} method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS{sub N} approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

Directory of Open Access Journals (Sweden)

Wenzhen Chen

2013-01-01

Full Text Available The singularly perturbed method (SPM is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

The GSC method for constructing the entropy solution of hyperbolic conservation laws and applications

International Nuclear Information System (INIS)

Werner, K.D.

1990-01-01

In this paper we introduce briefly the Geometrical Shock Correction (GSC) method and consider various fields of applications, with special emphasis on two-phase flow problems in porous media. Some test problems are taken from this field. GSC is a very efficient numerical method for constructing the entropy solution of the Cauchy problem of scalar hyperboli conservation laws (with source term) in one space dimension and in specific two-dimensional cases. The novelty consists in constructing the solution at an arbitrary fixed time t=T>0 in one time step, based on transporting the initial values along characteristics and, if shocks appear, on a correction of the multivalued relation by a geometrical averaging technique. (orig.) With 7 figs [de

A new sensitive method of dissociation constants determination based on the isohydric solutions principle.

Science.gov (United States)

Michałowski, Tadeusz; Pilarski, Bogusław; Asuero, Agustin G; Dobkowska, Agnieszka

2010-10-15

The paper provides a new formulation and analytical proposals based on the isohydric solutions concept. It is particularly stated that a mixture formed, according to titrimetric mode, from a weak acid (HX, C(0)mol/L) and a strong acid (HB, Cmol/L) solutions, assumes constant pH, independently on the volumes of the solutions mixed, provided that the relation C(0)=C+C(2)·10(pK(1)) is valid, where pK(1)=-log K(1), K(1) the dissociation constant for HX. The generalized formulation, referred to the isohydric solutions thus obtained, was extended also to more complex acid-base systems. Particularly in the (HX, HB) system, the titration occurs at constant ionic strength (I) value, not resulting from presence of a basal electrolyte. This very advantageous conjunction of the properties provides, among others, a new, very sensitive method for verification of pK(1) value. The new method is particularly useful for weak acids HX characterized by low pK(1) values. The method was tested experimentally on four acid-base systems (HX, HB), in aqueous and mixed-solvent media and compared with the literature data. Some useful (linear and hyperbolic) correlations were stated and applied for validation of pK(1) values. Finally, some practical applications of analytical interest of the isohydricity (pH constancy) principle as one formulated in this paper were enumerated, proving the usefulness of such a property which has its remote roots in the Arrhenius concept. Copyright © 2010 Elsevier B.V. All rights reserved.

Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

Directory of Open Access Journals (Sweden)

Norhasimah Mahiddin

2014-01-01

Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

Direct visualization of solute locations in laboratory ice samples

Directory of Open Access Journals (Sweden)

T. Hullar

2016-09-01

Full Text Available Many important chemical reactions occur in polar snow, where solutes may be present in several reservoirs, including at the air–ice interface and in liquid-like regions within the ice matrix. Some recent laboratory studies suggest chemical reaction rates may differ in these two reservoirs. While investigations have examined where solutes are found in natural snow and ice, few studies have examined either solute locations in laboratory samples or the possible factors controlling solute segregation. To address this, we used micro-computed tomography (microCT to examine solute locations in ice samples prepared from either aqueous cesium chloride (CsCl or rose bengal solutions that were frozen using several different methods. Samples frozen in a laboratory freezer had the largest liquid-like inclusions and air bubbles, while samples frozen in a custom freeze chamber had somewhat smaller air bubbles and inclusions; in contrast, samples frozen in liquid nitrogen showed much smaller concentrated inclusions and air bubbles, only slightly larger than the resolution limit of our images (∼ 2 µm. Freezing solutions in plastic vs. glass vials had significant impacts on the sample structure, perhaps because the poor heat conductivity of plastic vials changes how heat is removed from the sample as it cools. Similarly, the choice of solute had a significant impact on sample structure, with rose bengal solutions yielding smaller inclusions and air bubbles compared to CsCl solutions frozen using the same method. Additional experiments using higher-resolution imaging of an ice sample show that CsCl moves in a thermal gradient, supporting the idea that the solutes in ice are present in mobile liquid-like regions. Our work shows that the structure of laboratory ice samples, including the location of solutes, is sensitive to the freezing method, sample container, and solute characteristics, requiring careful experimental design and interpretation of results.

