Methods of producing adsorption media including a metal oxide
Mann, Nicholas R; Tranter, Troy J
2014-03-04
Methods of producing a metal oxide are disclosed. The method comprises dissolving a metal salt in a reaction solvent to form a metal salt/reaction solvent solution. The metal salt is converted to a metal oxide and a caustic solution is added to the metal oxide/reaction solvent solution to adjust the pH of the metal oxide/reaction solvent solution to less than approximately 7.0. The metal oxide is precipitated and recovered. A method of producing adsorption media including the metal oxide is also disclosed, as is a precursor of an active component including particles of a metal oxide.
Exact solutions to some nonlinear PDEs, travelling profiles method
Directory of Open Access Journals (Sweden)
Noureddine Benhamidouche
2008-04-01
\\end{equation*} by a new method that we call the travelling profiles method. This method allows us to find several forms of exact solutions including the classical forms such as travelling-wave and self-similar solutions.
Newton-like methods for Navier-Stokes solution
Qin, N.; Xu, X.; Richards, B. E.
1992-12-01
The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.
Klaehn, John R.; Dufek, Eric J.; Rollins, Harry W.; Harrup, Mason K.; Gering, Kevin L.
2017-09-12
An electrolyte solution comprising at least one phosphoranimine compound and a metal salt. The at least one phosphoranimine compound comprises a compound of the chemical structure ##STR00001## where X is an organosilyl group or a tert-butyl group and each of R.sup.1, R.sup.2, and R.sup.3 is independently selected from the group consisting of an alkyl group, an aryl group, an alkoxy group, or an aryloxy group. An energy storage device including the electrolyte solution is also disclosed.
Rapid spectrographic method for determining microcomponents in solutions
International Nuclear Information System (INIS)
Karpenko, L.I.; Fadeeva, L.A.; Gordeeva, A.N.; Ermakova, N.V.
1984-01-01
Rapid spectrographic method foe determining microcomponents (Cd, V, Mo, Ni, rare earths and other elements) in industrial and natural solutions has been developed. The analyses were conducted in argon medium and in the air. Calibration charts for determining individual rare earths in solutions are presented. The accuracy of analysis (Sr) was detection limit was 10 -3 -10 -4 mg/ml, that for rare earths - 1.10 -2 mg/ml. The developed method enables to rapidly analyze solutions (sewages and industrialllwaters, wine products) for 20 elements including 6 rare earths, using strandard equipment
Directory of Open Access Journals (Sweden)
Şükran Çopur
2013-09-01
Full Text Available Objective: As the external auditory canal is a moisturearea, it facilitates the growth of bacteria and fungi. Infectionsand inflammation due to Staphylococcus aureus,Pseudomonas aeruginosa, Aspergillus spp. and Candidaalbicans can develop in this area. Classical Castellanisolution including boric acid, fenol, fucsin, resorcinol, acetone,and alcohol is used for external ear tract infectionsdue to fungi and bacteria, and also for the superficial dermatophytoses,and eczematous dermatitis of the externalear tract infections.The purpose of this study is to investigate of the in vitroeffectiveness of classical Castellani solution and its differentformulations with different dilutions against the standardyeast and bacteria strains.Methods: C. albicans ATCC 10231, C. krusei ATCC6258, C. dubliniensis CD 36, C. guilliermondii ATCC6260, C. parapsilosis ATCC22019, E. coli ATCC 25922,P. aeruginosa ATCC 27853, MRSA ATCC 43300, Staphylococcusaureus ATCC 25923, and S. epidermidis ATCC12228 strains were included in the study. Broth microdilutionmethod was used for each microorganism and Castellaniformulation. The tests are repeated at least twice.Results: The inhibitory concentration of classical Castellanisolution against bacteria and fungi is 1/64-1/256,1/32-1/64 for fuchsin free solution, 1/32-1/128 for boricacid-free solution and, 1/64-1/128 for resorcinol-free solution.Conclusions: As a conclusion we think that the classicalCastellani solution and its different formulations at variousdilutions may be effective antimicrobial agents for differentpatient populations. J Clin Exp Invest 2013; 4 (3:302-305Key words: Castellani solution, antimicrobial activity, in vitro
An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations
International Nuclear Information System (INIS)
Wang Zhen; Zhang Hongqing
2006-01-01
In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).
Method of precipitating uranium from an aqueous solution and/or sediment
Tokunaga, Tetsu K; Kim, Yongman; Wan, Jiamin
2013-08-20
A method for precipitating uranium from an aqueous solution and/or sediment comprising uranium and/or vanadium is presented. The method includes precipitating uranium as a uranyl vanadate through mixing an aqueous solution and/or sediment comprising uranium and/or vanadium and a solution comprising a monovalent or divalent cation to form the corresponding cation uranyl vanadate precipitate. The method also provides a pathway for extraction of uranium and vanadium from an aqueous solution and/or sediment.
Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation
International Nuclear Information System (INIS)
Wang Dengshan; Zhang Hongqing
2005-01-01
In this paper, with the aid of the symbolic computation we improve the extended F-expansion method in [Chaos, Solitons and Fractals 2004; 22:111] and propose the further improved F-expansion method. Using this method, we have gotten many new exact solutions which we have never seen before within our knowledge of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. In addition,the solutions we get are more general than the solutions that the extended F-expansion method gets.The solutions we get include Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions and so on. Our method can also apply to other partial differential equations and can also get many new exact solutions
Solutions manual to accompany An introduction to numerical methods and analysis
Epperson, James F
2014-01-01
A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp
Milestones in the Development of Iterative Solution Methods
Directory of Open Access Journals (Sweden)
Owe Axelsson
2010-01-01
Full Text Available Iterative solution methods to solve linear systems of equations were originally formulated as basic iteration methods of defect-correction type, commonly referred to as Richardson's iteration method. These methods developed further into various versions of splitting methods, including the successive overrelaxation (SOR method. Later, immensely important developments included convergence acceleration methods, such as the Chebyshev and conjugate gradient iteration methods and preconditioning methods of various forms. A major strive has been to find methods with a total computational complexity of optimal order, that is, proportional to the degrees of freedom involved in the equation. Methods that have turned out to have been particularly important for the further developments of linear equation solvers are surveyed. Some of them are presented in greater detail.
The characterization methods for colloids in aqueous solutions
International Nuclear Information System (INIS)
Vuorinen, U.; Kumpulainen, H.
1993-11-01
This literature review deals with characterization methods for colloids in aqueous solutions and in groundwater. The basis for the review has been the needs of nuclear waste disposal studies and methods applicable in such studies. The methods considered include non-destructive laserspectroscopic methods (e.g. TRLFS, LPAS, PALS), several separation methods (e.g. ultrafiltration, dialysis, electrophoresis, field-flow-fractionation) and also some surface analytical methods, as well as some other methods giving additional information on formation and migration properties of colloids. (au.) (71 refs., 13 figs., 3 tabs.)
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
International Nuclear Information System (INIS)
Paixao, S.B.; Marzo, M.A.S.; Alvim, A.C.M.
1986-01-01
The calculation method used in WIGLE code is studied. Because of the non availability of such a praiseworthy solution, expounding the method minutely has been tried. This developed method has been applied for the solution of the one-dimensional, two-group, diffusion equations in slab, axial analysis, including non-boiling heat transfer, accountig for feedback. A steady-state program (CITER-1D), written in FORTRAN 4, has been implemented, providing excellent results, ratifying the developed work quality. (Author) [pt
Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method
International Nuclear Information System (INIS)
Fan Engui
2002-01-01
A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)
Generalized Truncated Methods for an Efficient Solution of Retrial Systems
Directory of Open Access Journals (Sweden)
Ma Jose Domenech-Benlloch
2008-01-01
Full Text Available We are concerned with the analytic solution of multiserver retrial queues including the impatience phenomenon. As there are not closed-form solutions to these systems, approximate methods are required. We propose two different generalized truncated methods to effectively solve this type of systems. The methods proposed are based on the homogenization of the state space beyond a given number of users in the retrial orbit. We compare the proposed methods with the most well-known methods appeared in the literature in a wide range of scenarios. We conclude that the proposed methods generally outperform previous proposals in terms of accuracy for the most common performance parameters used in retrial systems with a moderated growth in the computational cost.
2011-12-29
..., Inc., Automation and Control Solutions Division, Including On-Site Leased Workers From Manpower...., Automation and Control Solutions Division. The Department has determined that these workers were sufficiently...., Automation and Control Solutions Division, including on-site leased workers from Manpower, Spherion...
Comparison of DSMC and CFD Solutions of Fire II Including Radiative Heating
Liechty, Derek S.; Johnston, Christopher O.; Lewis, Mark J.
