Antimicrobial activity of a new preservative for multiuse ophthalmic solutions.

Science.gov (United States)

Ghelardi, Emilia; Celandroni, Francesco; Gueye, Sokhna A; Salvetti, Sara; Campa, Mario; Senesi, Sonia

2013-01-01

The aim of this study was to examine the antimicrobial activity and the preservative efficacy of a novel preservative solution containing sodium hydroxymethyl glycinate (SHMG) and edetate disodium (EDTA), which is used for preservation of some commercial ophthalmic formulations. In vitro susceptibility assays were performed against several gram-positive (Staphylococcus aureus, Staphylococcus epidermidis, and Bacillus cereus) and gram-negative (Escherichia coli and Pseudomonas aeruginosa) bacteria representative of the microbial flora of epithelial surfaces or colonizing the conjunctiva, as well as against Candida albicans and Aspergillus niger. Using different concentrations of SHMG alone or in combination with EDTA, the minimal inhibitory and microbicidal concentrations against these organisms were assessed. In addition, 8 brands of multidose eye drops containing 0.002% SHMG and 0.1% EDTA as preservative were tested for antimicrobial activity using the antimicrobial effectiveness test recommended by the international pharmacopoeias. The minimal inhibitory and bactericidal/fungicidal concentration values of SHMG ranged from 0.0025% to 0.0125% for bacteria and from 0.125% to 0.50% for mold and yeast. Susceptibility testing demonstrated that the addition of EDTA substantially increased the SHMG activity against all bacterial and fungal strains. The preservative effectiveness test was applied to commercial eye drops. All the drop solutions met the criteria reported by the U.S. Pharmacopeia for parenteral and ophthalmic preparations. All products also satisfied the major acceptance criteria of the European Pharmacopeia with respect to the antifungal activity. With regard to the antibacterial activity, the less-stringent criteria of the European Pharmacopeia were fulfilled. The present study demonstrates the efficacy of a novel preservative for ophthalmic solutions (SHMG/EDTA) and its activity in protecting selected commercial artificial tears against microbial

Sensitivity analysis of numerical solutions for environmental fluid problems

International Nuclear Information System (INIS)

Tanaka, Nobuatsu; Motoyama, Yasunori

2003-01-01

In this study, we present a new numerical method to quantitatively analyze the error of numerical solutions by using the sensitivity analysis. If a reference case of typical parameters is one calculated with the method, no additional calculation is required to estimate the results of the other numerical parameters such as more detailed solutions. Furthermore, we can estimate the strict solution from the sensitivity analysis results and can quantitatively evaluate the reliability of the numerical solution by calculating the numerical error. (author)

Exact solutions, numerical relativity and gravitational radiation

International Nuclear Information System (INIS)

Winicour, J.

1986-01-01

In recent years, there has emerged a new use for exact solutions to Einstein's equation as checks on the accuracy of numerical relativity codes. Much has already been written about codes based upon the space-like Cauchy problem. In the case of two Killing vectors, a numerical characteristic initial value formulation based upon two intersecting families of null hypersurfaces has successfully evolved the Schwarzschild and the colliding plane wave vacuum solutions. Here the author discusses, in the context of exact solutions, numerical studies of gravitational radiation based upon the null cone initial value problem. Every stage of progress in the null cone approach has been associated with exact solutions in some sense. He begins by briefly recapping this history. Then he presents two new examples illustrating how exact solutions can be useful

Analysis of numerical solutions for Bateman equations

International Nuclear Information System (INIS)

Loch, Guilherme G.; Bevilacqua, Joyce S.

2013-01-01

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

Cut flowers disinfestation by ionizing radiation, 3: preservative solution treatment of roses

International Nuclear Information System (INIS)

Kikuchi, O.K.; Mastro, N.L. del; Wiendl, F.M.

1995-01-01

This paper presents the results from laboratorial gamma irradiation processing of some mini-rose varieties, normally traded in Brazil. Rosebuds were irradiated in a Gammacell 220 with a single dose of 900 Gy. As the irradiation can accelerate flowers and leaves senescence and inhibit buds opening, conventional preservative solutions of aluminum or hydroxyquinoline sulfate were administered to the cut flowers. The irradiated buds did not open and the preservative solutions failed to promote opening, although the stems were soaked before and after irradiation. The preservative treated flowers maintained the vigor for a period longer than that for the controls and the irradiated ones. (author). 9 refs, 1 fig

Asymptotic preserving and all-regime Lagrange-Projection like numerical schemes: application to two-phase flows in low mach regime

International Nuclear Information System (INIS)

Girardin, Mathieu

2014-01-01

Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author) [fr

Numerical integration of asymptotic solutions of ordinary differential equations

Science.gov (United States)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Computation of Optimal Monotonicity Preserving General Linear Methods

KAUST Repository

Ketcheson, David I.

2009-07-01

Monotonicity preserving numerical methods for ordinary differential equations prevent the growth of propagated errors and preserve convex boundedness properties of the solution. We formulate the problem of finding optimal monotonicity preserving general linear methods for linear autonomous equations, and propose an efficient algorithm for its solution. This algorithm reliably finds optimal methods even among classes involving very high order accuracy and that use many steps and/or stages. The optimality of some recently proposed methods is verified, and many more efficient methods are found. We use similar algorithms to find optimal strong stability preserving linear multistep methods of both explicit and implicit type, including methods for hyperbolic PDEs that use downwind-biased operators.

Influence of a modified preservation solution in kidney transplantation: A comparative experimental study in a porcine model

Directory of Open Access Journals (Sweden)

Mohammad Golriz

2017-03-01

Conclusion: Although the new preservation HTK solution is in several points a well-thought-out modification of the standard HTK solution, its preservation efficacy, at least for kidney preservation in a pig model for 30 hours, seems to be comparable to the current used solutions. A real advantage, however, could be confirmed in clinical settings, where marginal organs may influence the clinical outcome.

Numerical solution of non-linear diffusion problems

International Nuclear Information System (INIS)

Carmen, A. del; Ferreri, J.C.

1998-01-01

This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

Prevention of ischemia-reperfusion lung injury during static cold preservation by supplementation of standard preservation solution with HEMO2life® in pig lung transplantation model.

Science.gov (United States)

Glorion, M; Polard, V; Favereau, F; Hauet, T; Zal, F; Fadel, E; Sage, E

2017-10-25

We describe the results of adding a new biological agent HEMO 2 life ® to a standard preservation solution for hypothermic static lung preservation aiming to improve early functional parameters after lung transplantation. HEMO 2 life ® is a natural oxygen carrier extracted from Arenicola marina with high oxygen affinity developed as an additive to standard organ preservation solutions. Standard preservation solution (Perfadex ® ) was compared with Perfadex ® associated with HEMO 2 life ® and with sham animals after 24 h of hypothermic preservation followed by lung transplantation. During five hours of lung reperfusion, functional parameters and biomarkers expression in serum and in bronchoalveolar lavage fluid (BALF) were measured. After five hours of reperfusion, HEMO 2 life ® group led to significant improvement in functional parameters: reduction of graft vascular resistance (p preservation improves early graft function after prolonged cold ischemia in lung transplantation.

Splenic implant preservation after conservation in lactated Ringer´s solution.

Science.gov (United States)

Matos Filho, Argos Soares DE; Petroianu, Andy; Cardoso, Valbert Nascimento; Vidigal, Paula Vieira Teixeira

2018-01-01

to evaluate the morphology and function of autogenous splenic tissue implanted in the greater omentum, 24 hours after storage in Ringer-lactate solution. we divided 35 male rats into seven groups (n=5): Group 1: no splenectomy; Group 2: total splenectomy without implant; Group 3: total splenectomy and immediate autogenous implant; Group 4: total splenectomy, preservation of the spleen in Ringer-lactate at room temperature, then sliced ​​and implanted; Group 5: total splenectomy, ​​spleen sliced and preserved in Ringer-lactate at room temperature before implantation; Group 6: total splenectomy with preservation of the spleen in Ringer-lactate at 4°C and then sliced ​​and implanted; Group 7: total splenectomy and the spleen sliced for preservation in Ringer-lactate at 4°C before implantation. After 90 days, we performed scintigraphic studies with Tc99m-colloidal tin (liver, lung, spleen or implant and clot), haematological exams (erythrogram, leucometry, platelets), biochemical dosages (protein electrophoresis) and anatomopathological studies. regeneration of autogenous splenic implants occurred in the animals of the groups with preservation of the spleen at 4ºC. The uptake of colloidal tin was higher in groups 1, 3, 6 and 7 compared with the others. There was no difference in hematimetric values ​​in the seven groups. Protein electrophoresis showed a decrease in the gamma fraction in the group of splenectomized animals in relation to the operated groups. the splenic tissue preserved in Ringer-lactate solution at 4ºC maintains its morphological structure and allows functional recovery after being implanted on the greater omentum.

Splenic implant preservation after conservation in lactated Ringer´s solution

Directory of Open Access Journals (Sweden)

ARGOS SOARES DE MATOS FILHO

2018-02-01

Full Text Available ABSTRACT Objective: to evaluate the morphology and function of autogenous splenic tissue implanted in the greater omentum, 24 hours after storage in Ringer-lactate solution. Methods: we divided 35 male rats into seven groups (n=5: Group 1: no splenectomy; Group 2: total splenectomy without implant; Group 3: total splenectomy and immediate autogenous implant; Group 4: total splenectomy, preservation of the spleen in Ringer-lactate at room temperature, then sliced and implanted; Group 5: total splenectomy, spleen sliced and preserved in Ringer-lactate at room temperature before implantation; Group 6: total splenectomy with preservation of the spleen in Ringer-lactate at 4°C and then sliced and implanted; Group 7: total splenectomy and the spleen sliced for preservation in Ringer-lactate at 4°C before implantation. After 90 days, we performed scintigraphic studies with Tc99m-colloidal tin (liver, lung, spleen or implant and clot, haematological exams (erythrogram, leucometry, platelets, biochemical dosages (protein electrophoresis and anatomopathological studies. Results: regeneration of autogenous splenic implants occurred in the animals of the groups with preservation of the spleen at 4ºC. The uptake of colloidal tin was higher in groups 1, 3, 6 and 7 compared with the others. There was no difference in hematimetric values in the seven groups. Protein electrophoresis showed a decrease in the gamma fraction in the group of splenectomized animals in relation to the operated groups. Conclusion: the splenic tissue preserved in Ringer-lactate solution at 4ºC maintains its morphological structure and allows functional recovery after being implanted on the greater omentum.

Cytotoxicity of ophthalmic solutions with and without preservatives to human corneal endothelial cells, epithelial cells and conjunctival epithelial cells.

Science.gov (United States)

Ayaki, Masahiko; Yaguchi, Shigeo; Iwasawa, Atsuo; Koide, Ryohei

2008-08-01

The cytotoxicity of a range of commercial ophthalmic solutions in the presence and absence of preservatives was assessed in human corneal endothelial cells (HCECs), corneal epithelia and conjunctival epithelia using in vitro techniques. Cell survival was measured using the WST-1 assay for endothelial cells and the MTT assay for epithelial cells. Commercially available timolol, carteolol, cromoglicate, diclofenac, bromfenac and hyaluronic acid ophthalmic solutions were assessed for cytotoxicity in the presence and absence of preservatives. The preservatives benzalkonium, chlorobutanol and polysorbate were also tested. The survival of cells exposed to test ophthalmic solutions was expressed as a percentage of cell survival in the control solution (distilled water added to media) after 48 h exposure. HCEC survival was 20-30% in ophthalmic solutions diluted 10-fold. The survival of HCEC was significantly greater in all solutions in the absence of preservative than in the presence of preservative. The survival of corneal and conjunctival epithelia was consistent with that of HCECs for all test ophthalmic solutions. The preservatives polysorbate and benzalkonium were highly cytotoxic with cell survival decreasing to 20% at the concentration estimated in commercial ophthalmic solutions. By comparison, the survival of cells exposed to chlorobutanol was 80% or greater. The cytotoxicity of ophthalmic solutions to HCEC, corneal epithelia and conjunctival epithelia decreased in the absence of preservative.

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

Energy Technology Data Exchange (ETDEWEB)

Allen, Christopher K. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

2017-07-01

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms of a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.

Numerical solution of singularity-perturbed two-point boundary-value problems

International Nuclear Information System (INIS)

Masenge, R.W.P.

1993-07-01

Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

Cytotoxicity and mutagenicity of opthalmic solution preservatives and UVA radiation in L5178Y cells

International Nuclear Information System (INIS)

Withrow, T.J.; Brown, N.T.; Hitchins, V.M.; Strickland, A.G.

1989-01-01

Four preservatives used in ophthalmic solutions were tested for toxic and mutagenic potential in mouse lymphoma cells with and without exposure of cells to ultraviolet A (UVA) radiation. The preservatives tested were benzalkonium chloride (BAK), chlorhexidine, thimerosal and ethylenediaminetetraacetic acid (EDTA). Cell survival and mutagenesis were measured using the L5178Y mouse lymphoma (TK +/- ) system. Cells were exposed to varying amounts of preservatives for 1 h at 37 0 C, and aliquots irradiated with UVA radiation (during exposure to preservative). Cells were then assayed for survival, and mutagenesis at the thymidine kinase (TK) locus. In concentrations commonly found in ophthalmic solutions, BAK, chlorhexidine, and thimerosal were toxic to cells, and thimerosal was slightly mutagenic. When cells were exposed to preservative and UVA radiation, chlorhexidine was mutagenic and the mutagenic activity of thimerosal was enhanced. (author)

Cytotoxicity and mutagenicity of opthalmic solution preservatives and UVA radiation in L5178Y cells

Energy Technology Data Exchange (ETDEWEB)

Withrow, T.J.; Brown, N.T.; Hitchins, V.M.; Strickland, A.G. (Food and Drug Administration, Rockville, MD (USA). Center for Devices and Radiological Health)

1989-09-01

Four preservatives used in ophthalmic solutions were tested for toxic and mutagenic potential in mouse lymphoma cells with and without exposure of cells to ultraviolet A (UVA) radiation. The preservatives tested were benzalkonium chloride (BAK), chlorhexidine, thimerosal and ethylenediaminetetraacetic acid (EDTA). Cell survival and mutagenesis were measured using the L5178Y mouse lymphoma (TK{sup +/-}) system. Cells were exposed to varying amounts of preservatives for 1 h at 37{sup 0}C, and aliquots irradiated with UVA radiation (during exposure to preservative). Cells were then assayed for survival, and mutagenesis at the thymidine kinase (TK) locus. In concentrations commonly found in ophthalmic solutions, BAK, chlorhexidine, and thimerosal were toxic to cells, and thimerosal was slightly mutagenic. When cells were exposed to preservative and UVA radiation, chlorhexidine was mutagenic and the mutagenic activity of thimerosal was enhanced. (author).

Numerically satisfactory solutions of Kummer recurrence relations

NARCIS (Netherlands)

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

2008-01-01

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

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

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

2018-04-01

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

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

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

Coconut water solutions for the preservation of spleen, ovary, and skin autotransplants in rats.