Solution of the Multigroup-Diffusion equation by the response matrix method

International Nuclear Information System (INIS)

Oliveira, C.R.E.

1980-10-01

A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt

Efficient numerical solution to vacuum decay with many fields

Energy Technology Data Exchange (ETDEWEB)

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

2017-01-01

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

A method for recovering and separating palladium, technetium, rhodium and ruthenium contained in solutions resulting from nuclear fuel recycling

International Nuclear Information System (INIS)

Moore, R.H.

1974-01-01

The invention relates to a method for recovering and separating technetium and metals of the platinum group, i.e. palladium, rhodium and ruthenium existing as fission products. The method according to the invention is characterized by contacting a residuary acid aqueous solution provided by nuclear fuel recycling with successive carbon beds which have adsorbed different chelating agents specific for the metals to be recovered in order that said metals be selectively chelated and extracted from the solution. This method is suitable for recovering the above metals from solutions provided by reprocessing spent fuels [fr

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

Yang, Haijian

2016-12-10

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

Yang, Haijian; Sun, Shuyu; Yang, Chao

2016-01-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Study On Analytical Methods Of Tellurium Content In Natriiodide (Na131I) Radiopharmaceutical Solution Produced In The Dalat Nuclear Reactor

International Nuclear Information System (INIS)

Vo Thi Cam Hoa; Duong Van Dong; Nguyen Thi Thu; Chu Van Khoa

2007-01-01

This report describes the practical methods for analyzing of Tellurium content in Na 131 I solution produced at the Dalat Nuclear Research Institute. We studied analytical methods to control Tellurium content in final Na 131 I solution product used in medical purposes by three methods such as: spot test, gamma spectrometric and spectrophotometric methods. These investigation results are shown that the spot test method is suitable for controlling Tellurium trace in the final product. This spot test can be determinate Tellurium trace less than 10 ppm and are used to quality control of Na 131 I solution using in medical application. (author)

Method of moments solution of volume integral equations using higher-order hierarchical Legendre basis functions

DEFF Research Database (Denmark)

Kim, Oleksiy S.; Jørgensen, Erik; Meincke, Peter

2004-01-01

An efficient higher-order method of moments (MoM) solution of volume integral equations is presented. The higher-order MoM solution is based on higher-order hierarchical Legendre basis functions and higher-order geometry modeling. An unstructured mesh composed of 8-node trilinear and/or curved 27...... of magnitude in comparison to existing higher-order hierarchical basis functions. Consequently, an iterative solver can be applied even for high expansion orders. Numerical results demonstrate excellent agreement with the analytical Mie series solution for a dielectric sphere as well as with results obtained...

Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem

Energy Technology Data Exchange (ETDEWEB)

Alchalabi, R.M. [BOC Group, Murray Hill, NJ (United States); Turinsky, P.J. [North Carolina State Univ., Raleigh, NC (United States)

1996-12-31

The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.

Regularized variable metric method versus the conjugate gradient method in solution of radiative boundary design problem

International Nuclear Information System (INIS)

Kowsary, F.; Pooladvand, K.; Pourshaghaghy, A.

2007-01-01

In this paper, an appropriate distribution of the heating elements' strengths in a radiation furnace is estimated using inverse methods so that a pre-specified temperature and heat flux distribution is attained on the design surface. Minimization of the sum of the squares of the error function is performed using the variable metric method (VMM), and the results are compared with those obtained by the conjugate gradient method (CGM) established previously in the literature. It is shown via test cases and a well-founded validation procedure that the VMM, when using a 'regularized' estimator, is more accurate and is able to reach at a higher quality final solution as compared to the CGM. The test cases used in this study were two-dimensional furnaces filled with an absorbing, emitting, and scattering gas

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

Energy Technology Data Exchange (ETDEWEB)

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

1998-12-31

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1997-12-31

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

Standard test method for isotopic analysis of hydrolyzed uranium hexafluoride and uranyl nitrate solutions by thermal ionization mass spectrometry