2011-01-01
The ability to compute rarefied, ionized hypersonic flows is becoming more important as missions such as Earth reentry, landing high mass payloads on Mars, and the exploration of the outer planets and their satellites are being considered. These flows may also contain significant radiative heating. To prepare for these missions, NASA is developing the capability to simulate rarefied, ionized flows and to then calculate the resulting radiative heating to the vehicle's surface. In this study, the DSMC codes DAC and DS2V are used to obtain charge-neutral ionization solutions. NASA s direct simulation Monte Carlo code DAC is currently being updated to include the ability to simulate charge-neutral ionized flows, take advantage of the recently introduced Quantum-Kinetic chemistry model, and to include electronic energy levels as an additional internal energy mode. The Fire II flight test is used in this study to assess these new capabilities. The 1634 second data point was chosen for comparisons to be made in order to include comparisons to computational fluid dynamics solutions. The Knudsen number at this point in time is such that the DSMC simulations are still tractable and the CFD computations are at the edge of what is considered valid. It is shown that there can be quite a bit of variability in the vibrational temperature inferred from DSMC solutions and that, from how radiative heating is computed, the electronic temperature is much better suited for radiative calculations. To include the radiative portion of heating, the flow-field solutions are post-processed by the non-equilibrium radiation code HARA. Acceptable agreement between CFD and DSMC flow field solutions is demonstrated and the progress of the updates to DAC, along with an appropriate radiative heating solution, are discussed. In addition, future plans to generate more high fidelity radiative heat transfer solutions are discussed.
Gering, Kevin L.; Harrup, Mason K.; Rollins, Harry W.
2015-12-08
An ionic liquid including a phosphazene compound that has a plurality of phosphorus-nitrogen units and at least one pendant group bonded to each phosphorus atom of the plurality of phosphorus-nitrogen units. One pendant group of the at least one pendant group comprises a positively charged pendant group. Additional embodiments of ionic liquids are disclosed, as are electrolyte solutions and energy storage devices including the embodiments of the ionic liquid.
International Nuclear Information System (INIS)
Chen Yong; Wang Qi; Li Biao
2005-01-01
Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally
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
Directory of Open Access Journals (Sweden)
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.
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
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
Directory of Open Access Journals (Sweden)
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.
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)
Directory of Open Access Journals (Sweden)
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
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.)
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.
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.
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.
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.
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
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.
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
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...
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.
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.
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
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). Its 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.
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.
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.
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
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
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
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
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.
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.
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
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 ...
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
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
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...
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
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
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
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
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.
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...
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
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...
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.
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
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
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
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.
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)
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
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.
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
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...
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
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
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
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
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.
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.
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
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)
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.
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
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.
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...
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
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
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)
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
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...
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
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
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
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.
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
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.
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.
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)
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)
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
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.
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
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
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
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
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
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)
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)
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.
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.
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)
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.
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.
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
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)
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.
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)
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
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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
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.
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
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.
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
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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.
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.
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
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)
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)
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…
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)
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.
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
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.
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...
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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.
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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
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
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
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.
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
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 ...
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
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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.
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)
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
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
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.
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...
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)
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.
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.
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.
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.
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.
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
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
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
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.
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)
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
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
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...
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.
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
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
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
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
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
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.
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.
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
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
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
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
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.
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)
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
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.
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.
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.
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
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
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
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
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.
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(ϵlogr. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.
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.
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)
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.
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
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
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.
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.
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
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.
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
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)
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.
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.
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.
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
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
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
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)
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.
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
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)
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
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.
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
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.
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.
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.
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
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
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.
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
Directory of Open Access Journals (Sweden)
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....
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)
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.
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.
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
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
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
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
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.
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
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
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)
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.
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
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.
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.
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
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.
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.
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)
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.
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
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)
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)
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.
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
International Nuclear Information System (INIS)
Coelho, Pedro J.
2014-01-01
Many methods are available for the solution of radiative heat transfer problems in participating media. Among these, the discrete ordinates method (DOM) and the finite volume method (FVM) are among the most widely used ones. They provide a good compromise between accuracy and computational requirements, and they are relatively easy to integrate in CFD codes. This paper surveys recent advances on these numerical methods. Developments concerning the grid structure (e.g., new formulations for axisymmetrical geometries, body-fitted structured and unstructured meshes, embedded boundaries, multi-block grids, local grid refinement), the spatial discretization scheme, and the angular discretization scheme are described. Progress related to the solution accuracy, solution algorithm, alternative formulations, such as the modified DOM and FVM, even-parity formulation, discrete-ordinates interpolation method and method of lines, and parallelization strategies is addressed. The application to non-gray media, variable refractive index media, and transient problems is also reviewed. - Highlights: • We survey recent advances in the discrete ordinates and finite volume methods. • Developments in spatial and angular discretization schemes are described. • Progress in solution algorithms and parallelization methods is reviewed. • Advances in the transient solution of the radiative transfer equation are appraised. • Non-gray media and variable refractive index media are briefly addressed
International Nuclear Information System (INIS)
Carreira, M.
1965-01-01
In order to reduce limitations of solubility, the cryoscopic method developed for benzene solutions of polyphenyl mixtures has been extended to diphenyl-ether solutions by introducing some modifications imposed by the physico-chemical properties of this solvent. The Nernsto theory of Beckman's method has been revised, taking into account the heat-transfer characteristics of the system, and the results of that analysis have been used to fix upon the design parameters of a cryoscopic apparatus for measurements on diphenyl-ether solutions. (Author) 9 refs
Directory of Open Access Journals (Sweden)
Dauda GuliburYAKUBU
2012-12-01
Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.
The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer
International Nuclear Information System (INIS)
Modest, M.F.
1991-01-01
In this paper the weighted-sum-of-gray-gases approach for radiative transfer in non-gray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (non-scattering media within a black-walled enclosure) any non-gray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-1 approximation of the equivalent gray media solution. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95%) which are achieved
Initiation devices, initiation systems including initiation devices and related methods
Energy Technology Data Exchange (ETDEWEB)
Daniels, Michael A.; Condit, Reston A.; Rasmussen, Nikki; Wallace, Ronald S.
2018-04-10
Initiation devices may include at least one substrate, an initiation element positioned on a first side of the at least one substrate, and a spark gap electrically coupled to the initiation element and positioned on a second side of the at least one substrate. Initiation devices may include a plurality of substrates where at least one substrate of the plurality of substrates is electrically connected to at least one adjacent substrate of the plurality of substrates with at least one via extending through the at least one substrate. Initiation systems may include such initiation devices. Methods of igniting energetic materials include passing a current through a spark gap formed on at least one substrate of the initiation device, passing the current through at least one via formed through the at least one substrate, and passing the current through an explosive bridge wire of the initiation device.
Solution chemistry techniques in SYNROC preparation
International Nuclear Information System (INIS)
Dosch, R.G.; Lynch, A.W.
1981-07-01
Investigations of titanate-based ceramic forms for radioactive waste immobilization are underway at Sandia National Laboratories (SNLA) and at Lawrence Livermore National Laboratory (LLNL). Although the waste forms differ as to overall product composition, the waste-containing phases in both ceramic products have similar crystalline structure types. These include metallic phases along with oxides with structure types of the mineral analogues perovskite, zirconolite, and hollandite. Significant differences also exist in the area of processing. More conventional ceramic processing methods are used at LLNL to produce SYNROC while solution chemistry techniques involving metal alkoxide chemistry and ion exchange have been developed at SNLA to prepare calcium titanate-based waste ceramics. The SNLA techniques were recently modified and applied to producing SYNROC (compositions C and D) as part of an interlaboratory information exchange between SNLA and LLNL. This report describes the methods used in preparing SYNROC including the solution interaction, and hot-pressing methods used to obtain fully dense SYNROC monoliths
Time-periodic solutions of the Benjamin-Ono equation
Energy Technology Data Exchange (ETDEWEB)
Ambrose , D.M.; Wilkening, Jon
2008-04-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.
Time-periodic solutions of the Benjamin-Ono equation
International Nuclear Information System (INIS)
Ambrose, D.M.; Wilkening, Jon
2008-01-01
We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one of the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations
On matrix diffusion: formulations, solution methods and qualitative effects
Carrera, Jesús; Sánchez-Vila, Xavier; Benet, Inmaculada; Medina, Agustín; Galarza, Germán; Guimerà, Jordi
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φm2RmDm / Lm2, whereas late-time behavior (long tracer tests) depends only on φmRm, and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. RésuméLa diffusion matricielle est un phénomène reconnu maintenant comme un mécanisme de transport important. Malheureusement, la prise en compte de la diffusion matricielle complique la simulation du transport de soluté. Ce problème a conduit à des formulations simplifiées, en partie à cause de la méthode de résolution. Il s'en est suivi une certaine confusion sur la façon de poser correctement le problème. L'un des objectifs de ce travail est de trouver une certaine unité parmi les formulations et les méthodes de résolution. C'est ainsi que certaines propriétés asymptotiques de la diffusion matricielle ont été dérivées. En particulier, le comportement à l'origine (expériences de traçage courtes) dépend uniquement du terme φm2RmDm / Lm2, alors que le comportement à long terme
Directory of Open Access Journals (Sweden)
Yanfang Xu
2016-01-01
Full Text Available A novel method for fabricating ordered double layers porous anodic alumina (DL-PAA with controllable nanopore size was presented. Highly ordered large pore layer with interpore distance of 480 nm was fabricated in phosphoric acid solution with oxalic acid addition at the potential of 195 V and the small pore layer was fabricated in oxalic acid solution at the potential from 60 to 100 V. Experimental results show that the thickness of large pore layer is linearly correlative with anodizing time, and pore diameter is linearly correlative with pore widening time. When the anodizing potential in oxalic acid solution was adjusted from 60 to 100 V, the small pore layers with continuously tunable interpore distance from 142 to 241 nm and pore density from 1.94×109 to 4.89×109 cm−2 were obtained. And the interpore distance and the pore density of small pore layers are closely correlative with the anodizing potential. The fabricated DL-PAA templates can be widely utilized for fabrication of ordered nanomaterials, such as superhydrophobic or gecko-inspired adhesive materials and metal or semiconductor nanowires.