Science.gov (United States)

Schettino César, J M; Petroianu, A; de Souza Vasconcelos, L; Cardoso, V N; das Graças Mota, L; Barbosa, A J A; Vianna Soares, C D; Lima de Oliveira, A

2015-03-01

The purpose of this study was to evaluate the efficacy of coconut water in the preservation of spleen, ovary, and skin autotransplantations in rats. Fifty female Wistar rats were divided randomly into 5 groups on the basis of the following tissue graft preservation solutions: group 1, lactated Ringer's; group 2, Belzer's solution; group 3, mature coconut water; group 4, green coconut water; and group 5, modified green coconut water. In group 5, the green coconut water solution was modified to obtain the same electrolyte composition as Belzer's solution. The spleen, ovaries, and a skin fragment were removed from each animal, stored for 6 hours in one of the solutions, and then re-implanted. The recoveries of tissue functions were assessed 90 days after surgery by means of spleen scintigraphy and blood tests. The implanted tissues were collected for histological analyses. Higher immunoglobulin G levels were observed in the animals of group 5 than in the animals of group 1. Differences in follicle-stimulating hormone levels were observed between groups 1 and 2 (P coconut water group (P coconut water allowed for the preservation of the spleen, ovaries, and skin for 6 hours, and the normal functions of these tissues were maintained in rats. Copyright © 2015 Elsevier Inc. All rights reserved.

[Safety and efficacy of a new preservative-free levocabastine ophthalmic solution (Levofree®) using the conjunctival provocation test].

Science.gov (United States)

Allaire, C; Siou-Mermet, R; Bassols, A

2012-09-01

To evaluate the safety and efficacy of preservative-free levocabastine 0.05 % ophthalmic solution compared to placebo (vehicle) and to preserved levocabastine 0.05 % ophthalmic suspension in the prevention of allergic conjunctivitis induced by a conjunctival provocation test. Ninety-two subjects (18-50 years) with a previous history of allergic conjunctivitis to pollen were randomised to receive either preservative-free levocabastine solution in one eye and preserved levocabastine suspension in the fellow eye (n=69), or preservative-free levocabastine in one eye and placebo in the fellow eye (n=23). One drop of each product was administered 10 minutes (visit 3) and 4 hours (visit 4) prior to the provocation test. The primary efficacy criterion was the sum of the itching and conjunctival hyperemia scores assessed at 3, 5 and 10 minutes after the provocation test. The safety evaluation included adverse events, visual acuity, intra-ocular pressure and study drug drop sensation. The efficacy of the preservative-free solution was significantly higher than that of placebo at all time points (P≤0.01) with one exception at visit 4 (3 minutes after the provocation test). It was significantly higher than that of the preserved suspension at visit 3, and equivalent at visit 4. The incidence of adverse events was lower with the preservative-free solution than with the preserved suspension. 94.2 % and 95.7 % subjects rated preservative-free levocabastine drop sensation as "good" or "very good" at visits 3 and 4 respectively, whereas these rates were 68.1 % and 63.8 % with preserved levocabastine. This difference between the two formulations was highly statistically significant (Ppreservative-free levocabastine was superior to that of the placebo and of the preserved suspension at visit 3, at least as effective as the preserved suspension at visit 4, and better tolerated at each visit. Copyright © 2012 Elsevier Masson SAS. All rights reserved.

Introduction to the numerical solutions of Markov chains

CERN Document Server

Stewart, Williams J

1994-01-01

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

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

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

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

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

2015-01-01

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

Rotationally symmetric numerical solutions to the sine-Gordon equation

DEFF Research Database (Denmark)

Olsen, O. H.; Samuelsen, Mogens Rugholm

1981-01-01

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

On numerical solution of Burgers' equation by homotopy analysis method

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

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

The role of preservation solution on acid-base regulation during machine perfusion of kidneys.

Science.gov (United States)

Baicu, Simona C; Taylor, Michael J; Brockbank, Kelvin G M

2006-01-01

To meet the current clinical organ demand, efficient preservation methods and solutions are needed to increase the number of viable kidneys for transplantation. In the present study, the influence of perfusion solution buffering strength on renal pH dynamics and regulation mechanisms during kidney ex vivo preservation was determined. Porcine kidneys were hypothermically machine perfused for 72 h with either Unisol-UHK or Belzer-Machine Perfusion solution, Belzer-MP solution. Renal perfusate samples were periodically collected and biochemically analyzed. The UHK solution, a Hepes-based solution (35 mM), provided a more efficient control of renal pH that, in turn, resulted in minor changes in the perfusate pH relative to baseline, in response to tissue CO2 and HCO3- production. In the perfusate of Belzer-MP kidney group a wider range of pH values were recorded and a pronounced pH reduction was seen in response to significant rises in pCO2 and HCO3- concentrations. The Belzer-MP solution, containing phosphate (25 mM) as its main buffer, and only 10 mM Hepes, had a greater buffering requirement to attenuate larger pH changes.

Effect of acid Lugol solution as preservative on two representative chitineous and gelatinous zooplankton groups

DEFF Research Database (Denmark)

Jaspers, Cornelia; Carstensen, Jacob

2009-01-01

The estimation of biomass from body lengths to carbon regressions is a common approach in plankton research. Several different chemicals for sample preservation are in use, and conversion factors to account for shrinkage effects exist, but to our knowledge the consequences of using potassium......-iodide and iodine (Lugol solution) as preservative on body sizes of different mesozooplankton groups have not been investigated. We tested the effect of 2% acidified Lugol solution on body sizes over time on two major marine mesozooplankton groups, namely larvaceans and copepods, which are representatives...

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

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

2015-01-01

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

Automatic validation of numerical solutions

DEFF Research Database (Denmark)

Stauning, Ole

1997-01-01

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

Pricing policy for declining demand using item preservation technology.

Science.gov (United States)

Khedlekar, Uttam Kumar; Shukla, Diwakar; Namdeo, Anubhav

2016-01-01

We have designed an inventory model for seasonal products in which deterioration can be controlled by item preservation technology investment. Demand for the product is considered price sensitive and decreases linearly. This study has shown that the profit is a concave function of optimal selling price, replenishment time and preservation cost parameter. We simultaneously determined the optimal selling price of the product, the replenishment cycle and the cost of item preservation technology. Additionally, this study has shown that there exists an optimal selling price and optimal preservation investment to maximize the profit for every business set-up. Finally, the model is illustrated by numerical examples and sensitive analysis of the optimal solution with respect to major parameters.

Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing

Directory of Open Access Journals (Sweden)

Jade Eloise eNorris

2015-07-01

Full Text Available Aging often leads to general cognitive decline in domains such as memory and attention. The effect of aging on numerical cognition, particularly on foundational numerical skills known as the Number Sense, is not well known. Early research focused on the effect of aging on arithmetic. Recent studies have begun to investigate the impact of healthy aging on basic numerical skills, but focused on non-symbolic quantity discrimination alone. Moreover, contradictory findings have emerged. The current study aimed to further investigate the impact of aging on basic non-symbolic and symbolic numerical skills. A group of 25 younger (18-25 and 25 older adults (60-77 participated in non-symbolic and symbolic numerical comparison tasks. Mathematical and spelling abilities were also measured. Results showed that aging had no effect on foundational non-symbolic numerical skills, as both groups performed similarly (RTs, accuracy and Weber fractions (w. All participants showed decreased non-symbolic acuity (accuracy and w in trials requiring inhibition. However, aging appears to be associated with a greater decline in discrimination speed in such trials. Furthermore, aging seems to have a positive impact on mathematical ability and basic symbolic numerical processing, as older participants attained significantly higher mathematical achievement scores, and performed significantly better on the symbolic comparison task than younger participants. The findings suggest that aging and its lifetime exposure to numbers may lead to better mathematical achievement and stronger basic symbolic numerical skills. Our results further support the observation that basic non-symbolic numerical skills are resilient to aging, but that aging may exacerbate poorer performance on trials requiring inhibitory processes. These findings lend further support to the notion that preserved basic numerical skills in aging may reflect the preservation of an innate, primitive and embedded Number

Acid-base buffering in organ preservation solutions as a function of temperature: new parameters for comparing buffer capacity and efficiency.

Science.gov (United States)

Baicu, Simona C; Taylor, Michael J

2002-08-01

Control of acidity and preventing intracellular acidosis are recognized as critical properties of an effective organ preservation solution. Buffer capacity and efficiency are therefore important for comparing the relative merits of preservation fluids for optimum hypothermic storage, but these parameters are not available for the variety of organ preservation solutions of interest in transplantation today. Moreover, buffer capacity is dependent upon both concentration and pH such that buffer capacity is not easily predicted for a complex solution containing multiple buffer species. Using standard electrometric methods to measure acid dissociation constants, this study was undertaken to determine the maximum and relative buffer capacities of a variety of new and commonly used hypothermic preservation solutions as a function of temperature. The reference data provided by these measurements show that comparative buffer capacity and efficiency vary widely between the commonly used solutions. Moreover, the fluids containing zwitterionic sulfonic acid buffers such as Hepes possess superior buffering for alpha-stat pH regulation in the region of physiological importance.

Morphology and function of dog arterial grafts preserved in UW-solution

NARCIS (Netherlands)

Vischjager, M.; van Gulik, T. M.; Pfaffendorf, M.; van Zwieten, P. A.; van Marle, J.; Kromhout, J. G.; Klopper, P. J.; Jacobs, M. J.

1995-01-01

To assess the function of arterial grafts after prolonged preservation in the University of Wisconsin solution (UW), in vitro and in vivo. Carotid arteries were harvested from dogs and stored for 1-21 days at 4 degrees C in UW (n = 10) or in PBS (0.9% NaCl, pH 7.4), (PBS) (n = 10). Slices were

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

International Nuclear Information System (INIS)

Adhikari, S.K.

1979-01-01

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

Numerical solution of electrostatic problems of the accelerator project VICKSI

International Nuclear Information System (INIS)

Janetzki, U.

1975-03-01

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

Efficient numerical solution to vacuum decay with many fields

Energy Technology Data Exchange (ETDEWEB)

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

2017-01-01

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

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

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

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

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2018-01-01

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special

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

International Nuclear Information System (INIS)

Pappas, George

2009-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2009-10-01

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

Numerical solution of distributed order fractional differential equations

Science.gov (United States)

Katsikadelis, John T.

2014-02-01

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

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

International Nuclear Information System (INIS)

Greenspan, D.

2006-01-01

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

Numerical solutions of the Vlasov equation

International Nuclear Information System (INIS)

Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

1985-01-01

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

Stability of fortified cefazolin ophthalmic solutions prepared in artificial tears containing surfactant-based versus oxidant-based preservatives.

Science.gov (United States)

Rojanarata, Theerasak; Tankul, Junlathip; Woranaipinich, Chayanee; Potawanich, Paweena; Plianwong, Samarwadee; Sakulma, Sirinart; Saehuan, Choedchai

2010-10-01

The aim of this study was to investigate the stability of fortified cefazolin sodium ophthalmic solutions (50 mg mL⁻¹) extemporaneously prepared in commercial artificial tears containing 2 different types of preservatives, namely the surfactants and oxidants. Fortified cefazolin sodium solutions were prepared by reconstituting cefazolin for injection with sterile water and further diluted with Tears Naturale II or Natear, 2 commercial artificial tears containing polyquaternium-1 and sodium perborate, respectively, as preservatives. The solutions were then kept at room temperature (28°C) or in the refrigerator (4°C). During the 28-day period, the formulations were periodically examined for the physical appearance, pH, and the remaining drug concentrations. The antibacterial potency was evaluated as the minimal inhibitory concentration against Staphylococcus aureus strain ATCC 29923 by broth dilution technique. The activity of the preservatives was demonstrated by antimicrobial effectiveness tests. On day 28, the microbial contamination in the preparations was tested. The stability profiles of cefazolin solutions prepared in Tears Naturale II, Natear, and water were not different, but they were significantly influenced by the storage temperature. The refrigerated formulations showed no loss of drug and antibacterial potency as well as alteration of physical appearance and pH throughout the 28 days. In contrast, those kept at room temperature showed gradual change in color and odor. The degradation of drug exceeded 10% from day 3 and the decrease of antibacterial potency could be observed at week 3. All cefazolin solutions prepared in artificial tears retained the antimicrobial activity of preservatives and were free from bacterial and fungal contamination throughout the 28-day period of study. Cefazolin sodium ophthalmic solutions can be extemporaneously prepared in Tears Naturale II or Natear without the influence from different types of preservatives used in

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

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

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

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

2008-04-14

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

Changes in Ocular Surface Characteristics after Switching from Benzalkonium Chloride-Preserved Latanoprost to Preservative-Free Tafluprost or Benzalkonium Chloride-Preserved Tafluprost

OpenAIRE

Tokuda, Naoto; Kitaoka, Yasushi; Matsuzawa, Akiko; Tsukamoto, Ayaka; Sase, Kana; Sakae, Shinsuke; Takagi, Hitoshi

2017-01-01

Purpose. The aim of the present study was to examine the effects of switching from Latanoprost ophthalmic solution containing a preservative to preservative-free Tafluprost ophthalmic solution or Tafluprost containing a preservative on ocular surfaces. Materials and Methods. Forty patients (40 eyes) with glaucoma (mean age: 62.0 ± 10.9 years) using Latanoprost with preservative for six months or longer were assigned either to a Tafluprost-containing-preservative group (20 eyes) or preservativ...

Implementing digital preservation in repositories: Knowledge and practices

Directory of Open Access Journals (Sweden)

Caterina Groposo Pavão

2016-09-01

Full Text Available Digital preservation has to be undertaken by institutional repositories, which are responsible for the preservation of the scientific output from academic institutions. However, due to the constant evolution of the field, to gain domain knowledge and recognise best practices is a complex task for people responsible for digital preservation in those institutions. Digital preservation research, practices and solutions address specific problems, such as formats, curation, reference models, authenticity, policies and preservation plans, tools, etc., while stakeholders need an integrated, contextualized and applicable overview. This paper focuses on the implementation of digital preservation in repositories, from the perspective of the team responsible for the project, regarding the necessary knowledge and best practices. Initially, it defines and contextualizes digital preservation repositories. The following section presents a conceptual model of digital preservation, synthesized from conceptual models developed in influential projects in the field, which allows us to identify the domain knowledge in digital preservation. Finally, aspects represented in the model are discussed in the light of the performance of teams implementing digital preservation repositories. It provides recommendations, guides and examples that may be useful for the implementation of digital preservation. It points to the need to strengthen the relationship between domain knowledge in digital preservation repositories with practices developed in numerous projects developed worldwide.

Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

Energy Technology Data Exchange (ETDEWEB)

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

2017-07-01

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

[Optimization of benzalkonium chloride concentration in 0.0015% tafluprost ophthalmic solution from the points of ocular surface safety and preservative efficacy].