CERN Document Server

American Society for Testing and Materials. Philadelphia

2005-01-01

1.1 This method applies to the determination of isotopic composition in hydrolyzed nuclear grade uranium hexafluoride. It covers isotopic abundance of 235U between 0.1 and 5.0 % mass fraction, abundance of 234U between 0.0055 and 0.05 % mass fraction, and abundance of 236U between 0.0003 and 0.5 % mass fraction. This test method may be applicable to other isotopic abundance providing that corresponding standards are available. 1.2 This test method can apply to uranyl nitrate solutions. This can be achieved either by transforming the uranyl nitrate solution to a uranyl fluoride solution prior to the deposition on the filaments or directly by depositing the uranyl nitrate solution on the filaments. In the latter case, a calibration with uranyl nitrate standards must be performed. 1.3 This test method can also apply to other nuclear grade matrices (for example, uranium oxides) by providing a chemical transformation to uranyl fluoride or uranyl nitrate solution. 1.4 This standard does not purport to address al...

Application of an analytical method for solution of thermal hydraulic conservation equations

Energy Technology Data Exchange (ETDEWEB)

Fakory, M.R. [Simulation, Systems & Services Technologies Company (S3 Technologies), Columbia, MD (United States)

1995-09-01

An analytical method has been developed and applied for solution of two-phase flow conservation equations. The test results for application of the model for simulation of BWR transients are presented and compared with the results obtained from application of the explicit method for integration of conservation equations. The test results show that with application of the analytical method for integration of conservation equations, the Courant limitation associated with explicit Euler method of integration was eliminated. The results obtained from application of the analytical method (with large time steps) agreed well with the results obtained from application of explicit method of integration (with time steps smaller than the size imposed by Courant limitation). The results demonstrate that application of the analytical approach significantly improves the numerical stability and computational efficiency.

Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods

DEFF Research Database (Denmark)

Capolei, Andrea; Jørgensen, John Bagterp

2012-01-01

of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent...... algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution...... discontinuities on each shooting interval are present. The ESDIRK methods are implemented using an inexact Newton method that reuses the factorization of the iteration matrix for the integration as well as the sensitivity computation. Numerical experiments are provided to demonstrate the algorithm....

Approximated solutions to the Schroedinger equation

International Nuclear Information System (INIS)

Rico, J.F.; Fernandez-Alonso, J.I.

1977-01-01

The authors are currently working on a couple of the well-known deficiencies of the variation method and present here some of the results that have been obtained so far. The variation method does not give information a priori on the trial functions best suited for a particular problem nor does it give information a posteriori on the degree of precision attained. In order to clarify the origin of both difficulties, a geometric interpretation of the variation method is presented. This geometric interpretation is the starting point for the exact formal solution to the fundamental state and for the step-by-step approximations to the exact solution which are also given. Some comments on these results are included. (Auth.)

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.

Composite materials and bodies including silicon carbide and titanium diboride and methods of forming same

Science.gov (United States)

Lillo, Thomas M.; Chu, Henry S.; Harrison, William M.; Bailey, Derek

2013-01-22

Methods of forming composite materials include coating particles of titanium dioxide with a substance including boron (e.g., boron carbide) and a substance including carbon, and reacting the titanium dioxide with the substance including boron and the substance including carbon to form titanium diboride. The methods may be used to form ceramic composite bodies and materials, such as, for example, a ceramic composite body or material including silicon carbide and titanium diboride. Such bodies and materials may be used as armor bodies and armor materials. Such methods may include forming a green body and sintering the green body to a desirable final density. Green bodies formed in accordance with such methods may include particles comprising titanium dioxide and a coating at least partially covering exterior surfaces thereof, the coating comprising a substance including boron (e.g., boron carbide) and a substance including carbon.

On solution to the problem of criticality by alternative Monte Carlo method

International Nuclear Information System (INIS)

Kyncl, J.

2005-03-01

The problem of criticality for the neutron transport equation is analyzed. The problem is transformed into an equivalent problem in a suitable set of complex functions, and the existence and uniqueness of its solution is demonstrated. The source iteration method is discussed. It is shown that the final result of the iterative process is strongly affected by the insufficient accuracy of the individual iterations. A modified method is suggested to circumvent this problem based on the theory of positive operators; the criticality problem is solved by the Monte Carlo method constructing special random process and variable so that the difference between the result and the true value can be arbitrarily small. The efficiency of this alternative method is analysed

Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media

International Nuclear Information System (INIS)

Coelho, Pedro J.

2014-01-01