International Nuclear Information System (INIS)
Abdou, M.A.
2008-01-01
The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics
The boundary element method for the solution of the multidimensional inverse heat conduction problem
International Nuclear Information System (INIS)
Lagier, Guy-Laurent
1999-01-01
This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author) [fr
Energy Technology Data Exchange (ETDEWEB)
Balate, J.; Sysala, T. [Technical Univ., Zlin (Czech Republic). Dept. of Automation and Control Technology
1997-12-31
The District Heating Systems - DHS (Centralized Heat Supply Systems - CHSS) are being developed in large cities in accordance with their growth. The systems are formed by enlarging networks of heat distribution to consumers and at the same time they interconnect the heat sources gradually built. The heat is distributed to the consumers through the circular networks, that are supplied by several cooperating heat sources, that means by power and heating plants and heating plants. The complicated process of heat production technology and supply requires the system approach when solving the concept of automatized control. The paper deals with comparison of the solution way using the analysis methods and using the artificial intelligence methods. (orig.)
International Nuclear Information System (INIS)
McCorkell, R.
1980-01-01
The author describes methods used in his laboratory to determine radon, radon daughter, uranium and radium concentrations in air, soil gas, and aqueous solutions. These methods include emanometry, the use of track detectors or collectors, filtration, and autoradiography
Hu, Hao; Liu, Haiyan
2013-05-30
Developments in computing hardware and algorithms have made direct molecular dynamics simulation with the combined quantum mechanical/molecular mechanical methods affordable for small solute molecules in solution, in which much improved accuracy can be obtained via the quantum mechanical treatment of the solute molecule and even sometimes water molecules in the first solvation shell. However, unlike the conventional molecular mechanical simulations of large molecules, e.g., proteins, in solutions, special care must be taken in the technical details of the simulation, including the thermostat of the solute/solvent system, so that the conformational space of the solute molecules can be properly sampled. We show here that the common setup for classical molecular mechanical molecular dynamics simulations, such as the Berendsen or single Nose-Hoover thermostat, and/or rigid water models could lead to pathological sampling of the solutes' conformation. In the extreme example of a methanol molecule in aqueous solution, improper and sluggish setups could generate two peaks in the distribution of the O-H bond length. We discuss the factors responsible for this somewhat unexpected result and evoke a simple and ancient technical fix-up to resolve this problem.
International Nuclear Information System (INIS)
Tumelero, Fernanda; Petersen, Claudio Z.; Goncalves, Glenio A.; Lazzari, Luana
2015-01-01
In this work, we present a solution of the Neutron Point Kinetics Equations with temperature feedback effects applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutrons precursors with temperature feedback effects and constant reactivity. The main idea is to expand the neutron density, delayed neutron precursors and temperature as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. In such a way, one varies the time step size of the Polynomial Approach Method and performs an analysis about the precision and computational time. Moreover, we compare the method with different types of approaches (linear, quadratic and cubic) of the power series. The answer of neutron density and temperature obtained by numerical simulations with linear approximation are compared with results in the literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Tumelero, Fernanda, E-mail: fernanda.tumelero@yahoo.com.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Petersen, Claudio Z.; Goncalves, Glenio A.; Lazzari, Luana, E-mail: claudiopeteren@yahoo.com.br, E-mail: gleniogoncalves@yahoo.com.br, E-mail: luana-lazzari@hotmail.com [Universidade Federal de Pelotas (DME/UFPEL), Capao do Leao, RS (Brazil). Instituto de Fisica e Matematica
2015-07-01
In this work, we present a solution of the Neutron Point Kinetics Equations with temperature feedback effects applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutrons precursors with temperature feedback effects and constant reactivity. The main idea is to expand the neutron density, delayed neutron precursors and temperature as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. In such a way, one varies the time step size of the Polynomial Approach Method and performs an analysis about the precision and computational time. Moreover, we compare the method with different types of approaches (linear, quadratic and cubic) of the power series. The answer of neutron density and temperature obtained by numerical simulations with linear approximation are compared with results in the literature. (author)
NMR determination of chemically related metals in solution as a new method of inorganic analysis
International Nuclear Information System (INIS)
Fedorov, L.A.
1989-01-01
An NMR spectroscopic method for the determination of chemically related metals in solution is suggested. The metals are determined in complexes with specially selected polydentate ligands. Structural requirements to ligands, analytical properties and general limits of the application of the method are discussed. (orig.)
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-03
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-01
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
Directory of Open Access Journals (Sweden)
Petráš Ivo
2011-01-01
Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.
International Nuclear Information System (INIS)
Patra, A.; Saha Ray, S.
2014-01-01
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet Collocation Method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: This paper emphasizes on finding the solution for a stationary transport equation using the technique of Haar wavelet Collocation Method (HWCM). Haar wavelet Collocation Method is efficient and powerful in solving wide class of linear and nonlinear differential equations. Recently Haar wavelet transform has gained the reputation of being a very effective tool for many practical applications. This paper intends to provide the great utility of Haar wavelets to nuclear science problem. In the present paper, two-dimensional Haar wavelets are applied for solution of the stationary Neutron Transport Equation in homogeneous isotropic medium. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency of the method, one test problem is discussed. It can be observed from the computational simulation that the numerical approximate solution is much closer to the exact solution
A novel technique for including surface tension in PLIC-VOF methods
Energy Technology Data Exchange (ETDEWEB)
Meier, M.; Yadigaroglu, G. [Swiss Federal Institute of Technology, Nuclear Engineering Lab. ETH-Zentrum, CLT, Zurich (Switzerland); Smith, B. [Paul Scherrer Inst. (PSI), Villigen (Switzerland). Lab. for Thermal-Hydraulics
2002-02-01
Various versions of Volume-of-Fluid (VOF) methods have been used successfully for the numerical simulation of gas-liquid flows with an explicit tracking of the phase interface. Of these, Piecewise-Linear Interface Construction (PLIC-VOF) appears as a fairly accurate, although somewhat more involved variant. Including effects due to surface tension remains a problem, however. The most prominent methods, Continuum Surface Force (CSF) of Brackbill et al. and the method of Zaleski and co-workers (both referenced later), both induce spurious or 'parasitic' currents, and only moderate accuracy in regards to determining the curvature. We present here a new method to determine curvature accurately using an estimator function, which is tuned with a least-squares-fit against reference data. Furthermore, we show how spurious currents may be drastically reduced using the reconstructed interfaces from the PLIC-VOF method. (authors)
Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.
2018-06-01
In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.
DEFF Research Database (Denmark)
Aidas, Kestutis; Møgelhøj, Andreas; Nilsson, Elna Johanna Kristina
2008-01-01
The performance of the Hartree–Fock method and the three density functionals B3LYP, PBE0, and CAM-B3LYP is compared to results based on the coupled cluster singles and doubles model in predictions of the solvatochromic effects on the vertical n¿* and ¿* electronic excitation energies of acrolein...... of acrolein in vapor phase and aqueous solution. The gas-to-aqueous solution shift of the n¿* excitation energy is well reproduced by using all density functional methods considered. However, the B3LYP and PBE0 functionals completely fail to describe the ¿* electronic transition in solution, whereas...... the recent CAM-B3LYP functional performs well also in this case. The ¿* excitation energy of acrolein in water solution is found to be very dependent on intermolecular induction and nonelectrostatic interactions. The computed excitation energies of acrolein in vacuum and solution compare well to experimental...
International Nuclear Information System (INIS)
Seitz, M.G.
1982-01-01
Reviewed in this statement are methods of preparing solutions to be used in laboratory experiments to examine technical issues related to the safe disposal of nuclear waste from power generation. Each approach currently used to prepare solutions has advantages and any one approach may be preferred over the others in particular situations, depending upon the goals of the experimental program. These advantages are highlighted herein for three approaches to solution preparation that are currently used most in studies of nuclear waste disposal. Discussion of the disadvantages of each approach is presented to help a user select a preparation method for his particular studies. Also presented in this statement are general observations regarding solution preparation. These observations are used as examples of the types of concerns that need to be addressed regarding solution preparation. As shown by these examples, prior to experimentation or chemical analyses, laboratory techniques based on scientific knowledge of solutions can be applied to solutions, often resulting in great improvement in the usefulness of results
Substep methods for burnup calculations with Bateman solutions
International Nuclear Information System (INIS)
Isotalo, A.E.; Aarnio, P.A.