Science.gov (United States)

Asada, Hiroyuki; Takaoka-Shichijo, Yuko; Nakamura, Masatsugu; Kimura, Akio

2010-06-01

Optimization of benzalkonium chloride (alkyl dimethylbenzylammonium chloride: BAK) concentration as preservative in 0.0015% tafluprost ophthalmic solution (Tapros 0.0015% ophthalmic solution), an anti-glaucoma medicine, was examined from the points of ocular surface safety and preservative efficacy. BAKC(12), which is dodecyl dimethylbenzylammonium chloride, and BAKmix, which is the mixture of dodecyl, tetradecyl and hexadecyl dimethylbenzylammonium chloride were used in this study. The effects of BAKC(12) concentrations and the BAK types, BAKC(12) and BAKmix, in tafluprost ophthalmic solution on ocular surface safety were evaluated using the in vitro SV 40-immobilized human corneal epithelium cell line (HCE-T). Following treatments of Tafluprost ophthalmic solutions with BAKC(12), its concentration dependency was observed on cell viability of HCE-T. The cell viability of HCE-T after treatment of these solutions with 0.001% to 0.003% BAKC(12) for 5 minutes were the same level as that after treatment of the solution without BAK. Tafluprost ophthalmic solution with 0.01% BAKC(12) was safer for the ocular surface than the same solution with 0.01% BAKmix. Preservatives-effectiveness tests of tafluprost ophthalmic solutions with various concentrations of BAKC(12) were performed according to the Japanese Pharmacopoeia (JP), and solutions with more than 0.0005% BAKC(12) conformed to JP criteria. It was concluded that 0.0005% to 0.003% of BAKC(12) in tafluprost ophthalmic solution was optimal, namely, well-balanced from the points of ocular surface safety and preservative efficacy.

Solution of Milne problem by Laplace transformation with numerical inversion

International Nuclear Information System (INIS)

Campos Velho, H.F. de.

1987-12-01

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

POSTHARVEST QUALITY OF FEIJOA FLOWERS TREATED WITH DIFFERENT PRESERVATIVE SOLUTIONS AND 1-METHYLCYCLOPROPENE

Directory of Open Access Journals (Sweden)

ALEXANDRA GOEDE DE SOUZA

Full Text Available ABSTRACT This study was carried out to assess the postharvest quality preservation of feijoa(Acca sellowiana Berg flowers in response to treatments with different preservative solutions and 1-methylcyclopropene (1-MCP. Recently opened feijoa flowers were harvested in the morning (between 8h and 10h and immediately after pulsed with preservative solutions of salicylic acid, ascorbic acid and sucrose, all at doses of 0 (control, 2, 5 or 10%, and treated with 1-MCP at doses of 0 (control, 250, 500 or 1,000 nL L-1. Each trial with preservative solutions or 1-MCP treatment was a distinct experiment conducted in a completely randomized design with four replicates, each replicate with four flowers. After the treatment, the flowers were stored for 12 days at 10±1 oC and 85±5% RH. At every two-days intervals the flower petals were visually evaluated for wilting and darkening according to a hedonic scale varying from 1 (less intense to 5 (more intense. Petal color was ranked from 1 (intense pink to 5 (white. The 1-MCP at 500 nL L-1 and the salicylic acid (regardless of the dose delayed the changes of petal color for up to eight and six days of storage, respectively. Flowers treated with salicylic acid, 1-MCP or ascorbic acid had a more substantial delay in petal wilting. Flowers treated with salicylic acid had wilting rank of 2 after six days of storage when treated with doses of 5% or 10%, and after eight days when treated with the dose of 2%, while flowers treated with 1-MCP at 500 and 1,000 nL L-1 and ascorbic acid at 2% and 5% had wilting rank of 2 after four days of storage. The most substantial delay of petal darkening (until the fourth day of storage was achieved with 1-MCP at 500 nL L-1.

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

Meurant, Gerard; Golub, Gene.

1982-02-01

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

Splenic implant preservation after conservation in lactated Ringer´s solution

OpenAIRE

MATOS FILHO, ARGOS SOARES DE; PETROIANU, ANDY; CARDOSO, VALBERT NASCIMENTO; VIDIGAL, PAULA VIEIRA TEIXEIRA

2018-01-01

ABSTRACT Objective: to evaluate the morphology and function of autogenous splenic tissue implanted in the greater omentum, 24 hours after storage in Ringer-lactate solution. Methods: we divided 35 male rats into seven groups (n=5): Group 1: no splenectomy; Group 2: total splenectomy without implant; Group 3: total splenectomy and immediate autogenous implant; Group 4: total splenectomy, preservation of the spleen in Ringer-lactate at room temperature, then sliced and implanted; Group 5: tot...

On mesh refinement and accuracy of numerical solutions

NARCIS (Netherlands)

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

1993-01-01

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

The numerical solution of boundary value problems over an infinite domain

International Nuclear Information System (INIS)

Shepherd, M.; Skinner, R.

1976-01-01

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

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

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2015-05-01

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

Reduced Ischemia-Reoxygenation Injury in Rat Intestine After Luminal Preservation With a Tailored Solution

NARCIS (Netherlands)

Roskott, A.M.; Nieuwenhuijs, V.B.; Leuvenink, H.G.D.; Dijkstra, G.; Ottens, P.; de Jager, M.H.; Pereira, P.G.D.; Fidler, V.; Groothuis, G.M.M.; Ploeg, R.J.; de Graaf, I.A.M.

2010-01-01

Background. The intestine is extremely sensitive to ischemic preservation and reoxygenation injury. Current vascular perfusion and cold storage with University of Wisconsin (UW) solution neglect the intestinal lumen and the ongoing mucosal metabolism during hypothermia. This study was designed to

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

Directory of Open Access Journals (Sweden)

Rahman Farnoosh

2014-07-01

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

Effects of some preservative solutions on vase life and keeping quality of snapdragon (Antirrhinum majus L. cut flowers

Directory of Open Access Journals (Sweden)

Abdul-Wasea A. Asrar

2012-01-01

Full Text Available The effect of selected chemical agents used as preservative solutions to improve the keeping quality of cut snapdragon (Antirrhinum majus L. cv. Yellow Butterfly flowers had been studied. These preservative solutions (treatments were: 2% sucrose, 200 ppm 8-hydroxyquinoline sulfate (8-HQS, pulsing treatment with 200 ppm 8-HQS in combination with 2% sucrose for 12 h, pulsing the spikes with 0.2 mM silver thiosulfate (STS for 1 h, pulsing with 0.2 mM STS for 1 h followed by 2% sucrose solution, or distilled water used as control. The results showed that all treatments had improved the keeping quality and vase life of the cut flowers comparing to control ones. Among all these treatments, the 8-HQS plus 2% sucrose treatment showed best water uptake, water balance, percentage of maximum increase in fresh weight of the cut flower stem and vase life which was extended up to 18 days. Moreover, this keeping solution treatment retarded the degradation of chlorophyll as well as carbohydrate of the cut flowers during their postharvest life. It has been concluded that 200 ppm 8-HQS combined with 2% sucrose solution has the potential to be used as a commercial cut flower preservative solution to delay flower senescence, enhance post-harvest quality and prolong the vase life of cut snapdragon flowers.

A comparative study of a preservative-free latanoprost cationic emulsion (Catioprost) and a BAK-preserved latanoprost solution in animal models.

Science.gov (United States)

Daull, Philippe; Buggage, Ronald; Lambert, Grégory; Faure, Marie-Odile; Serle, Janet; Wang, Rong-Fang; Garrigue, Jean-Sébastien

2012-10-01

Benzalkonium chloride (BAK), a common preservative in eye drops, can induce ocular surface toxicity that may decrease glaucoma therapy compliance. The ocular hypotensive effect, pharmacokinetic (PK) profiles, and local tolerance of a preservative-free latanoprost 0.005% cationic emulsion (Catioprost(®)), and a BAK-preserved latanoprost 0.005% solution (Xalatan(®)), were compared. The ocular hypotensive effect was evaluated in monkeys with elevated intraocular pressure (IOP) induced by laser photocoagulation of the trabecular meshwork. Each monkey (n=8) received both latanoprost formulations once daily for 5 consecutive treatment days in a crossover design with at least a 2-week washout period between treatments. IOP was measured at baseline (on day 1, no instillation), on vehicle treatment day (day 0), and on treatment days 1, 3, and 5 before drug instillation and then hourly for 6 h. In rabbits, the ocular and systemic concentrations of latanoprost free acid were determined following a single instillation and the local tolerance of twice daily instillations over 28 days was assessed. Both the preservative-free and BAK-preserved latanoprost formulations shared the same efficacy profile with the maximum IOP reduction occurring 2 h after each morning dose (-15%, -20%, and -26%; -15%, -23%, and -23% on days 1, 3, and 5, respectively) and lasting through 24 h. The equivalence in efficacy was confirmed by the PK data demonstrating similar area under the curves (AUCs). While both formulations were well tolerated, the incidence of conjunctival hyperemia was reduced by 42% with the BAK-free latanoprost cationic emulsion. In animal models, a preservative-free latanoprost cationic emulsion was as effective as Xalatan(®) for lowering IOP with an improved ocular tolerance profile.

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

Numerical solution of the resistive magnetohydrodynamic boundary-layer equations

International Nuclear Information System (INIS)

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

1983-10-01

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

Numerical solution of the radionuclide transport equation

International Nuclear Information System (INIS)

Hadermann, J.; Roesel, F.

1983-11-01

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

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

International Nuclear Information System (INIS)

Kalisch, Henrik; Lenells, Jonatan

2005-01-01

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

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

African Journals Online (AJOL)

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

Numerical solution of the polymer system

Energy Technology Data Exchange (ETDEWEB)

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

1999-05-01

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

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

International Nuclear Information System (INIS)

Kalla, C; Klein, C

2012-01-01

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

Numerical Solution of Differential Algebraic Equations and Applications

DEFF Research Database (Denmark)

Thomsen, Per Grove

2005-01-01

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

Numerical solution of field theories using random walks

International Nuclear Information System (INIS)

Barnes, T.; Daniell, G.J.

1985-01-01

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

Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs

KAUST Repository

Hadjimichael, Yiannis

2017-09-30

A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions

Numerical double layer solutions with ionization

International Nuclear Information System (INIS)

Andersson, D.; Soerensen, J.

1982-08-01

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

Numerical solution of dynamic equilibrium models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

2013-01-01

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

Case studies in the numerical solution of oscillatory integrals

International Nuclear Information System (INIS)

Adam, G.

1992-06-01

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

Solutions manual to accompany An introduction to numerical methods and analysis

CERN Document Server

Epperson, James F

2014-01-01

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

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

Directory of Open Access Journals (Sweden)

Ravi Kanth A.S.V.

2016-01-01

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

Numerical solution of a reaction-diffusion equation

International Nuclear Information System (INIS)

Moyano, Edgardo A.; Scarpettini, Alberto F.

2000-01-01

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

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

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

2nd International Workshop on the Numerical Solution of Markov Chains

CERN Document Server

1995-01-01

Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2014-03-01

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

Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil

Directory of Open Access Journals (Sweden)

Kozel K

2013-04-01

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

Numerical solutions of diffusive logistic equation

International Nuclear Information System (INIS)

Afrouzi, G.A.; Khademloo, S.

2007-01-01

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

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Directory of Open Access Journals (Sweden)

Kryštůfek P.

2014-03-01

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

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

KAUST Repository

Pathmanathan, Pras

2010-06-01

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

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

KAUST Repository

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

2010-01-01

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

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

DEFF Research Database (Denmark)

Quéau, Yvain; Durix, Bastien; Wu, Tao

2018-01-01

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

A privacy-preserving solution for compressed storage and selective retrieval of genomic data.

Science.gov (United States)

Huang, Zhicong; Ayday, Erman; Lin, Huang; Aiyar, Raeka S; Molyneaux, Adam; Xu, Zhenyu; Fellay, Jacques; Steinmetz, Lars M; Hubaux, Jean-Pierre

2016-12-01

In clinical genomics, the continuous evolution of bioinformatic algorithms and sequencing platforms makes it beneficial to store patients' complete aligned genomic data in addition to variant calls relative to a reference sequence. Due to the large size of human genome sequence data files (varying from 30 GB to 200 GB depending on coverage), two major challenges facing genomics laboratories are the costs of storage and the efficiency of the initial data processing. In addition, privacy of genomic data is becoming an increasingly serious concern, yet no standard data storage solutions exist that enable compression, encryption, and selective retrieval. Here we present a privacy-preserving solution named SECRAM (Selective retrieval on Encrypted and Compressed Reference-oriented Alignment Map) for the secure storage of compressed aligned genomic data. Our solution enables selective retrieval of encrypted data and improves the efficiency of downstream analysis (e.g., variant calling). Compared with BAM, the de facto standard for storing aligned genomic data, SECRAM uses 18% less storage. Compared with CRAM, one of the most compressed nonencrypted formats (using 34% less storage than BAM), SECRAM maintains efficient compression and downstream data processing, while allowing for unprecedented levels of security in genomic data storage. Compared with previous work, the distinguishing features of SECRAM are that (1) it is position-based instead of read-based, and (2) it allows random querying of a subregion from a BAM-like file in an encrypted form. Our method thus offers a space-saving, privacy-preserving, and effective solution for the storage of clinical genomic data. © 2016 Huang et al.; Published by Cold Spring Harbor Laboratory Press.

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

International Nuclear Information System (INIS)

Carrera, J.; Melloni, G.

1987-01-01

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

Performance analysis of numeric solutions applied to biokinetics of radionuclides

International Nuclear Information System (INIS)

Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva

2013-01-01

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

Positivity-preserving space-time CE/SE scheme for high speed flows

KAUST Repository

Shen, Hua

2017-03-02

We develop a space-time conservation element and solution element (CE/SE) scheme using a simple slope limiter to preserve the positivity of the density and pressure in computations of inviscid and viscous high-speed flows. In general, the limiter works with all existing CE/SE schemes. Here, we test the limiter on a central Courant number insensitive (CNI) CE/SE scheme implemented on hybrid unstructured meshes. Numerical examples show that the proposed limiter preserves the positivity of the density and pressure without disrupting the conservation law; it also improves robustness without losing accuracy in solving high-speed flows.

Positivity-preserving space-time CE/SE scheme for high speed flows

KAUST Repository

Shen, Hua; Parsani, Matteo

2017-01-01

We develop a space-time conservation element and solution element (CE/SE) scheme using a simple slope limiter to preserve the positivity of the density and pressure in computations of inviscid and viscous high-speed flows. In general, the limiter works with all existing CE/SE schemes. Here, we test the limiter on a central Courant number insensitive (CNI) CE/SE scheme implemented on hybrid unstructured meshes. Numerical examples show that the proposed limiter preserves the positivity of the density and pressure without disrupting the conservation law; it also improves robustness without losing accuracy in solving high-speed flows.