2011-01-01
Highlights: → Bateman solution based depletion requires constant microscopic reaction rates. → Traditionally constant approximation is used for each depletion step. → Here depletion steps are divided to substeps which are solved sequentially. → This allows piecewise constant, rather than constant, approximation for each step. → Discretization errors are almost completely removed with only minor slowdown. - Abstract: When material changes in burnup calculations are solved by evaluating an explicit solution to the Bateman equations with constant microscopic reaction rates, one has to first predict the development of the reaction rates during the step and then further approximate these predictions with their averages in the depletion calculation. Representing the continuously changing reaction rates with their averages results in some error regardless of how accurately their development was predicted. Since neutronics solutions tend to be computationally expensive, steps in typical calculations are long and the resulting discretization errors significant. In this paper we present a simple solution to reducing these errors: the depletion steps are divided to substeps that are solved sequentially, allowing finer discretization of the reaction rates without additional neutronics solutions. This greatly reduces the discretization errors and, at least when combined with Monte Carlo neutronics, causes only minor slowdown as neutronics dominates the total running time.
Exact solutions of (3 + 1-dimensional generalized KP equation arising in physics
Directory of Open Access Journals (Sweden)
Syed Tauseef Mohyud-Din
Full Text Available In this work, we have obtained some exact solutions to (3 + 1-dimensional generalized KP Equation. The improved tanϕ(ξ2-expansion method has been introduced to construct the exact solutions of nonlinear evolution equations. The obtained solutions include hyperbolic function solutions, trigonometric function solutions, exponential solutions, and rational solutions. Our study has added some new varieties of solutions to already available solutions. It is also worth mentioning that the computational work has been reduced significantly. Keywords: Improved tanϕ(ξ2-expansion method, Hyperbolic function solution, Trigonometric function solution, Rational solution, (3 + 1-dimensional generalized KP equation
Directory of Open Access Journals (Sweden)
Mingzhong Gao
Full Text Available Rectangular caverns are increasingly used in underground engineering projects, the failure mechanism of rectangular cavern wall rock is significantly different as a result of the cross-sectional shape and variations in wall stress distributions. However, the conventional computational method always results in a long-winded computational process and multiple displacement solutions of internal rectangular wall rock. This paper uses a Laurent series complex method to obtain a mapping function expression based on complex variable function theory and conformal transformation. This method is combined with the Schwarz-Christoffel method to calculate the mapping function coefficient and to determine the rectangular cavern wall rock deformation. With regard to the inverse mapping concept, the mapping relation between the polar coordinate system within plane ς and a corresponding unique plane coordinate point inside the cavern wall rock is discussed. The disadvantage of multiple solutions when mapping from the plane to the polar coordinate system is addressed. This theoretical formula is used to calculate wall rock boundary deformation and displacement field nephograms inside the wall rock for a given cavern height and width. A comparison with ANSYS numerical software results suggests that the theoretical solution and numerical solution exhibit identical trends, thereby demonstrating the method's validity. This method greatly improves the computing accuracy and reduces the difficulty in solving for cavern boundary and internal wall rock displacements. The proposed method provides a theoretical guide for controlling cavern wall rock deformation failure.
A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method
Directory of Open Access Journals (Sweden)
Sandile S. Motsa
2012-01-01
Full Text Available We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations. By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude. We demonstrate that the proposed method can be used to obtain the limit cycle and bifurcation diagrams of the governing equations. Comparison with exact and other results in the literature shows that the method is accurate and effective in finding solutions of nonlinear equations with oscillatory solutions, nonlinear eigenvalue problems, and other nonlinear problems with bifurcations.
Iterative solutions of finite difference diffusion equations
International Nuclear Information System (INIS)
Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.
1981-01-01
The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)
Analysis of the Block-Grid Method for the Solution of Laplace's Equation on Polygons with a Slit
Directory of Open Access Journals (Sweden)
S. Cival Buranay
2013-01-01
Full Text Available The error estimates obtained for solving Laplace's boundary value problem on polygons by the block-grid method contain constants that are difficult to calculate accurately. Therefore, the experimental analysis of the method could be essential. The real characteristics of the block-grid method for solving Laplace's equation on polygons with a slit are analysed by experimental investigations. The numerical results obtained show that the order of convergence of the approximate solution is the same as in the case of a smooth solution. To illustrate the singular behaviour around the singular point, the shape of the highly accurate approximate solution and the figures of its partial derivatives up to second order are given in the “singular” part of the domain. Finally a highly accurate formula is given to calculate the stress intensity factor, which is an important quantity in fracture mechanics.
International Nuclear Information System (INIS)
Polivanskij, V.P.
1989-01-01
The method to solve two-dimensional equations of neutron transport using 4P 0 -approximation is presented. Previously such approach was efficiently used for the solution of one-dimensional problems. New an attempt is made to apply the approach to solution of two-dimensional problems. Algorithm of the solution is given, as well as results of test neutron-physical calculations. A considerable as compared with diffusion approximation is shown. 11 refs
International Nuclear Information System (INIS)
Shirinov, T.I.; Florianovich, G.M.; Skuratnik, Ya.B.
1978-01-01
Radiometry method of simultaneous continuous registration of transfer rates of iron and chromium into solution from Fe-Cr alloys with various composition has been developed. Using gamma-spectrometer components of Fe-Cr alloys can be determined with high sensitivity in separate samples according to Fe 59 and Cr 51 radioactive labels, obtained by neutron activation. The above method is applied to estimate Fe and Cr transfer rates into H 2 SO 4 solution at the temperature of 50 deg from Fe - 28% Cr alloy during its active dissolution. It is established, that beginning with some seconds of alloy and solution contact, its components transfer into the solution in the same composition, as in the alloy. The method enables to determine Fe with the accuracy of up to 5% and Cr with that of up to 10%
Makedonska, N.; Sparks, D. W.; Aharonov, E.
2012-12-01
Pressure solution (also termed chemical compaction) is considered the most important ductile deformation mechanism operating in the Earth's upper crust. This mechanism is a major player in a variety of geological processes, including evolution of sedimentary basins, hydrocarbon reservoirs, aquifers, earthquake recurrence cycles, and fault healing. Pressure solution in massive rocks often localizes into solution seams or stylolites. Field observations of stylolites often show elastic/brittle interactions in regions between pressure solution features, including and shear fractures, veins and pull-apart features. To understand these interactions, we use a grain-scale model based on the Discrete Element Method that allows granular dissolution at stressed contacts between grains. The new model captures both the slow chemical compaction process and the more abrupt brittle fracturing and sliding between grains. We simulate a sample of rock as a collection of particles, each representing either a grain or a unit of rock, bonded to each other with breakable cement. We apply external stresses to this sample, and calculate elastic and frictional interactions between the grains. Dissolution is modeled by an irreversible penetration of contacting grains into each other at a rate that depends on the contact stress and an adjustable rate constant. Experiments have shown that dissolution rates at grain contacts are greatly enhanced when there is a mineralogical contrast. Therefore, we dissolution rate constant can be increased to account for an amount of impurities (e.g. clay in a quartz or calcite sandstone) that can accumulate on dissolving contacts. This approach allows large compaction and shear strains within the rock, while allowing examination of local grain-scale heterogeneity. For example, we will describe the effect of pressure solution on the distribution of contact forces magnitudes and orientations. Contact forces in elastic granular packings are inherently
Energy Technology Data Exchange (ETDEWEB)
Gabano, J.
1983-03-01
An electrolyte for an electric cell whose negative active material is constituted by lithium and whose positive active material is constituted by thionyl chloride. The electrolyte contains at least one solvent and at least one solute, said solvent being thionyl chloride and said solute being chosen from the group which includes lithium tetrachloroaluminate and lithium hexachloroantimonate. According to the invention said electrolyte further includes a complex chosen from the group which includes AlCl/sub 3/,SO/sub 2/ and SbCl/sub 5/,SO/sub 2/. The voltage rise of electric cells which include such an electrolyte takes negligible time.
DEFF Research Database (Denmark)
Yue, Zhao; Grivel, Jean-Claude
2013-01-01
Chemical solution deposition is a versatile technique to grow oxide thin films with self-organized nanostructures. Morphology and crystallographic orientation control of CeO2 thin films grown on technical NiW substrates by a chemical solution deposition method are achieved in this work. Based...
Exact Travelling Wave Solutions for Isothermal Magnetostatic Atmospheres by Fan Subequation Method
Directory of Open Access Journals (Sweden)
Hossein Jafari
2012-01-01
ignorable coordinate corresponding to a uniform gravitational field in a plane geometry is carried out. These equations transform to a single nonlinear elliptic equation for the magnetic vector potential . This equation depends on an arbitrary function of that must be specified. With choices of the different arbitrary functions, we obtain analytical solutions of elliptic equation using the Fan subequation method.
The method of fundamental solutions for computing acoustic interior transmission eigenvalues
Kleefeld, Andreas; Pieronek, Lukas
2018-03-01
We analyze the method of fundamental solutions (MFS) in two different versions with focus on the computation of approximate acoustic interior transmission eigenvalues in 2D for homogeneous media. Our approach is mesh- and integration free, but suffers in general from the ill-conditioning effects of the discretized eigenoperator, which we could then successfully balance using an approved stabilization scheme. Our numerical examples cover many of the common scattering objects and prove to be very competitive in accuracy with the standard methods for PDE-related eigenvalue problems. We finally give an approximation analysis for our framework and provide error estimates, which bound interior transmission eigenvalue deviations in terms of some generalized MFS output.
International Nuclear Information System (INIS)
Obradovic, D.