Changes in Ocular Surface Characteristics after Switching from Benzalkonium Chloride-Preserved Latanoprost to Preservative-Free Tafluprost or Benzalkonium Chloride-Preserved Tafluprost

Directory of Open Access Journals (Sweden)

Naoto Tokuda

2017-01-01

Full Text Available Purpose. The aim of the present study was to examine the effects of switching from Latanoprost ophthalmic solution containing a preservative to preservative-free Tafluprost ophthalmic solution or Tafluprost containing a preservative on ocular surfaces. Materials and Methods. Forty patients (40 eyes with glaucoma (mean age: 62.0 ± 10.9 years using Latanoprost with preservative for six months or longer were assigned either to a Tafluprost-containing-preservative group (20 eyes or preservative-free-Tafluprost group (20 eyes. The intraocular pressure, corneal epithelial barrier function (fluorescein uptake concentration with fluorophotometer FL-500, superficial punctate keratopathy (AD classification, and tear film breakup time (TBUT were assessed before switching and at 12 weeks after switching. Results. No significant differences in intraocular pressure were noted after switching in either group. Corneal epithelial barrier function was improved significantly after switching in both the Tafluprost-containing-preservative and the preservative-free-Tafluprost groups. There were no significant differences in AD scores after switching in the Tafluprost-containing-preservative group, but significant improvements were noted in the preservative-free-Tafluprost group. No significant differences in TBUT were noted in the Tafluprost-containing-preservative or preservative-free-Tafluprost groups after switching. Conclusion. After switching from preservative Latanoprost to Tafluprost containing-preservative or preservative-free Tafluprost, corneal epithelial barrier function was improved while the intraocular pressure reduction was retained.

Changes in Ocular Surface Characteristics after Switching from Benzalkonium Chloride-Preserved Latanoprost to Preservative-Free Tafluprost or Benzalkonium Chloride-Preserved Tafluprost.

Science.gov (United States)

Tokuda, Naoto; Kitaoka, Yasushi; Matsuzawa, Akiko; Tsukamoto, Ayaka; Sase, Kana; Sakae, Shinsuke; Takagi, Hitoshi

2017-01-01

The aim of the present study was to examine the effects of switching from Latanoprost ophthalmic solution containing a preservative to preservative-free Tafluprost ophthalmic solution or Tafluprost containing a preservative on ocular surfaces. Forty patients (40 eyes) with glaucoma (mean age: 62.0 ± 10.9 years) using Latanoprost with preservative for six months or longer were assigned either to a Tafluprost-containing-preservative group (20 eyes) or preservative-free-Tafluprost group (20 eyes). The intraocular pressure, corneal epithelial barrier function (fluorescein uptake concentration with fluorophotometer FL-500), superficial punctate keratopathy (AD classification), and tear film breakup time (TBUT) were assessed before switching and at 12 weeks after switching. No significant differences in intraocular pressure were noted after switching in either group. Corneal epithelial barrier function was improved significantly after switching in both the Tafluprost-containing-preservative and the preservative-free-Tafluprost groups. There were no significant differences in AD scores after switching in the Tafluprost-containing-preservative group, but significant improvements were noted in the preservative-free-Tafluprost group. No significant differences in TBUT were noted in the Tafluprost-containing-preservative or preservative-free-Tafluprost groups after switching. After switching from preservative Latanoprost to Tafluprost containing-preservative or preservative-free Tafluprost, corneal epithelial barrier function was improved while the intraocular pressure reduction was retained.

Numerical solution of a model for a superconductor field problem

International Nuclear Information System (INIS)

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

1979-01-01

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

On the numerical solution of fault trees

International Nuclear Information System (INIS)

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

2003-01-01

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

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

Science.gov (United States)

Gómez-Aguilar, J. F.

2018-03-01

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

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

International Nuclear Information System (INIS)

Hazi, G.; Por, G.

1997-01-01

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

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

African Journals Online (AJOL)

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

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

Science.gov (United States)

Park, Chan-Hee; Aral, Mustafa M.

2007-06-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1994-04-01

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

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

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

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

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

Digital Repository Service at National Institute of Oceanography (India)

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

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

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

International Nuclear Information System (INIS)

Novokhatski, Alexander

2011-01-01

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

Effectiveness of ophthalmic solution preservatives: a comparison of latanoprost with 0.02% benzalkonium chloride and travoprost with the sofZia preservative system

OpenAIRE

Ryan, Gerard; Fain, Joel M; Lovelace, Cherie; Gelotte, Karl M

2011-01-01

Abstract Background Although in vitro and in vivo laboratory studies have suggested that benzalkonium chloride (BAK) in topical ophthalmic solutions may be detrimental to corneal epithelial cells, multiple short- and long-term clinical studies have provided evidence supporting the safety of BAK. Despite the conflicting evidence, BAK is the most commonly used preservative in ophthalmic products largely due to its proven antimicrobial efficacy. This study was designed to characterize the antimi...

Comparison of lung preservation solutions in human lungs using an ex vivo lung perfusion experimental model

Directory of Open Access Journals (Sweden)

Israel L. Medeiros

2012-09-01

Full Text Available OBJECTIVE: Experimental studies on lung preservation have always been performed using animal models. We present ex vivo lung perfusion as a new model for the study of lung preservation. Using human lungs instead of animal models may bring the results of experimental studies closer to what could be expected in clinical practice. METHOD: Brain-dead donors whose lungs had been declined by transplantation teams were used. The cases were randomized into two groups. In Group 1, Perfadex®was used for pulmonary preservation, and in Group 2, LPDnac, a solution manufactured in Brazil, was used. An ex vivo lung perfusion system was used, and the lungs were ventilated and perfused after 10 hours of cold ischemia. The extent of ischemic-reperfusion injury was measured using functional and histological parameters. RESULTS: After reperfusion, the mean oxygenation capacity was 405.3 mmHg in Group 1 and 406.0 mmHg in Group 2 (p = 0.98. The mean pulmonary vascular resistance values were 697.6 and 378.3 dyn·s·cm-5, respectively (p =0.035. The mean pulmonary compliance was 46.8 cm H20 in Group 1 and 49.3 ml/cm H20 in Group 2 (p =0.816. The mean wet/dry weight ratios were 2.06 and 2.02, respectively (p=0.87. The mean Lung Injury Scores for the biopsy performed after reperfusion were 4.37 and 4.37 in Groups 1 and 2, respectively (p = 1.0, and the apoptotic cell counts were 118.75/mm² and 137.50/mm², respectively (p=0.71. CONCLUSION: The locally produced preservation solution proved to be as good as Perfadex®. The clinical use of LPDnac may reduce costs in our centers. Therefore, it is important to develop new models to study lung preservation.

Assessing the effectiveness of 30% sodium chloride aqueous solution for the preservation of fixed anatomical specimens: a 5-year follow-up study.

Science.gov (United States)

de Oliveira, Fabrício Singaretti

2014-07-01

Anatomical specimens used in human or veterinary anatomy laboratories are usually prepared with formaldehyde (a cancerous and teratogenic substance), glycerin (an expensive and viscous fluid), or ethanol (which is flammable). This research aimed to verify the viability of an aqueous 30% sodium chloride solution for preservation of anatomical specimens previously fixed with formaldehyde. Anatomical specimens of ruminant, carnivorous, equine, swine and birds were used. All were previously fixed with an aqueous 20% formaldehyde solution and held for 7 days in a 10% aqueous solution of the same active ingredient. During the first phase of the experiment, small specimens of animal tissue previously fixed in formaldehyde were distributed in vials with different concentrations of formaldehyde, with or without 30% sodium chloride solution, a group containing only 30% sodium chloride, and a control group containing only water. During this phase, no contamination was observed in any specimen containing 30% sodium chloride solution, whether alone or in combination with different concentrations of formaldehyde. In the second phase of the experiment, the 30% sodium chloride solution, found to be optimal in the first phase of the experiment, was tested for its long-term preservation properties. For a period of 5 years, the preserved specimens were evaluated three times a week for visual contamination, odors, and changes in color and texture. There was no visual contamination or decay found in any specimen. Furthermore, no strange odors, or changes in color or softness were noted. The 30% sodium chloride solution was determined to be effective in the preservation of anatomic specimens previously fixed in formaldehyde. © 2014 Anatomical Society.

Numerical solution of High-kappa model of superconductivity

Energy Technology Data Exchange (ETDEWEB)

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

1996-12-31

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

Comparing numerical methods for the solutions of the Chen system

International Nuclear Information System (INIS)

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

2007-01-01

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

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

Directory of Open Access Journals (Sweden)

Bolandtalat A.

2016-01-01

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

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

International Nuclear Information System (INIS)

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

1990-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-07-01

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

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

Science.gov (United States)

Holst, Terry L.

1995-01-01

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

Numerical solution of the ekpyrotic scenario in the moduli space approximation

International Nuclear Information System (INIS)

Soerensen, Torquil MacDonald

2005-01-01

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

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

International Nuclear Information System (INIS)

Adam, G.

1979-01-01

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

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

African Journals Online (AJOL)

Nwokem et al.

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

Positivity-preserving CE/SE schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes

KAUST Repository

Shen, Hua

2018-05-28

We construct positivity-preserving space–time conservation element and solution element (CE/SE) schemes for solving the compressible Euler and Navier–Stokes equations on hybrid unstructured meshes consisting of triangular and rectangular elements. The schemes use an a posteriori limiter to prevent negative densities and pressures based on the premise of preserving optimal accuracy. The limiter enforces a constraint for spatial derivatives and does not change the conservative property of CE/SE schemes. Several numerical examples suggest that the proposed schemes preserve accuracy for smooth flows and strictly preserve positivity of densities and pressures for the problems involving near vacuum and very strong discontinuities.

Induction of necrosis and DNA fragmentation during hypothermic preservation of hepatocytes in UW, HTK, and Celsior solutions

NARCIS (Netherlands)

Abrahamse, Salomon L.; van Runnard Heimel, Pieter; Hartman, Robin J.; Chamuleau, Rob A. F. M.; van Gulik, Thomas M.

2003-01-01

Donor cells can be preserved in University of Wisconsin (UW), histidine-tryptophan-ketoglutarate (HTK), or Celsior solution. However, differences in efficacy and mode of action in preventing hypothermia-induced cell injury have not been unequivocally clarified. Therefore, we investigated and

New Numerical Treatment for Solving the KDV Equation

Directory of Open Access Journals (Sweden)

khalid ali

2017-01-01

Full Text Available In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using collocation method with the modified exponential cubic B-spline. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.

Pancreas preservation for pancreas and islet transplantation

Science.gov (United States)

Iwanaga, Yasuhiro; Sutherland, David E.R.; Harmon, James V.; Papas, Klearchos K.

2010-01-01

Purpose of review To summarize advances and limitations in pancreas procurement and preservation for pancreas and islet transplantation, and review advances in islet protection and preservation. Recent findings Pancreases procured after cardiac death, with in-situ regional organ cooling, have been successfully used for islet transplantation. Colloid-free Celsior and histidine-tryptophan-ketoglutarate preservation solutions are comparable to University of Wisconsin solution when used for cold storage before pancreas transplantation. Colloid-free preservation solutions are inferior to University of Wisconsin solution for pancreas preservation prior to islet isolation and transplantation. Clinical reports on pancreas and islet transplants suggest that the two-layer method may not offer significant benefits over cold storage with the University of Wisconsin solution: improved oxygenation may depend on the graft size; benefits in experimental models may not translate to human organs. Improvements in islet yield and quality occurred from pancreases treated with inhibitors of stress-induced apoptosis during procurement, storage, isolation or culture. Pancreas perfusion may be desirable before islet isolation and transplantation and may improve islet yields and quality. Methods for real-time, noninvasive assessment of pancreas quality during preservation have been implemented and objective islet potency assays have been developed and validated. These innovations should contribute to objective evaluation and establishment of improved pancreas preservation and islet isolation strategies. Summary Cold storage may be adequate for preservation before pancreas transplants, but insufficient when pancreases are processed for islets or when expanded donors are used. Supplementation of cold storage solutions with cytoprotective agents and perfusion may improve pancreas and islet transplant outcomes. PMID:18685343

Effect of melatonin on kidney cold ischemic preservation injury

Science.gov (United States)

Aslaner, Arif; Gunal, Omer; Turgut, Hamdi Taner; Celik, Erdal; Yildirim, Umran; Demirci, Rojbin Karakoyun; Gunduz, Umut Riza; Calis, Hasan; Dogan, Sami

2013-01-01

Melatonin is a potent free radical scavenger of reactive oxygen species, nitric oxide synthase inhibitor and a well-known antioxidant secreted from pineal gland. This hormone has been reported to protect tissue from oxidative damage. In this study, we aim to investigate the effect of melatonin on kidney cold ischemia time when added to preservation solution. Thirty male Wistar albino rats were divided equally into three groups; Ringer Lactate (RL) solution, University of Wisconsin (UW) solution with and without melatonin. The serum Lactate Dehydrogenase (LDH) activities of the preservation solutions at 2nd, 24th, 36th, and 48th hours were determined. Tissue malondialdehyde (MDA) levels were also measured and a histological examination was performed at 48th hour. Melatonin that added to preservation solution prevented enzyme elevation and decreased lipid peroxidation in preservation solution when compared to the control group (p<0.05). The histological examination revealed that UW solution containing melatonin significantly prevented the kidney from pathological injury (p<0.05). Melatonin added to preservation solutions such as UW solution seemed to protect the tissue preserved effectively from cold ischemic injury for up to 48 hour. PMID:24179573

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

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

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

Directory of Open Access Journals (Sweden)

Marina Popolizio

2018-01-01

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

Structure-Preserving Methods for the Navier-Stokes-Cahn-Hilliard System to Model Immiscible Fluids

KAUST Repository

Sarmiento, Adel F.

2017-12-03

This work presents a novel method to model immiscible incompressible fluids in a stable manner. Here, the immiscible behavior of the flow is described by the incompressible Navier-Stokes-Cahn-Hilliard model, which is based on a diffuse interface method. We introduce buoyancy effects in the model through the Boussinesq approximation in a consistent manner. A structure-preserving discretization is used to guarantee the linear stability of the discrete problem and to satisfy the incompressibility of the discrete solution at every point in space by construction. For the solution of the model, we developed the Portable Extensible Toolkit for Isogeometric Analysis with Multi-Field discretizations (PetIGA-MF), a high-performance framework that supports structure-preserving spaces. PetIGA-MF is built on top of PetIGA and the Portable Extensible Toolkit for Scientific Computation (PETSc), sharing all their user-friendly, performance, and flexibility features. Herein, we describe the implementation of our model in PetIGA-MF and the details of the numerical solution. With several numerical tests, we verify the convergence, scalability, and validity of our approach. We use highly-resolved numerical simulations to analyze the merging and rising of droplets. From these simulations, we detailed the energy exchanges in the system to evaluate quantitatively the quality of our simulations. The good agreement of our results when compared against theoretical descriptions of the merging, and the small errors found in the energy analysis, allow us to validate our approach. Additionally, we present the development of an unconditionally energy-stable generalized-alpha method for the Swift-Hohenberg model that offers control over the numerical dissipation. A pattern formation example demonstrates the energy-stability and convergence of our method.

Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

Directory of Open Access Journals (Sweden)

F. Hosseini Shekarabi

2016-03-01

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

Numerical solution for heave of expansive soils

International Nuclear Information System (INIS)

Sadrnezhad, S. A.

1999-01-01

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

The numerical solution of ICRF fields in axisymmetric mirrors

International Nuclear Information System (INIS)

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

1986-01-01

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

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

Science.gov (United States)

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

2014-01-01

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

Endothelial cell preservation at hypothermic to normothermic conditions using clinical and experimental organ preservation solutions

NARCIS (Netherlands)

Post, Ivo C. J. H.; de Boon, Wadim M. I.; Heger, Michal; van Wijk, Albert C. W. A.; Kroon, Jeffrey; van Buul, Jaap D.; van Gulik, Thomas M.