1970-04-01
In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)
Carbamazepine-Fumaric Acid Co-Crystal Screening Using Solution Based Method
Directory of Open Access Journals (Sweden)
Abd Rahim Syarifah
2016-01-01
Full Text Available Co-crystals is a multi-component system which connected by non-covalent interactions, present physically as a solid form under ambient conditions. Nowadays, co-crystal has becoming as an alternative approach to improve the bioavailability of poor water soluble drugs especially for a weakly ionisable groups or neutral compounds. In this study the co-crystal screening was carried out for carbamazepine (CBZ and fumaric acid (FUM co-crystal former (CCF using non-stoichiometric method (addition of CBZ to CCF saturated solution and stoichiometric method (evaporation of 1:1 molar ratio of CBZ to CCF in acetonitrile, ethyl acetate, propanol, ethanol and formic acid solvent systems. The crystals produced from the screening were characterized using Powder X-ray Diffraction (PXRD, Differential Scanning Calorimetry (DSC and Fourier Transform Infrared (FT-IR. The PXRD analysis had confirmed that the co-crystal was successfully formed in both methods for all of the solvent system studied with an exception to formic acid in the stoichiometric method where no crystal was found precipitate. The findings from this study revealed that Form A and Form B of CBZ-FUM co-crystal had been successfully formed from different solvent systems.
Energy Technology Data Exchange (ETDEWEB)
Munir, Sundas; Park, Soo-Young, E-mail: psy@knu.ac.kr
2015-09-17
Sodium dodecyl sulphate (SDS) including β-cyclodextrin (β-CD) (β-CD{sub SDS}) was used to detect cholesterol at the 4-cyano-4′-pentylbiphenyl (5CB)/aqueous interface in transmission electron microscopy (TEM) grid cells. The β-CD acts as a host for SDS (guest). The guest SDS enclosed within the β-CD cavity was replaced with cholesterol by injecting cholesterol solution into the TEM cell at concentrations greater than 3 μM. The replacement of SDS with cholesterol was confirmed by pH measurement and high performance liquid chromatography (HPLC). The SDS excluded from the β-CD altered the planar orientation of the 5CB confined within the TEM grid cell to a homeotropic orientation. This planar-to-homeotropic transition was observed using a polarized optical microscope under crossed polarizers. This convenient TEM grid cell provides a new method for the selective detection of cholesterol without immobilization of the detecting receptors (enzyme, antibody, or aptamer) or the use of sophisticated instruments. - Highlights: • β-CD-SDS inclusion was used for the detection of cholesterol at 5CB/aqueous interface. • The SDS enclosed within the β-CD cavity was replaced by cholesterol. • The released SDS from the β-CD caused homeotropic orientation of 5CB. • The cholesterol was detected from planar-to-homeotropic transition of 5CB. • This convenient TEM grid cell provides a new method for the selective detection of cholesterol.
International Nuclear Information System (INIS)
Munir, Sundas; Park, Soo-Young
2015-01-01
Sodium dodecyl sulphate (SDS) including β-cyclodextrin (β-CD) (β-CD_S_D_S) was used to detect cholesterol at the 4-cyano-4′-pentylbiphenyl (5CB)/aqueous interface in transmission electron microscopy (TEM) grid cells. The β-CD acts as a host for SDS (guest). The guest SDS enclosed within the β-CD cavity was replaced with cholesterol by injecting cholesterol solution into the TEM cell at concentrations greater than 3 μM. The replacement of SDS with cholesterol was confirmed by pH measurement and high performance liquid chromatography (HPLC). The SDS excluded from the β-CD altered the planar orientation of the 5CB confined within the TEM grid cell to a homeotropic orientation. This planar-to-homeotropic transition was observed using a polarized optical microscope under crossed polarizers. This convenient TEM grid cell provides a new method for the selective detection of cholesterol without immobilization of the detecting receptors (enzyme, antibody, or aptamer) or the use of sophisticated instruments. - Highlights: • β-CD-SDS inclusion was used for the detection of cholesterol at 5CB/aqueous interface. • The SDS enclosed within the β-CD cavity was replaced by cholesterol. • The released SDS from the β-CD caused homeotropic orientation of 5CB. • The cholesterol was detected from planar-to-homeotropic transition of 5CB. • This convenient TEM grid cell provides a new method for the selective detection of cholesterol.
International Nuclear Information System (INIS)
Alomari, A. K.; Noorani, M. S. M.; Nazar, R.
2008-01-01
We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter ħ, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method
Matrix method for two-dimensional waveguide mode solution
Sun, Baoguang; Cai, Congzhong; Venkatesh, Balajee Seshasayee
2018-05-01
In this paper, we show that the transfer matrix theory of multilayer optics can be used to solve the modes of any two-dimensional (2D) waveguide for their effective indices and field distributions. A 2D waveguide, even composed of numerous layers, is essentially a multilayer stack and the transmission through the stack can be analysed using the transfer matrix theory. The result is a transfer matrix with four complex value elements, namely A, B, C and D. The effective index of a guided mode satisfies two conditions: (1) evanescent waves exist simultaneously in the first (cladding) layer and last (substrate) layer, and (2) the complex element D vanishes. For a given mode, the field distribution in the waveguide is the result of a 'folded' plane wave. In each layer, there is only propagation and absorption; at each boundary, only reflection and refraction occur, which can be calculated according to the Fresnel equations. As examples, we show that this method can be used to solve modes supported by the multilayer step-index dielectric waveguide, slot waveguide, gradient-index waveguide and various plasmonic waveguides. The results indicate the transfer matrix method is effective for 2D waveguide mode solution in general.
Energy Technology Data Exchange (ETDEWEB)
Schmal, M; Russo, Q [Rio de Janeiro Univ. (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia; Almeida, M S; Bozzo, S [Rio de Janeiro Univ. (Brazil). Instituto de Quimica
1975-03-01
A method of solutions is presented for the determination of the velocity profiles in turbulent flow through annular tubes, based on the Von Karman similarity theory developed by Quarmby. The parameters found by Quarmby appearing in the velocity profiles and determined experimentally by different authors were approximated by polynonial functions of variable degree, as function of the Reynolds numbers. The Runge-Kutta-Nystrom method was used in the integration of the differential equations and the systematic of solution is presented in a computer program. The calculated results were compared to the experimental date and presented a deviation of 10/sup -2/%.
Constructing exact symmetric informationally complete measurements from numerical solutions
Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne
2018-04-01
Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.
SIVA/DIVA- INITIAL VALUE ORDINARY DIFFERENTIAL EQUATION SOLUTION VIA A VARIABLE ORDER ADAMS METHOD
Krogh, F. T.
1994-01-01
The SIVA/DIVA package is a collection of subroutines for the solution of ordinary differential equations. There are versions for single precision and double precision arithmetic. These solutions are applicable to stiff or nonstiff differential equations of first or second order. SIVA/DIVA requires fewer evaluations of derivatives than other variable order Adams predictor-corrector methods. There is an option for the direct integration of second order equations which can make integration of trajectory problems significantly more efficient. Other capabilities of SIVA/DIVA include: monitoring a user supplied function which can be separate from the derivative; dynamically controlling the step size; displaying or not displaying output at initial, final, and step size change points; saving the estimated local error; and reverse communication where subroutines return to the user for output or computation of derivatives instead of automatically performing calculations. The user must supply SIVA/DIVA with: 1) the number of equations; 2) initial values for the dependent and independent variables, integration stepsize, error tolerance, etc.; and 3) the driver program and operational parameters necessary for subroutine execution. SIVA/DIVA contains an extensive diagnostic message library should errors occur during execution. SIVA/DIVA is written in FORTRAN 77 for batch execution and is machine independent. It has a central memory requirement of approximately 120K of 8 bit bytes. This program was developed in 1983 and last updated in 1987.
Solution chemistry and separation of metal ions in leached solution
International Nuclear Information System (INIS)
Shibata, J.
1991-01-01
The method to presume a dissolved state of metal ions in an aqueous solution and the technology to separate and concentrate metal ions in a leached solution are described in this paper. It is very important for the separation of metal ions to know the dissolved state of metal ions. If we know the composition of an aqueous solution and the stability constants of metal-ligand complexes, we can calculate and estimate the concentration of each species in the solution. Then, we can decide the policy to separate and concentrate metal ions. There are several methods for separation and purification; hydroxide precipitation method, sulfide precipitation method, solvent extraction method and ion exchange resin method. Solvent extraction has been used in purification processes of copper refinery, uranium refinery, platinum metal refinery and rare earth metal refinery. Fundamental process of solvent extraction, a kind of commercial extractants, a way of determining a suitable extractant and an equipment are discussed. Finally, it will be emphasized how the separation of rare earths is improved in solvent extraction. (author) 21 figs., 8 tabs., 8 refs
Sousa, A. N. Laurindo; Ojeda-González, A.; Prestes, A.; Klausner, V.; Caritá, L. A.
2018-02-01
This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere's law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker's generating function in details without omitting any step. The Walker's generating function g( ζ) is written in a new way as the tangent of an unspecified function K( ζ). In this trend, the general solution of the GS equation is expressed as exp(- 2Ψ) = 4| K '( ζ)|2/cos2[ K( ζ) - K( ζ ∗)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris's solution as a test, in this case K( ζ) = arctan(exp( i ζ)). In summary, one of the article purposes is to present a review of the Harris's solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g( ζ) = tan( K( ζ)). We also present a new analytical solution to the equilibrium Ampere's law using g( ζ) = cosh( b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.
Potentiometric titration of free acid in uranium solutions
International Nuclear Information System (INIS)
Suh, M. Y.; Kim, W. H.; Kim, J. S.; Sohn, S. C.; Eom, T. Y.; Lee, C. H.; Jeon, Y. S.; Han, S. H.
1998-02-01
Hydrolysis properties of metal cations and fundamental principles of the potentiometric titration of free acid in aqueous solutions containing metal cations were described. The published papers and reports for the alkalimetric and acidimetric titration of free acid were surveyed, and the applicability of these titration methods to the uranium and/or plutonium solutions were discussed. This technical report also includes the various results obtained from the authors' researches to establish the alkalimetric and acidimetric titration methods for the determination of free acid in nitric acid solutions containing uranium and/or oxalic acid, and aluminum. The procedure manuals used in chemical processes and the newly prepared manuals based on the authors' researches are appended. (author). 26 refs., 54 figs
Potentiometric titration of free acid in uranium solutions
Energy Technology Data Exchange (ETDEWEB)
Suh, M. Y.; Kim, W. H.; Kim, J. S.; Sohn, S. C.; Eom, T. Y.; Lee, C. H.; Jeon, Y. S.; Han, S. H.
1998-02-01
Hydrolysis properties of metal cations and fundamental principles of the potentiometric titration of free acid in aqueous solutions containing metal cations were described. The published papers and reports for the alkalimetric and acidimetric titration of free acid were surveyed, and the applicability of these titration methods to the uranium and/or plutonium solutions were discussed. This technical report also includes the various results obtained from the authors` researches to establish the alkalimetric and acidimetric titration methods for the determination of free acid in nitric acid solutions containing uranium and/or oxalic acid, and aluminum. The procedure manuals used in chemical processes and the newly prepared manuals based on the authors` researches are appended. (author). 26 refs., 54 figs.
Insight solutions are correct more often than analytic solutions
Salvi, Carola; Bricolo, Emanuela; Kounios, John; Bowden, Edward; Beeman, Mark
2016-01-01
How accurate are insights compared to analytical solutions? In four experiments, we investigated how participants’ solving strategies influenced their solution accuracies across different types of problems, including one that was linguistic, one that was visual and two that were mixed visual-linguistic. In each experiment, participants’ self-judged insight solutions were, on average, more accurate than their analytic ones. We hypothesised that insight solutions have superior accuracy because they emerge into consciousness in an all-or-nothing fashion when the unconscious solving process is complete, whereas analytic solutions can be guesses based on conscious, prematurely terminated, processing. This hypothesis is supported by the finding that participants’ analytic solutions included relatively more incorrect responses (i.e., errors of commission) than timeouts (i.e., errors of omission) compared to their insight responses. PMID:27667960
Advances on reverse strike co-precipitation method of uranium-plutonium mixed solutions
International Nuclear Information System (INIS)
Menghini, Jorge E.; Marchi, Daniel E.; Orosco, Edgardo H.; Greco, Luis
2000-01-01
The reverse strike coprecipitation of uranium-plutonium mixed solutions, is an alternative way to obtain MOX fuel pellets. Previous tests, carried out in the Alpha Laboratory, included a stabilization step for transforming 100 % of plutonium into Pu +4 . Therefore, the plutonium precipitated as Pu(OH) 4 . In this second step, the stabilization process was suppressed. In this way, besides Pu(OH) 4 , a part of the precipitated is composed of a mixed salt: AD(U,Pu). Then, a homogeneous solid solution is formed in the early steps of the process. The powders showed higher tap density, better performance during the pressing and lower sinterability than the powders obtained in previous tests. The advantageous and disadvantageous effects of the stabilization step are analyzed in this paper. (author)
A finite volume method for cylindrical heat conduction problems based on local analytical solution
Li, Wang
2012-10-01
A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.
A finite volume method for cylindrical heat conduction problems based on local analytical solution
Li, Wang; Yu, Bo; Wang, Xinran; Wang, Peng; Sun, Shuyu
2012-01-01
A new finite volume method for cylindrical heat conduction problems based on local analytical solution is proposed in this paper with detailed derivation. The calculation results of this new method are compared with the traditional second-order finite volume method. The newly proposed method is more accurate than conventional ones, even though the discretized expression of this proposed method is slightly more complex than the second-order central finite volume method, making it cost more calculation time on the same grids. Numerical result shows that the total CPU time of the new method is significantly less than conventional methods for achieving the same level of accuracy. © 2012 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Song Lina; Wang Weiguo
2010-01-01
In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.
International Nuclear Information System (INIS)
Ponomarev, L.I.; Puzynin, I.V.; Puzynina, T.P.
1975-01-01
The paper is a part of further development of investigations in which a numerical solution method of the Schroedinger equation for the case of a discrete spectrum has been developed and applied. The suggested algorithm (CAMEN scheme) is generalized and applied to quasistationary solutions of the Schroedinger equation system. Some specific features of the CAMEN scheme realization (such as establishing boundary conditions are observed while calculating quasistationary levels of hydrogen mesic molecules. The calculations have been carried out for energies and wave functions of quasistationary states of hydrogen mesic molecules. The choice of the initial approximation, the accuracy of calculations and characteristics of the convergence of the method have been investigated. The CAMEN algorithm has been realized in the form of the FORTRAN program packet. The CAMEN scheme can be also used for solving scatering problems
Brown, Steven G; Eberly, Shelly; Paatero, Pentti; Norris, Gary A
2015-06-15
The new version of EPA's positive matrix factorization (EPA PMF) software, 5.0, includes three error estimation (EE) methods for analyzing factor analytic solutions: classical bootstrap (BS), displacement of factor elements (DISP), and bootstrap enhanced by displacement (BS-DISP). These methods capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. To demonstrate the utility of the EE methods, results are presented for three data sets: (1) speciated PM2.5 data from a chemical speciation network (CSN) site in Sacramento, California (2003-2009); (2) trace metal, ammonia, and other species in water quality samples taken at an inline storage system (ISS) in Milwaukee, Wisconsin (2006); and (3) an organic aerosol data set from high-resolution aerosol mass spectrometer (HR-AMS) measurements in Las Vegas, Nevada (January 2008). We present an interpretation of EE diagnostics for these data sets, results from sensitivity tests of EE diagnostics using additional and fewer factors, and recommendations for reporting PMF results. BS-DISP and BS are found useful in understanding the uncertainty of factor profiles; they also suggest if the data are over-fitted by specifying too many factors. DISP diagnostics were consistently robust, indicating its use for understanding rotational uncertainty and as a first step in assessing a solution's viability. The uncertainty of each factor's identifying species is shown to be a useful gauge for evaluating multiple solutions, e.g., with a different number of factors. Published by Elsevier B.V.
Alam, Md Nur; Akbar, M Ali
2013-01-01
The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.
A new water permeability measurement method for unsaturated tight materials using saline solutions
International Nuclear Information System (INIS)
Malinsky, Laurent; Talandier, Jean
2012-01-01
Document available in extended abstract form only. Relative water permeability of material in a radioactive waste disposal is a key parameter to simulate and predict saturation state evolution. In this paper we present a new measurement method and the results obtained for Callovo-Oxfordian (Cox) clay-stone, host rock of the underground Andra laboratory at Bure (Meuse/Haute-Marne). Relative water permeability of such a low permeability rock as Cox clay-stone has been measured up to now by an indirect method. It consists in submitting a rock sample to successive relative humidity steps imposed by saline solutions. The transient mass variation during each step and the mass at hydric equilibrium are interpreted generally by using an inverse analysis method. The water relative permeability function of water saturation is derived from water diffusion coefficient evolution and water retention curve. The proposed new method consists in directly measuring the water flux across a flat cylindrical submitted to a relative humidity gradient. Two special cells have been developed. The tightness of the lateral sample surface is insured by crushing a polyurethane ring surrounding the sample set in an aluminium device placed over a Plexiglas vessel filled with a saline solution. One of the cells is designed to allow humidity measurement in the cell. These cells can also be used to measure the relative humidity produced by a saline solution or by an unsaturated material. During a permeability measurement, the cell with the sample to be tested is continuously weighted in a Plexiglas box in which a saline solution imposes a different relative humidity at the upper sample face. The experimental set-up is shown on Figure 1. The mean permeability of the sample is proportional to the rate of mass variation when steady state is reached. The result of one test is shown on Figure 2(a). Twenty four permeability measurements have been performed on four argillite samples of 15 mm in height and
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Vaporization study on vanadium-oxygen solid solution by mass spectrometric method
International Nuclear Information System (INIS)
Banchorndhevakul, W.; Matsui, Tsuneo; Naito, Keiji
1986-01-01
The vapor pressures over vanadium-oxygen solid solution (0.001 ≤ O/V ≤ 0.145) were measured by mass-spectrometric method in the temperature range of 1,855 ∼ 2,117 K. The main vapor species were observed to be V(g) and VO(g). The vapor pressure of V(g) is higher than that of VO(g) over the solid solutions with all O/V ratios except for O/V = 0.145. The vapor pressure of V(g) is nearly independent of O/V ratio. The vapor pressure of VO(g) decreases with decreasing O/V ratio. The oxygen partial pressure was calculated as a function of temperature and O/V ratio from the vapor pressures of V(g) and VO(g), from which the partial molar enthalpy and entropy of oxygen in the solid solution were determined. The partial molar enthalpy of oxygen was observed to be independent of composition, suggesting the presence of very weak interaction between interstitial oxygens. The compositional dependence of the partial molar entropy of oxygen can be explained by assuming the occupation of the octahedral site in bcc vanadium lattice by the interstitial oxygens. The excess partial molar entropy of oxygen was compared with the value derived from the sum of the contributions from the volume expansion, electronic heat capacity and vibrational terms. (author)
Pretreatment Solution for Water Recovery Systems
Muirhead, Dean (Inventor)
2018-01-01
Chemical pretreatments are used to produce usable water by treating a water source with a chemical pretreatment that contains a hexavalent chromium and an acid to generate a treated water source, wherein the concentration of sulfate compounds in the acid is negligible, and wherein the treated water source remains substantially free of precipitates after the addition of the chemical pretreatment. Other methods include reducing the pH in urine to be distilled for potable water extraction by pretreating the urine before distillation with a pretreatment solution comprising one or more acid sources selected from a group consisting of phosphoric acid, hydrochloric acid, and nitric acid, wherein the urine remains substantially precipitate free after the addition of the pretreatment solution. Another method described comprises a process for reducing precipitation in urine to be processed for water extraction by mixing the urine with a pretreatment solution comprising hexavalent chromium compound and phosphoric acid.