2013-01-01

Endothelial barrier function is pivotal for the outcome of organ transplantation. Since hypothermic preservation (gold standard) is associated with cold-induced endothelial damage, endothelial barrier function may benefit from organ preservation at warmer temperatures. We therefore assessed

[Preservation of live eggs of Schistosoma japonicum].

Science.gov (United States)

Lan, Wei-ming; Xie, Shu-ying; Wang, Qin; Jiang, Wei-sheng; Hu, Ren-mei; Ge, Jun; Zeng, Xiao-jun

2015-10-01

To observe the preservation time and activity of miracidium hatching from schistosome eggs preserved in different solutions, so as to obtain the optimal preservation conditions and then provide quality control products for field application. The rectum stool of rabbits infected with Schistosoma japonicum was collected and the coarse fecal residue was removed with a series of sample sieves of 80, 100, 160 and 200 meshes respectively, and then the schistosome eggs were concentrated with the sample sieve of 260 meshes. The concentrated eggs were preserved in 0.9% sodium chloride solution, 1.2% sodium chloride solution, phosphate buffered saline solution (PBS, PH 7.2), 1.0% sucrose solution, and Mili-Q water, respectively, and then were conserved in a 4 °C refrigerator and 15 °C constant temperature incubator, respectively. The preserved eggs were hatched in different time (7-day interval) , the vitality and quantity of the miracidia were observed, and the hatching rates were calculated. Under the condition of 4 °C, the hatching rates of eggs dropped to 0 in 1.0% sucrose solution and 1.2% sodium chloride solution at the 49th and 126th day, respectively, and the hatching rates of eggs in the 0.9% sodium chloride solution and PBS solution dropped to 10% at the 112th day, and the activity of miracidium was weakened since 140th. In the Mili-Q water, the hatching rate dropped less than 10% at the 196th day and the activity of miracidia was weakened since the 280th day. Under the condition of 15 °C, the hatching rate of eggs in different solutions gradually dropped to 0 from the 49th day to 105th day. The eggs preserved in Mili-Q water at the temperature of 4 °C can be used as the positive reference for hatching tests within 196 days.

Numerical solution of modified fokker-planck equation with poissonian input

Czech Academy of Sciences Publication Activity Database

Náprstek, Jiří; Král, Radomil

2010-01-01

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

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

OpenAIRE

Karkar , Sami; Vergez , Christophe; Cochelin , Bruno

2012-01-01

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

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

Directory of Open Access Journals (Sweden)

Elmira Ashpazzadeh

2018-04-01

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

Numerical benchmarking of SPEEDUP trademark against point kinetics solutions

International Nuclear Information System (INIS)

Gregory, M.V.

1993-02-01

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

A note on numerical solution of a parabolic-Schrödinger equation

Science.gov (United States)

Ozdemir, Yildirim; Alp, Mustafa

2016-08-01

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

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

Directory of Open Access Journals (Sweden)

Pimenov Vladimir G.

2017-09-01

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

Random ordinary differential equations and their numerical solution

CERN Document Server

Han, Xiaoying

2017-01-01

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

Six-dimensional localized black holes: Numerical solutions

International Nuclear Information System (INIS)

Kudoh, Hideaki

2004-01-01

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

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

International Nuclear Information System (INIS)

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

De-Gang Wang

2012-01-01

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

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

Institute of Scientific and Technical Information of China (English)

WANG; Shunjin; ZHANG; Hua

2006-01-01

The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

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

Science.gov (United States)

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

2017-08-01

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

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

International Nuclear Information System (INIS)

Foias, C.

1986-01-01

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

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

Directory of Open Access Journals (Sweden)

Nikola V. Georgiev

2003-01-01

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

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

Directory of Open Access Journals (Sweden)

Hakon A. Hoel

2007-07-01

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

Development of numerical solution techniques in the KIKO3D code

International Nuclear Information System (INIS)

Panka, Istvan; Kereszturi, Andras; Hegedus, Csaba

2005-01-01

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

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

NARCIS (Netherlands)

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

2007-01-01

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

Numerical solution for identification of feedback coefficients in nuclear reactors

International Nuclear Information System (INIS)

Ebizuka, Yoshie; Sakai, Hideo

1975-01-01

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

Flexible Bit Preservation on a National Basis

DEFF Research Database (Denmark)

Jurik, Bolette; Nielsen, Anders Bo; Zierau, Eld

2012-01-01

In this paper we present the results from The Danish National Bit Repository project. The project aim was establishment of a system that can offer flexible and sustainable bit preservation solutions to Danish cultural heritage institutions. Here the bit preservation solutions must include support...... of bit safety as well as other requirements like e.g. confidentiality and availability. The Danish National Bit Repository is motivated by the need to investigate and handle bit preservation for digital cultural heritage. Digital preservation relies on the integrity of the bits which digital material...

A cell transportation solution that preserves live circulating tumor cells in patient blood samples

International Nuclear Information System (INIS)

Stefansson, Steingrimur; Adams, Daniel L.; Ershler, William B.; Le, Huyen; Ho, David H.

2016-01-01

Circulating tumor cells (CTCs) are typically collected into CellSave fixative tubes, which kills the cells, but preserves their morphology. Currently, the clinical utility of CTCs is mostly limited to their enumeration. More detailed investigation of CTC biology can be performed on live cells, but obtaining live CTCs is technically challenging, requiring blood collection into biocompatible solutions and rapid isolation which limits transportation options. To overcome the instability of CTCs, we formulated a sugar based cell transportation solution (SBTS) that stabilizes cell viability at ambient temperature. In this study we examined the long term viability of human cancer cell lines, primary cells and CTCs in human blood samples in the SBTS for transportation purposes. Four cell lines, 5 primary human cells and purified human PBMCs were tested to determine the viability of cells stored in the transportation solution at ambient temperature for up to 7 days. We then demonstrated viability of MCF-7 cells spiked into normal blood with SBTS and stored for up to 7 days. A pilot study was then run on blood samples from 3 patients with metastatic malignancies stored with or without SBTS for 6 days. CTCs were then purified by Ficoll separation/microfilter isolation and identified using CTC markers. Cell viability was assessed using trypan blue or CellTracker™ live cell stain. Our results suggest that primary/immortalized cell lines stored in SBTS remain ~90 % viable for > 72 h. Further, MCF-7 cells spiked into whole blood remain viable when stored with SBTS for up to 7 days. Finally, live CTCs were isolated from cancer patient blood samples kept in SBTS at ambient temperature for 6 days. No CTCs were isolated from blood samples stored without SBTS. In this proof of principle pilot study we show that viability of cell lines is preserved for days using SBTS. Further, this solution can be used to store patient derived blood samples for eventual isolation of viable CTCs

A cell transportation solution that preserves live circulating tumor cells in patient blood samples.

Science.gov (United States)

Stefansson, Steingrimur; Adams, Daniel L; Ershler, William B; Le, Huyen; Ho, David H

2016-05-06

Circulating tumor cells (CTCs) are typically collected into CellSave fixative tubes, which kills the cells, but preserves their morphology. Currently, the clinical utility of CTCs is mostly limited to their enumeration. More detailed investigation of CTC biology can be performed on live cells, but obtaining live CTCs is technically challenging, requiring blood collection into biocompatible solutions and rapid isolation which limits transportation options. To overcome the instability of CTCs, we formulated a sugar based cell transportation solution (SBTS) that stabilizes cell viability at ambient temperature. In this study we examined the long term viability of human cancer cell lines, primary cells and CTCs in human blood samples in the SBTS for transportation purposes. Four cell lines, 5 primary human cells and purified human PBMCs were tested to determine the viability of cells stored in the transportation solution at ambient temperature for up to 7 days. We then demonstrated viability of MCF-7 cells spiked into normal blood with SBTS and stored for up to 7 days. A pilot study was then run on blood samples from 3 patients with metastatic malignancies stored with or without SBTS for 6 days. CTCs were then purified by Ficoll separation/microfilter isolation and identified using CTC markers. Cell viability was assessed using trypan blue or CellTracker™ live cell stain. Our results suggest that primary/immortalized cell lines stored in SBTS remain ~90% viable for > 72 h. Further, MCF-7 cells spiked into whole blood remain viable when stored with SBTS for up to 7 days. Finally, live CTCs were isolated from cancer patient blood samples kept in SBTS at ambient temperature for 6 days. No CTCs were isolated from blood samples stored without SBTS. In this proof of principle pilot study we show that viability of cell lines is preserved for days using SBTS. Further, this solution can be used to store patient derived blood samples for eventual isolation of viable CTCs after

Coccidian oöcysts as type-specimens: long-term storage in aqueous potassium dichromate solution preserves DNA.

Science.gov (United States)

Williams, R B; Thebo, P; Marshall, R N; Marshall, J A

2010-05-01

Preservation of the exogenous oöcyst stage of coccidian parasites (phylum Apicomplexa N.D. Levine, 1970) as type-specimens of newly described species has long been problematical. Conventional fixatives have proved unsatisfactory, and compromises such as embedding oöcysts in resin or photographing them are not entirely appropriate for various reasons. As an alternative, chilled potassium dichromate solution (normally used in the laboratory to prevent putrefaction of temporary preparations of live oöcysts) has been tested as a long-term preservative of sporulated oöcysts of Eimeria brunetti P.P. Levine, 1942, E. maxima Tyzzer, 1929, E. mitis Tyzzer, 1929, E. necatrix Johnson, 1930, E. praecox Johnson, 1930 and E. tenella (Railliet & Lucet, 1891) (suborder Eimeriorina Léger, 1911; family Eimeriidae Minchin, 1903). Oöcysts from faeces of chickens Gallus gallus (Linnaeus) were placed in 2.5% w/v aqueous potassium dichromate solution (PDS) and stored in the dark at 4 +/- 2 degrees C. After 23 years in storage, oöcysts of each species were administered orally to chickens and failed to initiate infections, indicating that the oöcysts were dead. Nevertheless, after about 24 years, DNA was still recoverable from the oöcysts, and the original species identifications made by classic parasitological methods were confirmed by polymerase chain reaction assays. Furthermore, after almost 25 years, microscopical examination revealed that the walls and internal structures remained well preserved in 83-98% of the oöcysts of the six species investigated. Hence, PDS is potentially suitable for the long-term preservation of sporulated coccidian oöcysts as type-specimens for taxonomic purposes. The samples used in this study are now in the care of the Natural History Museum, London, UK. It is recommended that they be monitored in like manner, by suitably qualified scientists, at intervals of about 5 years to assess their state of preservation and the recoverability of DNA

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

International Nuclear Information System (INIS)

Makarious, S.H.

1981-08-01

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

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

International Nuclear Information System (INIS)

Wehner, M.F.

1983-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Neuberger, J.M.

1996-12-31

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

Numerical convergence of discrete exterior calculus on arbitrary surface meshes

KAUST Repository

Mohamed, Mamdouh S.

2018-02-13

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires special (Delaunay) triangulations, which complicated the mesh generation process especially for curved surfaces. This paper presents numerical evidence demonstrating that this restriction is unnecessary. Convergence experiments are carried out for various physical problems using both Delaunay and non-Delaunay triangulations. Signed diagonal definition for the key DEC operator (Hodge star) is adopted. The errors converge as expected for all considered meshes and experiments. This relieves the DEC paradigm from unnecessary triangulation limitation.

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.

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

Directory of Open Access Journals (Sweden)

Andrea Lani

2006-01-01

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

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

DEFF Research Database (Denmark)

Celia, Michael A.; Binning, Philip John

1992-01-01

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

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

Directory of Open Access Journals (Sweden)

Henrique Silva Furtado

2009-09-01

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

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

Directory of Open Access Journals (Sweden)

Won-Tak Hong

2016-01-01

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

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

International Nuclear Information System (INIS)

Houfek, Karel

2008-01-01

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

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

International Nuclear Information System (INIS)

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

1999-01-01

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

A holistic approach to bit preservation

DEFF Research Database (Denmark)

Zierau, Eld

2012-01-01

Purpose: The purpose of this paper is to point out the importance of taking a holistic approach to bit preservation when setting out to find an optimal bit preservation solution for specific digital materials. In the last decade there has been an increasing awareness that bit preservation, which ...

Modern High Technology Solutions for Quality and Longterm Vegetable Preservation

International Nuclear Information System (INIS)

Nacheva, I.; Miteva, D.; Todorov, Y.; Loginovska, K.; Tsvetkov, Ts.

2012-01-01

In the publication the authors present the results of the applying of two modern technologies for long term and safe vegetable preservation – freeze-drying and gamma sterilization. The freeze-dried vegetables feature minimum moisture – from 2 – 5% and taste-aroma complex preserved to the highest degree. The carried out gamma sterilization ensures a high microbial purity of the vegetables and guarantees for their long term preservation - up to 5 years in polymer packing, under usual conditions

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

Science.gov (United States)

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

2002-01-01

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

Direct-to-PCR tissue preservation for DNA profiling.

Science.gov (United States)

Sorensen, Amy; Berry, Clare; Bruce, David; Gahan, Michelle Elizabeth; Hughes-Stamm, Sheree; McNevin, Dennis

2016-05-01

Disaster victim identification (DVI) often occurs in remote locations with extremes of temperatures and humidities. Access to mortuary facilities and refrigeration are not always available. An effective and robust DNA sampling and preservation procedure would increase the probability of successful DNA profiling and allow faster repatriation of bodies and body parts. If the act of tissue preservation also released DNA into solution, ready for polymerase chain reaction (PCR), the DVI process could be further streamlined. In this study, we explored the possibility of obtaining DNA profiles without DNA extraction, by adding aliquots of preservative solutions surrounding fresh human muscle and decomposing human muscle and skin tissue samples directly to PCR. The preservatives consisted of two custom preparations and two proprietary solutions. The custom preparations were a salt-saturated solution of dimethyl sulfoxide (DMSO) with ethylenediaminetetraacetic (EDTA) and TENT buffer (Tris, EDTA, NaCl, Tween 20). The proprietary preservatives were DNAgard (Biomatrica(®)) and Tissue Stabilising Kit (DNA Genotek). We obtained full PowerPlex(®) 21 (Promega) and GlobalFiler(®) (Life Technologies) DNA profiles from fresh and decomposed tissue preserved at 35 °C for up to 28 days for all four preservatives. The preservative aliquots removed from the fresh muscle tissue samples had been stored at -80 °C for 4 years, indicating that long-term archival does not diminish the probability of successful DNA typing. Rather, storage at -80 °C seems to reduce PCR inhibition.

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

International Nuclear Information System (INIS)

Meyer-Spasche, R.

1975-12-01

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

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

Directory of Open Access Journals (Sweden)

Slouka Martin

2016-01-01

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

Numerical solutions of differential equations of an ionization chamber

International Nuclear Information System (INIS)

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

1998-01-01

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

Numerical solution of plasma fluid equations using locally refined grids

International Nuclear Information System (INIS)

Colella, P.

1997-01-01

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

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

Science.gov (United States)

Felici, Helene M.; Drela, Mark

1993-01-01

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

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

Science.gov (United States)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

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

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

Science.gov (United States)

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

2014-01-01

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

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

Science.gov (United States)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

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

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

Science.gov (United States)

Hossain, Murshed; Mullan, D. J.