New Explicit Solutions of (1 + 1)-Dimensional Variable-Coefficient Broer-Kaup System
International Nuclear Information System (INIS)
Yan Zhilian; Zhou Jianping
2010-01-01
By using the compatibility method, many explicit solutions of the (1 + 1)-dimensional variable-coefficient Broer-Kaup system are constructed, which include new solutions expressed by error function, Bessel function, exponential function, and Airy function. Some figures of the solutions are given by the symbolic computation system Maple. (general)
A simple digestion method with a Lefort aqua regia solution for diatom extraction.
Wang, Huipin; Liu, Yan; Zhao, Jian; Hu, Sunlin; Wang, Yuzhong; Liu, Chao; Zhang, Yanji
2015-01-01
Presence of diatoms in tissues has been considered as a significant sign of drowning. However, there are limitations in the present extraction methods. We developed a new digestion method using the Lefort aqua regia solution (3:1 nitric acid to hydrochloric acid) for diatom extraction and evaluated the digestive capability, diatom destruction, and diatoms' recovery of this new method. The kidney tissues from rabbit mixed with water rich in diatoms were treated by the Lefort aqua regia digestion method (n = 10) and the conventional acid digestion method (n = 10). The results showed that the digestive capability of Lefort aqua regia digestion method was superior to conventional acid digestion method (p 0.05). The Lefort aqua regia reagent is an improvement over the conventional acid digestion for recovery of diatoms from tissue samples. © 2014 American Academy of Forensic Sciences.
International Nuclear Information System (INIS)
2003-01-01
This International Standard specifies a precise and accurate gravimetric method for determining the mass fraction of uranium in uranyl nitrate solutions of nuclear grade quality containing more than 100 g/kg of uranium. Non-volatile impurities influence the accuracy of the method
The preparation method of solid boron solution in silicon carbide in the form of micro powder
International Nuclear Information System (INIS)
Pampuch, R.; Stobierski, L.; Lis, J.; Bialoskorski, J.; Ermer, E.
1993-01-01
The preparation method of solid boron solution in silicon carbide in the form of micro power has been worked out. The method consists in introducing mixture of boron, carbon and silicon and heating in the atmosphere of inert gas to the 1573 K
Presentation of some methods for the solution of the monoenergetic neutrons transport equation
International Nuclear Information System (INIS)
Valle G, E. del.
1978-01-01
The neutrons transport theory problems whose solution has been reached were collected in order to show that the transport equation is so complicated that different techniques were developed so as to give approximative numerical solutions to problems concerning the practical application. Such a technique, which had not been investigated in the literature dealing with these problems, is described here. The results which were obtained through this technique in undimensional problems of criticity are satisfactory and speaking in a conceptual way this method is extremely simple because it times. There is no limitation to deal with problems related neutrons sources with an arbitrary distribution and in principle the application of this technique can be extended to unhomogeneous environments. (author)
TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS
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SERIFE MUGE EGE
2016-07-01
Full Text Available The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation D_t^α u − γD_x^α u − 6u(D_x^α u^2 − (3u^2 − 1D_x^α (D_x^α u + D_x^α(D_x^α(D_x^α(D_x^α u = 0 and the space-time fractional symmetric regularized long wave (SRLW equation D_t^α(D_t^α u + D_x^α(D_x^α u + uD_t^α(D_x^α u + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u = 0 via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.
Method of synthesizing pyrite nanocrystals
Wadia, Cyrus; Wu, Yue
2013-04-23
A method of synthesizing pyrite nanocrystals is disclosed which in one embodiment includes forming a solution of iron (III) diethyl dithiophosphate and tetra-alkyl-ammonium halide in water. The solution is heated under pressure. Pyrite nanocrystal particles are then recovered from the solution.
On the solution of the Hartree-Fock-Bogoliubov equations by the conjugate gradient method
International Nuclear Information System (INIS)
Egido, J.L.; Robledo, L.M.
1995-01-01
The conjugate gradient method is formulated in the Hilbert space for density and non-density dependent Hamiltonians. We apply it to the solution of the Hartree-Fock-Bogoliubov equations with constraints. As a numerical application we show calculations with the finite range density dependent Gogny force. The number of iterations required to reach convergence is reduced by a factor of three to four as compared with the standard gradient method. (orig.)
International Nuclear Information System (INIS)
Yasuk, F.; Tekin, S.; Boztosun, I.
2010-01-01
In this study, the exact solutions of the d-dimensional Schroedinger equation with a position-dependent mass m(r)=1/(1+ζ 2 r 2 ) is presented for a free particle, V(r)=0, by using the method of point canonical transformations. The energy eigenvalues and corresponding wavefunctions for the effective potential which is to be a generalized Poeschl-Teller potential are obtained within the framework of the asymptotic iteration method.
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1993-01-01
The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation
Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza
2018-06-01
Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.
A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion
Huynh, H. T.
2009-01-01
We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.
Methods for measuring risk-aversion: problems and solutions
International Nuclear Information System (INIS)
Thomas, P J
2013-01-01
Risk-aversion is a fundamental parameter determining how humans act when required to operate in situations of risk. Its general applicability has been discussed in a companion presentation, and this paper examines methods that have been used in the past to measure it and their attendant problems. It needs to be borne in mind that risk-aversion varies with the size of the possible loss, growing strongly as the possible loss becomes comparable with the decision maker's assets. Hence measuring risk-aversion when the potential loss or gain is small will produce values close to the risk-neutral value of zero, irrespective of who the decision maker is. It will also be shown how the generally accepted practice of basing a measurement on the results of a three-term Taylor series will estimate a limiting value, minimum or maximum, rather than the value utilised in the decision. A solution is to match the correct utility function to the results instead
Methods for measuring risk-aversion: problems and solutions
Thomas, P. J.
2013-09-01
Risk-aversion is a fundamental parameter determining how humans act when required to operate in situations of risk. Its general applicability has been discussed in a companion presentation, and this paper examines methods that have been used in the past to measure it and their attendant problems. It needs to be borne in mind that risk-aversion varies with the size of the possible loss, growing strongly as the possible loss becomes comparable with the decision maker's assets. Hence measuring risk-aversion when the potential loss or gain is small will produce values close to the risk-neutral value of zero, irrespective of who the decision maker is. It will also be shown how the generally accepted practice of basing a measurement on the results of a three-term Taylor series will estimate a limiting value, minimum or maximum, rather than the value utilised in the decision. A solution is to match the correct utility function to the results instead.
Solution of stochastic media transport problems using a numerical quadrature-based method
International Nuclear Information System (INIS)
Pautz, S. D.; Franke, B. C.; Prinja, A. K.; Olson, A. J.
2013-01-01
We present a new conceptual framework for analyzing transport problems in random media. We decompose such problems into stratified subproblems according to the number of material pseudo-interfaces within realizations. For a given subproblem we assign pseudo-interface locations in each realization according to product quadrature rules, which allows us to deterministically generate a fixed number of realizations. Quadrature integration of the solutions of these realizations thus approximately solves each subproblem; the weighted superposition of solutions of the subproblems approximately solves the general stochastic media transport problem. We revisit some benchmark problems to determine the accuracy and efficiency of this approach in comparison to randomly generated realizations. We find that this method is very accurate and fast when the number of pseudo-interfaces in a problem is generally low, but that these advantages quickly degrade as the number of pseudo-interfaces increases. (authors)
Cepstrum analysis and applications to computational fluid dynamic solutions
Meadows, Kristine R.
1990-04-01
A novel approach to the problem of spurious reflections introduced by artificial boundary conditions in computational fluid dynamic (CFD) solutions is proposed. Instead of attempting to derive non-reflecting boundary conditions, the approach is to accept the fact that spurious reflections occur, but to remove these reflections with cepstrum analysis, a signal processing technique which has been successfully used to remove echoes from experimental data. First, the theory of the cepstrum method is presented. This includes presentation of two types of cepstra: The Power Cepstrum and the Complex Cepstrum. The definitions of the cepstrum methods are applied theoretically and numerically to the analytical solution of sinusoidal plane wave propagation in a duct. One-D and 3-D time dependent solutions to the Euler equations are computed, and hard-wall conditions are prescribed at the numerical boundaries. The cepstrum method is applied, and the reflections from the boundaries are removed from the solutions. One-D and 3-D solutions are computed with so called nonreflecting boundary conditions, and these solutions are compared to those obtained by prescribing hard wall conditions and processing with the cepstrum.
International Nuclear Information System (INIS)
Meloun, M.; Havel, J.; Hogfeldt, E.
1988-01-01
Although this book contains a very good review of computation methods applicable to equilibrium systems, most of the book is dedicated to the description and evaluation of computer programs available for doing such calculations. As stated in the preface, the authors (two computniks and a user of graphical and computer methods) have joined forces in order to present the reader with the points of view of both the creator and user of modern computer program tools available for the study of solution equilibria. The successful presentation of such a complicated amalgamation of concepts is greatly aided by the structure of the book, which begins with a brief but thorough discussion of equilibrium concepts in general, followed by an equally brief discussion of experimental methods used to study equilibria with potentiometric, extraction, and spectroscopic methods. These sections would not be sufficient to teach these topics to the beginner but offer an informative presentation of concepts in relation to one another to those already familiar with basic equilibrium concepts. The importance of evaluating and analyzing the suitability of data for further analysis is then presented before an in depth (by a chemist's standards) look at the individual parts that make up a detailed equilibrium analysis program. The next one-third of the book is an examination of specific equilibrium problems and the programs available to study them. These are divided into chapters devoted to potentiometric, extraction, and spectroscopic methods. The format is to discuss a variety of programs, one at a time, including the parts of the program, the types of problems to which it has been applied, and the program's limitations. A number of problems are then presented, which are representative of the type of questions that are normally addressed by research projects in the area
Study on CexLa1-xO2 Buffer Layer used in Coated Conductors by Chemical Solution Method
DEFF Research Database (Denmark)
Zhao, Yue; Suo, Hongli; Grivel, Jean-Claude
2009-01-01
Developing multi-functional single buffer layer is one of the most important challenges for simplification of coated conductors configuration. Ladoped CeO2 films were prepared by chemical solution method. And surface morphology and texture quality of the La-doped CeO2 films were investigated...... method. It suggects that Ce0.9La0.1O2 film prepared by chemical solution route have a promising prospect for the simplification of coated conductors configuration....
Directory of Open Access Journals (Sweden)
D. Olvera
2015-01-01
Full Text Available We expand the application of the enhanced multistage homotopy perturbation method (EMHPM to solve delay differential equations (DDEs with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.
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SURE KÖME
2014-12-01
Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.
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Djordjevich Alexandar
2017-12-01
Full Text Available The two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finitedifference method for the transport of solutes through a homogenous two-dimensional domain that is finite and porous. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity. Included are the firstorder decay and zero-order production parameters proportional to the seepage velocity, and periodic boundary conditions at the origin and at the end of the domain. Results agree well with analytical solutions that were reported in the literature for special cases. It is shown that the solute concentration profile is influenced strongly by periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in finite media, which is especially important when arbitrary initial and boundary conditions are required.
Born approximation to a perturbative numerical method for the solution of the Schroedinger equation
International Nuclear Information System (INIS)
Adam, Gh.
1978-01-01
A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)
Kinetic determination of As(III in solution
Directory of Open Access Journals (Sweden)
TODOR G. PECEV
2003-10-01
Full Text Available A new reaction is suggested and a new kinetic method is elaborated for the As(III traces determination in solution, on the basis of their catalyzing effect on komplexon III (EDTA oxidation by KMnO4 in a strong acid solution (H2SO4. Using a spectrophotometric technique, a sensitivity of 72 ng/cm3 As(III was achieved. The relative error of method varies from 5.5 to 13.9 % for As(III concentration range from 83 to 140 ng/cm3. Appropriate kinetic equations are formulated and the influence of some other ions, including the As(V, upon the reaction rate is tested.
International Nuclear Information System (INIS)
Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.; Buchan, A. G.; Eaton, M. D.
2009-01-01
This paper describes a new Non-Linear Discontinuous Petrov-Galerkin (NDPG) method and application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The amount of dissipation added acts internal to each element. This is done using a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is designed to be independent of angular expansion framework. This is demonstrated for the both discrete ordinates (S N ) and spherical harmonics (P N ) descriptions of the angular variable. Results show the scheme performs consistently well in demanding time dependent and multi-dimensional radiation transport problems. (authors)
Directory of Open Access Journals (Sweden)
Luyuan Chen
2018-04-01
Full Text Available With the challenge of transportation environment, a large amount of attention is paid to sustainable mobility worldwide, thus bringing the problem of the evaluation of sustainable transport solutions. In this paper, a modified method based on analytical hierarchy process (AHP and Dempster–Shafer evidence theory (D-S theory is proposed for evaluating the impact of transport measures on city sustainability. AHP is adapted to determine the weight of sustainability criteria while D-S theory is used for data fusion of the sustainability assessment. A Transport Sustainability Index (TSI is presented as a primary measure to determine whether transport solutions have a positive impact on city sustainability. A case study of car-sharing is illustrated to show the efficiency of our proposed method. Our modified method has two desirable properties. One is that the BPA is generated with a new modification framework of evaluation levels, which can flexibly manage uncertain information. The other is that the modified method has excellent performance in sensitivity analysis.
Berti, Claudio; Gillespie, Dirk; Bardhan, Jaydeep P; Eisenberg, Robert S; Fiegna, Claudio
2012-07-01
Particle-based simulation represents a powerful approach to modeling physical systems in electronics, molecular biology, and chemical physics. Accounting for the interactions occurring among charged particles requires an accurate and efficient solution of Poisson's equation. For a system of discrete charges with inhomogeneous dielectrics, i.e., a system with discontinuities in the permittivity, the boundary element method (BEM) is frequently adopted. It provides the solution of Poisson's equation, accounting for polarization effects due to the discontinuity in the permittivity by computing the induced charges at the dielectric boundaries. In this framework, the total electrostatic potential is then found by superimposing the elemental contributions from both source and induced charges. In this paper, we present a comparison between two BEMs to solve a boundary-integral formulation of Poisson's equation, with emphasis on the BEMs' suitability for particle-based simulations in terms of solution accuracy and computation speed. The two approaches are the collocation and qualocation methods. Collocation is implemented following the induced-charge computation method of D. Boda et al. [J. Chem. Phys. 125, 034901 (2006)]. The qualocation method is described by J. Tausch et al. [IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 20, 1398 (2001)]. These approaches are studied using both flat and curved surface elements to discretize the dielectric boundary, using two challenging test cases: a dielectric sphere embedded in a different dielectric medium and a toy model of an ion channel. Earlier comparisons of the two BEM approaches did not address curved surface elements or semiatomistic models of ion channels. Our results support the earlier findings that for flat-element calculations, qualocation is always significantly more accurate than collocation. On the other hand, when the dielectric boundary is discretized with curved surface elements, the
American Society for Testing and Materials. Philadelphia
2010-01-01
1.1 These test methods cover procedures for the chemical, mass spectrometric, spectrochemical, nuclear, and radiochemical analysis of nuclear-grade plutonium nitrate solutions to determine compliance with specifications. 1.2 The analytical procedures appear in the following order: Sections Plutonium by Controlled-Potential Coulometry Plutonium by Amperometric Titration with Iron(II) Plutonium by Diode Array Spectrophotometry Free Acid by Titration in an Oxalate Solution 8 to 15 Free Acid by Iodate Precipitation-Potentiometric Titration Test Method 16 to 22 Uranium by Arsenazo I Spectrophotometric Test Method 23 to 33 Thorium by Thorin Spectrophotometric Test Method 34 to 42 Iron by 1,10-Phenanthroline Spectrophotometric Test Method 43 to 50 Impurities by ICP-AES Chloride by Thiocyanate Spectrophotometric Test Method 51 to 58 Fluoride by Distillation-Spectrophotometric Test Method 59 to 66 Sulfate by Barium Sulfate Turbidimetric Test Method 67 to 74 Isotopic Composition by Mass Spectrom...
International Nuclear Information System (INIS)
Sabundjian, Gaiane
1999-01-01
This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)
International Nuclear Information System (INIS)
Terwilliger, Thomas C.; Berendzen, Joel
1999-01-01
The presence of distinct regions of high and low density variation in electron-density maps is found to be a good indicator of the correctness of a heavy-atom solution in the MIR and MAD methods. An automated examination of the native Fourier is tested as a means of evaluation of a heavy-atom solution in MAD and MIR methods for macromolecular crystallography. It is found that the presence of distinct regions of high and low density variation in electron-density maps is a good indicator of the correctness of a heavy-atom solution in the MIR and MAD methods. The method can be used to evaluate heavy-atom solutions during MAD and MIR structure solutions and to determine the handedness of the structure if anomalous data have been measured