1990-01-01

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

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

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Valášek J.

2016-01-01

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

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

Science.gov (United States)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

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

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

OpenAIRE

El-Sayed, Amr A.

2006-01-01

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

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

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

2014-01-01

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

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

International Nuclear Information System (INIS)

Martell, M.; Vaughn, P.

1999-01-01

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

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

Directory of Open Access Journals (Sweden)

Qicheng Meng

2016-04-01

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

A Privacy-Preserving Distributed Optimal Scheduling for Interconnected Microgrids

Directory of Open Access Journals (Sweden)

Nian Liu

2016-12-01

Full Text Available With the development of microgrids (MGs, interconnected operation of multiple MGs is becoming a promising strategy for the smart grid. In this paper, a privacy-preserving distributed optimal scheduling method is proposed for the interconnected microgrids (IMG with a battery energy storage system (BESS and renewable energy resources (RESs. The optimal scheduling problem is modeled to minimize the coalitional operation cost of the IMG, including the fuel cost of conventional distributed generators and the life loss cost of BESSs. By using the framework of the alternating direction method of multipliers (ADMM, a distributed optimal scheduling model and an iteration solution algorithm for the IMG is introduced; only the expected exchanging power (EEP of each MG is required during the iterations. Furthermore, a privacy-preserving strategy for the sharing of the EEP among MGs is designed to work with the mechanism of the distributed algorithm. According to the security analysis, the EEP can be delivered in a cooperative and privacy-preserving way. A case study and numerical results are given in terms of the convergence of the algorithm, the comparison of the costs and the implementation efficiency.

Numerical modeling of solute transport in deformable unsaturated layered soil

Directory of Open Access Journals (Sweden)

Sheng Wu

2017-07-01

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

Assessment of reagent effectiveness and preservation methods for equine faecal samples

Directory of Open Access Journals (Sweden)

Eva Vavrouchova

2015-03-01

Full Text Available The aim of our study was to identify the most suitable flotation solution and effective preservation method for the examination of equine faeces samples using the FLOTAC technique. Samples from naturally infected horses were transported to the laboratory andanalysed accordingly. The sample from each horse was homogenized and divided into four parts: one was frozen, another two were preserved in different reagents such as sodium acetate-acetic-acid–formalin (SAF or 5% formalin.The last part was examined as a fresh sample in three different flotation solutions (Sheather´s solution, sodium chloride and sodium nitrate solution, all with a specific gravity 1.200. The preserved samples were examined in the period from 14 to21days after collection. According to our results, the sucrose solution was the most suitable flotation solution for fresh samples (small strongyle egg per gram was 706 compared to 360 in sodium chlorid and 507 in sodium nitrate and the sodium nitrate solution was the most efficient for the preserved samples (egg per gram was 382 compared to 295 in salt solution and 305 in sucrose solution. Freezing appears to be the most effective method of sample preservation, resulting in minimal damage to fragile strongyle eggs and therefore it is the most simple and effective preservation method for the examination of large numbers of faecal samples without the necessity of examining them all within 48 hours of collection. Deep freezing as a preservation method for equine faeces samples has not, according to our knowledge, been yet published.

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

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

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

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

Science.gov (United States)

Lötstedt, Erik; Jentschura, Ulrich D

2009-02-01

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

Relaxation and Numerical Approximation of a Two-Fluid Two-Pressure Diphasic Model

International Nuclear Information System (INIS)

Ambroso, A.; Chalons, Ch.; Galie, Th.; Chalons, Ch.; Coquel, F.; Coquel, F.

2009-01-01

This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach. (authors)

THE EFFECT OF HERBAL ESSENTIAL OIL IN PRESERVATIVE SOLUTION, ON QUANTITATIVE, VASE LIFE, BACTERIA-INDUCED STEM XYLEM BLOCKAGE OF LISIANTHUS VAR. ECHO

Directory of Open Access Journals (Sweden)

Farzaneh Pourianejad

2014-06-01

Full Text Available In this study the effect of essential oil taken from medicinal plant as antibacterial components in preservative solution of Lisianthus var. Echo (Eustoma grandiflorum was investigated. The test was done with application of preservative solution. Cut flowers were treated with different concentrations of Thyme (Thymus vulgaris, Spearmint (Mentha spicata and Lavender (Lavandula officinalis essential oil in addition to Sucrose 2.5%. The results showed that there was the longest time in vase life with Thyme in 50 ppm (15.6 days and the control treatment showed the shortest vase life (11.6 days. Moreover, Thyme with 50 ppm had the highest effect on relative fresh weight and solution uptake. In addition, bacteria-induced stem xylem blockage, extracted from the end of stem, was cultured in NA medium culture with several concentrations of essential oil. The result showed that in pure concentration (100% inhibition was completed and in various concentrations of essential oil the bacterial population was reduced.

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

Directory of Open Access Journals (Sweden)

Petráš Ivo

2011-01-01

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

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

International Nuclear Information System (INIS)

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

2008-01-01

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

Liquid growth hormone: preservatives and buffers

DEFF Research Database (Denmark)

Kappelgaard, Anne-Marie; Anders, Bojesen; Skydsgaard, Karen

2004-01-01

injection are dependent on the preservative used in the formulation and the concentration of GH. Injection pain may also be related to the buffer substance and injection volume. A liquid formulation of GH, Norditropi SimpleXx, has been developed that dispenses with the need for reconstitution before...... solution. More pain was also reported following large volume injections and following injections with solutions containing high protein concentrations. In summary, optimization of the preservative and buffer content of a liquid GH formulation may reduce injection pain and lead to improved patient...... administration. The formulation uses phenol (3 mg/ml) as a preservative (to protect product from microbial degradation or contamination) and histidine as a buffer. Alternative preservatives used in other GH formulations include m-cresol (9 mg/ml) and benzyl alcohol (3-9 mg/ml). Buffering agents include citrate...

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

International Nuclear Information System (INIS)

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

2005-01-01

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

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

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

2012-01-01

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

Solved problems in classical mechanics analytical and numerical solutions with comments

CERN Document Server

de Lange, O L

2010-01-01

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

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

KAUST Repository

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

2015-01-01

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

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

KAUST Repository

Frohne, Jörg

2015-08-06

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

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

International Nuclear Information System (INIS)

Walters, W.F.

1983-01-01

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

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

OpenAIRE

GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

2016-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

Improved biochemical preservation of lung slices during cold storage.

Science.gov (United States)

Bull, D A; Connors, R C; Reid, B B; Albanil, A; Stringham, J C; Karwande, S V

2000-05-15

Development of lung preservation solutions typically requires whole-organ models which are animal and labor intensive. These models rely on physiologic rather than biochemical endpoints, making accurate comparison of the relative efficacy of individual solution components difficult. We hypothesized that lung slices could be used to assess preservation of biochemical function during cold storage. Whole rat lungs were precision cut into slices with a thickness of 500 microm and preserved at 4 degrees C in the following solutions: University of Wisconsin (UW), Euro-Collins (EC), low-potassium-dextran (LPD), Kyoto (K), normal saline (NS), or a novel lung preservation solution (NPS) developed using this model. Lung biochemical function was assessed by ATP content (etamol ATP/mg wet wt) and capacity for protein synthesis (cpm/mg protein) immediately following slicing (0 h) and at 6, 12, 18, and 24 h of cold storage. Six slices were assayed at each time point for each solution. The data were analyzed using analysis of variance and are presented as means +/- SD. ATP content was significantly higher in the lung slices stored in NPS compared with all other solutions at each time point (P cold storage. Copyright 2000 Academic Press.

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

Science.gov (United States)

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

2016-01-01

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

User Experience and Heritage Preservation

Science.gov (United States)

Orfield, Steven J.; Chapman, J. Wesley; Davis, Nathan

2011-01-01

In considering the heritage preservation of higher education campus buildings, much of the attention gravitates toward issues of selection, cost, accuracy, and value, but the model for most preservation projects does not have a clear method of achieving the best solutions for meeting these targets. Instead, it simply relies on the design team and…

Oxidative Damage in Erythrocytes During Cold Storage With Organ Preservation Solution

OpenAIRE

MEMMEDOĞLU, Akif B.

1999-01-01

It is known that erythrocyte aggregation in renal tissue during preserva-tion is cause of microcirculation defects in the reperfusion period. The aim of our study is to investigate oxidative damage in erythrocytes relative to the time of cold ischemia during organ preservation and relationship between lipid peroxidation and development of these damages. In experiments with a rabbit model, explanted kidneys were exposed to perfusion and 96 hours preservation with Euro-Collins (EC) in the 1...

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

International Nuclear Information System (INIS)

Esmail, S.F.H.

2011-01-01

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

Indiana Pavement Preservation Program

OpenAIRE

Ong, Ghim Ping (Raymond); Nantung, Tommy E.; Sinha, Kumares C.

2010-01-01

State highway agencies are facing immense pressure to maintain roads at acceptable levels amidst the challenging financial and economic situations. In recent years, pavement preservation has been sought as a potential alternative for managing the pavement assets, believing that it would provide a cost-effective solution in maintaining infrastructural conditions and meeting user expectations. This study explores the potential of pavement preservation concepts in managing the agency‘s pavement ...

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

DEFF Research Database (Denmark)

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

A note on numerical solution to the problem of criticality

International Nuclear Information System (INIS)

Kyncl, J.

2002-01-01

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

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

Science.gov (United States)

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

1974-01-01

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

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

Science.gov (United States)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

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

Effectiveness of ophthalmic solution preservatives: a comparison of latanoprost with 0.02% benzalkonium chloride and travoprost with the sofZia preservative system

Directory of Open Access Journals (Sweden)

Lovelace Cherie

2011-04-01

Full Text Available Abstract Background Although in vitro and in vivo laboratory studies have suggested that benzalkonium chloride (BAK in topical ophthalmic solutions may be detrimental to corneal epithelial cells, multiple short- and long-term clinical studies have provided evidence supporting the safety of BAK. Despite the conflicting evidence, BAK is the most commonly used preservative in ophthalmic products largely due to its proven antimicrobial efficacy. This study was designed to characterize the antimicrobial performance of two commonly used topical ocular hypotensive agents that employ different preservative systems: latanoprost 0.005% with 0.02% BAK and travoprost 0.004% with sofZia, a proprietary ionic buffer system. Methods Each product was tested for antimicrobial effectiveness by European Pharmacopoeia A (EP-A standards, the most stringent standards of the three major compendia, which specify two early sampling time points (6 and 24 hours not required by the United States Pharmacopeia or Japanese Pharmacopoeia. Aliquots were inoculated with between 105 and 106 colony-forming units of the test organisms: Staphylococcus aureus, Pseudomonas aeruginosa, Escherichia coli, Candida albicans and Aspergillus brasiliensis. Sampling and enumeration were conducted at protocol-defined time points through 28 days. Results BAK-containing latanoprost met EP-A criteria by immediately reducing all bacterial challenge organisms to the test sensitivity and fungal challenges within the first six hours while the preservative activity of travoprost with sofZia did not. Complete bacterial reduction by travoprost with sofZia was not shown until seven days into the test, and fungal reduction never exceeded the requisite 2 logs during the 28-day test. Travoprost with sofZia also did not meet EP-B criteria due to its limited effectiveness against Staphylococcus aureus. Both products satisfied United States and Japanese pharmacopoeial criteria. Conclusions Latanoprost with 0

Effectiveness of ophthalmic solution preservatives: a comparison of latanoprost with 0.02% benzalkonium chloride and travoprost with the sofZia preservative system.

Science.gov (United States)

Ryan, Gerard; Fain, Joel M; Lovelace, Cherie; Gelotte, Karl M

2011-04-21

Although in vitro and in vivo laboratory studies have suggested that benzalkonium chloride (BAK) in topical ophthalmic solutions may be detrimental to corneal epithelial cells, multiple short- and long-term clinical studies have provided evidence supporting the safety of BAK. Despite the conflicting evidence, BAK is the most commonly used preservative in ophthalmic products largely due to its proven antimicrobial efficacy. This study was designed to characterize the antimicrobial performance of two commonly used topical ocular hypotensive agents that employ different preservative systems: latanoprost 0.005% with 0.02% BAK and travoprost 0.004% with sofZia, a proprietary ionic buffer system. Each product was tested for antimicrobial effectiveness by European Pharmacopoeia A (EP-A) standards, the most stringent standards of the three major compendia, which specify two early sampling time points (6 and 24 hours) not required by the United States Pharmacopeia or Japanese Pharmacopoeia. Aliquots were inoculated with between 10(5) and 10(6) colony-forming units of the test organisms: Staphylococcus aureus, Pseudomonas aeruginosa, Escherichia coli, Candida albicans and Aspergillus brasiliensis. Sampling and enumeration were conducted at protocol-defined time points through 28 days. BAK-containing latanoprost met EP-A criteria by immediately reducing all bacterial challenge organisms to the test sensitivity and fungal challenges within the first six hours while the preservative activity of travoprost with sofZia did not. Complete bacterial reduction by travoprost with sofZia was not shown until seven days into the test, and fungal reduction never exceeded the requisite 2 logs during the 28-day test. Travoprost with sofZia also did not meet EP-B criteria due to its limited effectiveness against Staphylococcus aureus. Both products satisfied United States and Japanese pharmacopoeial criteria. Latanoprost with 0.02% BAK exhibited more effective microbial protection than

Algebraic dynamics algorithm: Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Institute of Scientific and Technical Information of China (English)

WANG ShunJin; ZHANG Hua

2007-01-01

Based on the exact analytical solution of ordinary differential equations,a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm.A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models.The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision,and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

Algebraic dynamics algorithm:Numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm

Institute of Scientific and Technical Information of China (English)

2007-01-01

Based on the exact analytical solution of ordinary differential equations, a truncation of the Taylor series of the exact solution to the Nth order leads to the Nth order algebraic dynamics algorithm. A detailed numerical comparison is presented with Runge-Kutta algorithm and symplectic geometric algorithm for 12 test models. The results show that the algebraic dynamics algorithm can better preserve both geometrical and dynamical fidelity of a dynamical system at a controllable precision, and it can solve the problem of algorithm-induced dissipation for the Runge-Kutta algorithm and the problem of algorithm-induced phase shift for the symplectic geometric algorithm.

Improved biochemical preservation of heart slices during cold storage.

Science.gov (United States)

Bull, D A; Reid, B B; Connors, R C; Albanil, A; Stringham, J C; Karwande, S V

2000-01-01

Development of myocardial preservation solutions requires the use of whole organ models which are animal and labor intensive. These models rely on physiologic rather than biochemical endpoints, making accurate comparison of the relative efficacy of individual solution components difficult. We hypothesized that myocardial slices could be used to assess preservation of biochemical function during cold storage. Whole rat hearts were precision cut into slices with a thickness of 200 microm and preserved at 4 degrees C in one of the following solutions: Columbia University (CU), University of Wisconsin (UW), D5 0.2% normal saline with 20 meq/l KCL (QNS), normal saline (NS), or a novel cardiac preservation solution (NPS) developed using this model. Myocardial biochemical function was assessed by ATP content (etamoles ATP/mg wet weight) and capacity for protein synthesis (counts per minute (cpm)/mg protein) immediately following slicing (0 hours), and at 6, 12, 18, and 24 hours of cold storage. Six slices were assayed at each time point for each solution. The data were analyzed using analysis of variance and are presented as the mean +/- standard deviation. ATP content was higher in the heart slices stored in the NPS compared to all other solutions at 6, 12, 18 and 24 hours of cold storage (p cold storage (p cold storage.

Preservative loss from silicone tubing during filling processes.

Science.gov (United States)

Saller, Verena; Matilainen, Julia; Rothkopf, Christian; Serafin, Daniel; Bechtold-Peters, Karoline; Mahler, Hanns-Christian; Friess, Wolfgang

2017-03-01

Significant loss of preservative was observed during filling of drug products during filling line stops. This study evaluated the losses of three commonly used preservatives in protein drugs, i.e. benzyl alcohol, phenol, and m-cresol. Concentration losses during static incubation were quantified and interpreted with regard to the potential driving forces for the underlying sorption, diffusion, and desorption steps. Partitioning from the solution into the silicone polymer was identified as the most decisive parameter for the extent of preservative loss. Additionally, the influence of tubing inner diameter, starting concentration as well as silicone tubing type was evaluated. Theoretical calculations assuming equilibrium between solution and tubing inner surface and one-directional diffusion following Fick's first law were used to approximate experimental data. Since significant losses were found already after few minutes, adequate measures must be taken to avoid deviations during filling of preservative-containing protein solutions that may impact product quality or antimicrobial efficacy. As a possible alternative to the highly permeable silicone tubing, a specific make of fluoropolymer tubing was identified being suitable for peristaltic pumps and not showing any preservative losses. Copyright © 2016 Elsevier B.V. All rights reserved.

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

International Nuclear Information System (INIS)

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

2007-01-01

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

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

Science.gov (United States)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

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

Numerical solution of ordinary differential equations

CERN Document Server

Fox, L

1987-01-01

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

Numerical solution of the Schroedinger equation with a polynomial potential

International Nuclear Information System (INIS)

Campoy, G.; Palma, A.

1986-01-01

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

Long-time behavior in numerical solutions of certain dynamical systems

International Nuclear Information System (INIS)

Vazquez, L.

1987-01-01

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

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

Directory of Open Access Journals (Sweden)

Roman Cherniha

2016-06-01

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

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

Directory of Open Access Journals (Sweden)

Markou A.A.

2018-03-01

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

A Holistic Approach to Bit Preservation

DEFF Research Database (Denmark)

Zierau, Eld Maj-Britt Olmütz

2011-01-01

This thesis presents three main results for a holistic approach to bit preservation, where the ultimate goal is to find the optimal bit preservation strategy for specific digital material that must be digitally preserved. Digital material consists of sequences of bits, where a bit is a binary digit...... which can have the value 0 or 1. Bit preservation must ensure that the bits remain intact and readable in the future, but bit preservation is not concerned with how bits can be interpreted as e.g. an image. A holistic approach to bit preservation includes aspects that influence the final choice of a bit...... a holistic approach and include aspects of digital representation, confidentiality, availability, bit safety and costs when defining requirements for the bit preservation. Analysis of such requirements and choice of the final bit preservation solution can be supported by the three main results presented...

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

Science.gov (United States)

Crevoisier, David; Voltz, Marc

2013-04-01

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

The mixture of liquid foam soap, ethanol and citric acid as a new fixative-preservative solution in veterinary anatomy.

Science.gov (United States)

Turan, Erkut; Gules, Ozay; Kilimci, Figen Sevil; Kara, Mehmet Erkut; Dilek, Omer Gurkan; Sabanci, Seyyid Said; Tatar, Musa

2017-01-01

The present study investigates the efficiency of liquid foam soap, ethanol, citric acid and benzalkonium chloride as a fixative-preservative solution (a soap-and ethanol-based fixing solution, or SEFS). In this study, ethanol serves as the fixative and preservative, liquid foam soap as the modifying agent, citric acid as the antioxidant and benzalkonium chloride as the disinfectant. The goat cadavers perfused with SEFS (n=8) were evaluated over a period of one year with respect to hardness, colour and odour using objective methods. Colour and hardness were compared between one fresh cadaver and the SEFS-embalmed cadavers. Histological and microbiological examinations were also performed in tissue samples. Additionally, the cadavers were subjectively evaluated after dissection and palpation. The SEFS provided the effectiveness expected over a 1-year embalming period for the animal cadavers. No bacteria or fungi were isolated except for some non-pathogenic Bacillus species. Visible mould was not present on either cadavers or in the surrounding environment. The cadavers maintained an appearance close to their original anatomical appearance, with muscles having good hardness and elasticity for dissection. Copyright © 2016 Elsevier GmbH. All rights reserved.

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

Science.gov (United States)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

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

Stability studies of oxytetracycline in methanol solution

Science.gov (United States)

Wang, Wei; Wu, Nan; Yang, Jinghui; Zeng, Ming; Xu, Chenshan; Li, Lun; Zhang, Meng; Li, Liting

2018-02-01

As one kind of typical tetracycline antibiotics, antibiotic residues of oxytetracycline have been frequently detected in many environmental media. In this study, the stability of oxytetracycline in methanol solution was investigated by high-performance liquid chromatography combined with UV-vis (HPLC-UV). The results show that the stability of oxytetracycline in methanol solution is highly related to its initial concentration and the preserved temperature. Under low temperature condition, the solution was more stable than under room temperature preservation. Under the same temperature preservation condition, high concentrations of stock solutions are more stable than low concentrations. The study provides a foundation for preserving the oxytetracycline-methanol solution.

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

Directory of Open Access Journals (Sweden)

Andresa Pescador

2016-04-01

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

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

International Nuclear Information System (INIS)

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

1993-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-08-01

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

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

Directory of Open Access Journals (Sweden)

Dmitry V. Lukyanenko

2017-01-01

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

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

Directory of Open Access Journals (Sweden)

SURE KÖME

2014-12-01

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

Preservation Copying Endangered Historic Negative Collections

DEFF Research Database (Denmark)

Kejser, Ulla Bøgvad

2008-01-01

This article discusses preservation copying of unstable B&W nitrate and acetate still photographic negatives. It focuses on evaluating two different strategies for preserving the copies from a point of view of quality and cost-effectiveness. The evaluated strategies are preservation of the master...... by describing essential characteristics of negatives, which must be passed on to the copies, and the required metadata and technical imaging specifications. Next the paper discusses strategies for preservation and makes an analysis with the LIFE2 Costing Model. The paper concludes that the most beneficial...... and cost-effective preservation solution for large format negatives is to keep the preservation copies as digital files. However, it also acknowledges that it is important to revisit such strategies regularly to monitor changes in user expectations, technologies and costs....

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

Science.gov (United States)

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

2018-05-01

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

Multiresolution strategies for the numerical solution of optimal control problems

Science.gov (United States)

Jain, Sachin

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

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

International Nuclear Information System (INIS)

Wang, Yaqi

2012-01-01

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

Numerical analysis

CERN Document Server

Rao, G Shanker

2006-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-10-15

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

Integral-preserving integrators

International Nuclear Information System (INIS)

McLaren, D I; Quispel, G R W

2004-01-01

Ordinary differential equations having a first integral may be solved numerically using one of several methods, with the integral preserved to machine accuracy. One such method is the discrete gradient method. It is shown here that the order of the method can be bootstrapped repeatedly to higher orders of accuracy. The method is illustrated using the Henon-Heiles system. (letter to the editor)

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

Science.gov (United States)

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

2017-02-01

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

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

Science.gov (United States)

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

Structure-preserving algorithms for oscillatory differential equations II

CERN Document Server

Wu, Xinyuan; Shi, Wei

2015-01-01

This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods.  The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and sc...

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

International Nuclear Information System (INIS)

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

2008-01-01

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

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

Science.gov (United States)

Hu, Jiancheng

2016-01-01

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

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

NARCIS (Netherlands)

Rienstra, S.W.; Eversman, W.

2001-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

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

International Nuclear Information System (INIS)

Karabulut, Halit; Ipci, Duygu; Cinar, Can

2016-01-01

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

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

International Nuclear Information System (INIS)

Vasileva, D.P.

1993-01-01

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

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Glycerol and microwave preservation of annual statice (Limonium sinuatum Mill.)

International Nuclear Information System (INIS)

Paparozzi, E.T.; McCallister, D.E.

1988-01-01

Stems of annual statice (Limonium sinuatum Mill.) were harvested from the field in 1982 and soaked in varying concentrations of glycerol: water solutions for 24 and 48 h and then microwaved for 0, 1, 3 or 5 min. Half of the branch stems were measured for flexibility, with the remainder being assessed 1 year later. Stems harvested in 1983 were wet- and dry-stored at 3°C for varying lengths of time and then preserved. Preservation was best when statice was preserved immediately. Cold storage decreased preserved statice flexibility, but was better than air-drying. Fresh cut statice stems, up to 34 cm long, should be preserved by soaking in a 1:2 or 1:3 glycerol: water solution for 48 h followed by microwaving for 1 min at medium-high (34°C)

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

Science.gov (United States)

Gupta, K. K.

1975-01-01

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

On the formation, growth, and shapes of solution pipes - insights from numerical modeling

Science.gov (United States)

Szymczak, Piotr; Tredak, Hanna; Upadhyay, Virat; Kondratiuk, Paweł; Ladd, Anthony J. C.

2015-04-01

Cylindrical, vertical structures called solution pipes are a characteristic feature of epikarst, encountered in different parts of the world, both in relatively cold areas such as England and Poland (where their formation is linked to glacial processes) [1] and in coastal areas in tropical or subtropical climate (Bermuda, Australia, South Africa, Caribbean, Mediterranean) [2,3]. They are invariably associated with weakly cemented, porous limestones and relatively high groundwater fluxes. Many of them develop under the colluvial sandy cover and contain the fill of clayey silt. Although it is widely accepted that they are solutional in origin, the exact mechanism by which the flow becomes focused is still under debate. The hypotheses include the concentration of acidified water around stems and roots of plants, or the presence of pre-existing fractures or steeply dipping bedding planes, which would determine the points of entry for the focused groundwater flows. However, there are field sites where neither of this mechanisms was apparently at play and yet the pipes are formed in large quantities [1]. In this communication we show that the systems of solution pipes can develop spontaneously in nearly uniform matrix due to the reactive-infiltration instability: a homogeneous porous matrix is unstable with respect to small variations in local permeability; regions of high permeability dissolve faster because of enhanced transport of reactants, which leads to increased rippling of the front. This leads to the formation of a system of solution pipes which then advance into the matrix. We study this process numerically, by a combination of 2d- and 3d-simulations, solving the coupled flow and transport equations at the Darcy scale. The relative simplicity of this system (pipes developing in a uniform porous matrix, without any pre-existing structure) makes it very attractive from the modeling standpoint. We quantify the factors which control the pipe diameters and the

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

Energy Technology Data Exchange (ETDEWEB)

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

1998-10-01

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

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

Science.gov (United States)

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

2017-09-01

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

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

International Nuclear Information System (INIS)

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

1987-01-01

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

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

Science.gov (United States)

Fuller, Franklyn B.

1961-01-01

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

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

International Nuclear Information System (INIS)

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

2009-01-01

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

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

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

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

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

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

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

Preliminary study of coconut water for graft tissues preservation in transplantation

Directory of Open Access Journals (Sweden)

Jorge Miguel Schettino César

Full Text Available OBJECTIVE: to verify the effectiveness of coconut water in preserving tissues for transplant. METHODS: Fifty male Wistar rats were randomly distributed in five groups, according to the following preservation solutions for tissue grafts: Group 1: Lactated Ringer; Group 2: Belzer solution; Group 3: mature coconut water; Group 4: green coconut water; Group 5: modified coconut water. In Group 5, the green coconut water has been modified like the Belzer solution. From each animal we harvasted the spleen, ovaries and skin of the back segment. These tissues were preserved for six hours in one of the solutions. Then, the grafts were reimplanted. The recovery of the function of the implanted tissues was assessed 90 days after surgery, by splenic scintigraphy and blood exame. The implanted tissues were collected for histopathological examination. RESULTS: The serum levels did not differ among groups, except for the animals in Group 5, which showed higher levels of IgG than Group 1, and differences in relation to FSH between groups 1 and 2 (p <0.001, 4 and 2 (p = 0.03 and 5 and 2 (p = 0.01. The splenic scintigraphy was not different between groups. The ovarian tissue was better preserved in mature coconut water (p <0.007. CONCLUSION: the coconut water-based solutions preserves spleen, ovary, and rat skin for six hours, maintaining their normal function.

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

Science.gov (United States)

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

2017-10-01

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

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

Directory of Open Access Journals (Sweden)

Panou G.

2017-02-01

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

Preliminary study of coconut water for graft tissues preservation in transplantation.

Science.gov (United States)

César, Jorge Miguel Schettino; Petroianu, Andy; Vasconcelos, Leonardo de Souza; Cardoso, Valbert Nascimento; Mota, Luciene das Graças; Barbosa, Alfredo José Afonso; Soares, Cristina Duarte Vianna; de Oliveira, Amanda Lima

2015-01-01

to verify the effectiveness of coconut water in preserving tissues for transplant. Fifty male Wistar rats were randomly distributed in five groups, according to the following preservation solutions for tissue grafts: Group 1: Lactated Ringer; Group 2: Belzer solution; Group 3: mature coconut water; Group 4: green coconut water; Group 5: modified coconut water. In Group 5, the green coconut water has been modified like the Belzer solution. From each animal we harvested the spleen, ovaries and skin of the back segment. These tissues were preserved for six hours in one of the solutions. Then, the grafts were reimplanted. The recovery of the function of the implanted tissues was assessed 90 days after surgery, by splenic scintigraphy and blood exam. The implanted tissues were collected for histopathological examination. The serum levels did not differ among groups, except for the animals in Group 5, which showed higher levels of IgG than Group 1, and differences in relation to FSH between groups 1 and 2 (p coconut water (p coconut water-based solutions preserves spleen, ovary, and rat skin for six hours, maintaining their normal function.

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

International Nuclear Information System (INIS)

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

1999-01-01

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

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

OpenAIRE

Hassan Fathabadi

2013-01-01

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

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Science.gov (United States)

Rehman, Asad; Ali, Ishtiaq; Qamar, Shamsul

An upwind space-time conservation element and solution element (CE/SE) scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme.

Supercooling as a viable non-freezing cell preservation method of rat hepatocytes.

Directory of Open Access Journals (Sweden)

O Berk Usta

Full Text Available Supercooling preservation holds the potential to drastically extend the preservation time of organs, tissues and engineered tissue products, and fragile cell types that do not lend themselves well to cryopreservation or vitrification. Here, we investigate the effects of supercooling preservation (SCP at -4(oC on primary rat hepatocytes stored in cryovials and compare its success (high viability and good functional characteristics to that of static cold storage (CS at +4(oC and cryopreservation. We consider two prominent preservation solutions a Hypothermosol (HTS-FRS and b University of Wisconsin solution (UW and a range of preservation temperatures (-4 to -10 (oC. We find that there exists an optimum temperature (-4(oC for SCP of rat hepatocytes which yields the highest viability; at this temperature HTS-FRS significantly outperforms UW solution in terms of viability and functional characteristics (secretions and enzymatic activity in suspension and plate culture. With the HTS-FRS solution we show that the cells can be stored for up to a week with high viability (~56%; moreover we also show that the preservation can be performed in large batches (50 million cells with equal or better viability and no loss of functionality as compared to smaller batches (1.5 million cells performed in cryovials.

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

International Nuclear Information System (INIS)

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

1991-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1991-02-01

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

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

Science.gov (United States)

Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

2014-02-01

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

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

International Nuclear Information System (INIS)

Valdes Parra, J.J.

1986-01-01

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

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

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

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

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

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

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

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

International Nuclear Information System (INIS)

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

1984-01-01

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

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

International Nuclear Information System (INIS)

Milioli, F.E.

1985-01-01

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

An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

International Nuclear Information System (INIS)

Sun, Wenjun; Jiang, Song; Xu, Kun

2015-01-01

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach

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

Science.gov (United States)

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

2014-01-01

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

Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

Science.gov (United States)

Vanel, Florence O.; Baysal, Oktay

1995-01-01

Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

Emerging concepts in liver graft preservation

Science.gov (United States)

Bejaoui, Mohamed; Pantazi, Eirini; Folch-Puy, Emma; Baptista, Pedro M; García-Gil, Agustín; Adam, René; Roselló-Catafau, Joan

2015-01-01

The urgent need to expand the donor pool in order to attend to the growing demand for liver transplantation has obliged physicians to consider the use of suboptimal liver grafts and also to redefine the preservation strategies. This review examines the different methods of liver graft preservation, focusing on the latest advances in both static cold storage and machine perfusion (MP). The new strategies for static cold storage are mainly designed to increase the fatty liver graft preservation via the supplementation of commercial organ preservation solutions with additives. In this paper we stress the importance of carrying out effective graft washout after static cold preservation, and present a detailed discussion of the future perspectives for dynamic graft preservation using MP at different temperatures (hypothermia at 4 °C, normothermia at 37 °C and subnormothermia at 20 °C-25 °C). Finally, we highlight some emerging applications of regenerative medicine in liver graft preservation. In conclusion, this review discusses the “state of the art” and future perspectives in static and dynamic liver graft preservation in order to improve graft viability. PMID:25593455

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

Science.gov (United States)

Mohebbi, Akbar

2018-02-01

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

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

International Nuclear Information System (INIS)

Colombant, Denis; Manheimer, Wallace

2010-01-01

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

A Novel Support Vector Machine with Globality-Locality Preserving

Directory of Open Access Journals (Sweden)

Cheng-Long Ma

2014-01-01

Full Text Available Support vector machine (SVM is regarded as a powerful method for pattern classification. However, the solution of the primal optimal model of SVM is susceptible for class distribution and may result in a nonrobust solution. In order to overcome this shortcoming, an improved model, support vector machine with globality-locality preserving (GLPSVM, is proposed. It introduces globality-locality preserving into the standard SVM, which can preserve the manifold structure of the data space. We complete rich experiments on the UCI machine learning data sets. The results validate the effectiveness of the proposed model, especially on the Wine and Iris databases; the recognition rate is above 97% and outperforms all the algorithms that were developed from SVM.

Securing the Future of Cultural Heritage by Identifying Barriers to and Strategizing Solutions for Preservation under Changing Climate Conditions

Directory of Open Access Journals (Sweden)

Sandra Fatorić

2017-11-01

Full Text Available Climate change challenges cultural heritage management and preservation. Understanding the barriers that can impede preservation is of paramount importance, as is developing solutions that facilitate the planning and management of vulnerable cultural resources. Using online survey research, we elicited the opinions of diverse experts across southeastern United States, a region with cultural resources that are particularly vulnerable to flooding and erosion from storms and sea level rise. We asked experts to identify the greatest challenges facing cultural heritage policy and practice from coastal climate change threats, and to identify strategies and information needs to overcome those challenges. Using content analysis, we identified institutional, technical and financial barriers and needs. Findings revealed that the most salient barriers included the lack of processes and preservation guidelines for planning and implementing climate adaptation actions, as well as inadequate funding and limited knowledge about the intersection of climate change and cultural heritage. Experts perceived that principal needs to overcome identified barriers included increased research on climate adaptation strategies and impacts to cultural heritage characteristics from adaptation, as well as collaboration among diverse multi-level actors. This study can be used to set cultural heritage policy and research agendas at local, state, regional and national scales.

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

Science.gov (United States)

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

2018-04-01

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

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

Science.gov (United States)

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

2018-05-01

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

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

Science.gov (United States)

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

2015-09-01

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

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

International Nuclear Information System (INIS)

Saha Ray, S.; Patra, A.

2012-01-01

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

Numerical and analytical solutions for problems relevant for quantum computers

International Nuclear Information System (INIS)

Spoerl, Andreas

2008-01-01

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

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

Science.gov (United States)

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

2017-12-01

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

Copper naphthenate: a proven solution for new wood preservative problems

Energy Technology Data Exchange (ETDEWEB)

McNair, W.S. [Merichem Chemicals and Refinery Services LLC, Houston, TX (United States); Loecner, P. [Pacific Gas and Electric, Davis, CA (United States)

2002-08-01

Today's engineers have the responsibility of considering cost, availability and climbability, as well as the environmental alternatives available to the traditional wood preservatives used in the production of utility poles: creosote, pentachlorophenol (PCP) and chromated copper arsenate (CCA). The leading alternative now emerging for utilities in this field is copper naphthenate. The authors present a case study that clearly demonstrates copper naphthenate as one of the most environmentally sensitive and effective wood preservative. When first introduced, copper naphthenate seemed to frequently result in early failure of the poles treated with this preservative. It was discovered that it was a phenomenon that had been largely exaggerated, and the failure rate was less than one per cent. A recent review has concluded that premature failures have basically disappeared. Several reasons can explain premature failures, such as pretreatment decay, improper sterilization/conditioning/drying, inadequate copper penetration and retention, and others. The long term effectiveness and performance of copper naphthenate has been documented in a number of field trials. The ultimate disposal of the product must be considered by the specifying engineer, and it is possible to dispose of copper naphthenate poles in a sanitary landfill. Due in part to recent manufacturing economies, the cost of copper naphthenate is similar to other oil-borne treatments. The case study of Pacific Gas and Electric was discussed. 7 refs., 2 figs.

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

Czech Academy of Sciences Publication Activity Database

Bartels, S.; Kružík, Martin

2011-01-01

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

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

Science.gov (United States)

Keslerová, Radka; Trdlička, David

2015-09-01

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

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

Science.gov (United States)

Wu, Yang; Kelly, Damien P.

2014-12-01

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

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

Science.gov (United States)

Lee, Yang-Sub

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

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

Directory of Open Access Journals (Sweden)

Hy Dinh

2013-01-01

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

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

Directory of Open Access Journals (Sweden)

Gajda Paweł

2016-01-01

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

Preserving spherical symmetry in axisymmetric coordinates for diffusion problems

International Nuclear Information System (INIS)

Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.

2013-01-01

Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)

Numerical solutions of the N-body problem

International Nuclear Information System (INIS)

Marciniak, A.

1985-01-01

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

Numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1982-01-01

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

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

Science.gov (United States)

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

2017-09-01

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

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

International Nuclear Information System (INIS)

Chen Zhijiang; Kong Fanmei; Din Yibin

1987-01-01

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

Numerical solutions of conservation laws

International Nuclear Information System (INIS)

Shu, C.W.

1986-01-01

In the computation of conservation laws u/sub t/ + f(u)/sub x/ 0, TVD (total-variation-diminishing) schemes have been very successful. TVB (total-variation-bounded) schemes share most the advantages and may remove some of the disadvantages (e.g. local degeneracy of accuracy at critical points) TVD schemes. Included in this dissertation are a class of m-step Runge-Kutta type TVD schemes with CFL number equaling m; a procedure to obtain uniformly high order in space TVB schemes; a class of TVD high order time discretizations; a special boundary treatment which keeps the high order of the scheme up to the boundary and preserves the TVB properties in the nonlinear scalar and linear system cases; a discrete entropy inequality for a modified Lax-Wendroff scheme applied to Burgers' equation; and discusses about error propagation in large regions

Structure-preserving geometric algorithms for plasma physics and beam physics

Science.gov (United States)

Qin, Hong

2017-10-01

Standard algorithms in the plasma physics and beam physics do not possess the long-term accuracy and fidelity required in the study of multi-scale dynamics, because they do not preserve the geometric structures of the physical systems, such as the local energy-momentum conservation, symplectic structure and gauge symmetry. As a result, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty, since 2008 structure-preserving geometric algorithms have been developed. This new generation of algorithms utilizes advanced techniques, such as interpolating differential forms, canonical and non-canonical symplectic integrators, and finite element exterior calculus to guarantee gauge symmetry and charge conservation, and the conservation of energy-momentum and symplectic structure. It is our vision that future numerical capabilities in plasma physics and beam physics will be based on the structure-preserving geometric algorithms.

A new technique to preserve raw materials of ancient monuments against the humidity and its test using 22Na labeled solutions

International Nuclear Information System (INIS)

Martinez, G.L.; Navarrete, J.M.

2007-01-01

Erosion caused by external factors such as wind, rain, sunlight and temperature changes is considerable in raw materials used to build pre-hispanic monuments. However, there does exist an internal destruction factor even stronger: the humidity coming from the soil, which goes up by capillarity, depositing soluble salts on the walls surface. Therefore, one way to find some figure related to the specific capillarity or porosity shown by each raw material, is to obtain small prism-shaped pieces cut out from the large debris fallen down spontaneously from ancient walls due to internal humidity. Once these small samples are placed in contact with a 22 Na labeled solution during a given time, at the same geometrical conditions, dried overnight, conditioned either in test tubes or wrapped into polyethylene and detected in a well type 3' x 3' scintillation detector, the counts accumulated per time and weight units are a measure of the relative porosity shown by each material. In order to pull down this porosity, the samples are impregnated with a gelatin solution (50 g/l) at 60-80 deg C plus food preservatives such as potassium sorbate (2.5%) and sodium benzoate (2.5%). When gelatin begins to be formed 3 hours later and the samples look humid and brilliant, they are impregnated with formaldehyde solution (38%), and their absorption rate is dramatically reduced overnight (75-100%), which can be proven when samples are tested by making use of the 22 Na labeled solution. This technique has been applied at real scale in some pre-hispanic monuments. Ancient raw materials seems to be much more compact and well preserved during one limited period of time (10 to 13 months). Treatment is unnoticeable and reversible, and it may be applied periodically. (author)

On the numerical solution of the neutron fractional diffusion equation

International Nuclear Information System (INIS)

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

2014-01-01

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

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

OpenAIRE

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

2008-01-01

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

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

Science.gov (United States)

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

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

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

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

International Nuclear Information System (INIS)

Woznicki, Z.I.

1995-01-01

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

Histologic features of harvested canine kidneys preserved in four ...

African Journals Online (AJOL)

Endless efforts are required in the investigation of the best organ preservative. Normal Saline, 5% dextrose, Darrows and Ringers' Lactate were used as preservatives with the view to investigate the prospect of kidney survival in these solutions post harvest at the Veterinary Teaching Hospital, Ahmadu Bello University-Zaria.

Cloud-supported preservation of digital papers: A solution for special collections?

Directory of Open Access Journals (Sweden)

Dirk Weisbrod

2016-01-01

Full Text Available Computers and other digital communication media have replaced paper and pencil from the writer’s desk. This development has confronted special collections with a problem, as digital papers are difficult to process using established digital preservation strategies, because of their individual and unique nature. According to the proposal suggested in this paper, the creators should instead be involved in the preservation process, and special collections should integrate pre-custodial forms of curation within their range of tasks. The article outlines the use of a cloud architecture as a suitable instrument for accomplishing this task. The benefits and the prospects for such a collection cloud are exposed and discussed.

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

DEFF Research Database (Denmark)

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

2012-01-01

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

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

NARCIS (Netherlands)

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

1972-01-01

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

Optimising concentrations of antimicrobial agents in pharmaceutical preparations: Case of an oral solution of glycerol and an ophthalmic solution containing cysteamine.

Science.gov (United States)

Chan Hew Wai, A; Becasse, P; Tworski, S; Pradeau, D; Planas, V

2014-11-01

In the context of current distrust of antimicrobial preservatives, the quantities of these substances in two pharmaceutical formulas were studied: an ophthalmic solution of cysteamine preserved benzalkonium chloride at 1mg/5mL and Glycerotone(®) preserved with sorbic acid at 0.1g/100g. The purpose of this work was to verify that a reduction of the quantities of preservative continues to fulfil the requirements for antimicrobial preservation. The Test of efficacy of antimicrobial preservation, section 5.1.3 of the 8th edition of the European Pharmacopoeia, was carried out on each formulation prepared with decreasing quantities of preservative. The results show that formulations whose preservative concentration was reduced by a factor of four remained compliant with standards. It is to be noted that in formulas without preservative, fungal growth was observed in both the solution of Glycerotone(®) and the ophthalmic solution containing cysteamine. Although there is no question that an antimicrobial preservative is necessary, the quantity of preservative can be reduced without deteriorating the quality of the pharmaceutical product but the minimal effective concentration remains to be determined. The formulations of many pharmaceutical products should therefore be examined in order to limit the quantities of preservative while continuing to guarantee patient's safety. Copyright © 2014 Elsevier Masson SAS. All rights reserved.

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

International Nuclear Information System (INIS)

Garratt, T.J.

1989-05-01

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

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

Directory of Open Access Journals (Sweden)

Reza Jalilian

2014-07-01

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

An upwind space-time conservation element and solution element scheme for solving dusty gas flow model

Directory of Open Access Journals (Sweden)

Asad Rehman

Full Text Available An upwind space-time conservation element and solution element (CE/SE scheme is extended to numerically approximate the dusty gas flow model. Unlike central CE/SE schemes, the current method uses the upwind procedure to derive the numerical fluxes through the inner boundary of conservation elements. These upwind fluxes are utilized to calculate the gradients of flow variables. For comparison and validation, the central upwind scheme is also applied to solve the same dusty gas flow model. The suggested upwind CE/SE scheme resolves the contact discontinuities more effectively and preserves the positivity of flow variables in low density flows. Several case studies are considered and the results of upwind CE/SE are compared with the solutions of central upwind scheme. The numerical results show better performance of the upwind CE/SE method as compared to the central upwind scheme. Keywords: Dusty gas flow, Solid particles, Upwind schemes, Rarefaction wave, Shock wave, Contact discontinuity

Is my network module preserved and reproducible?

Directory of Open Access Journals (Sweden)

Peter Langfelder

2011-01-01

Full Text Available In many applications, one is interested in determining which of the properties of a network module change across conditions. For example, to validate the existence of a module, it is desirable to show that it is reproducible (or preserved in an independent test network. Here we study several types of network preservation statistics that do not require a module assignment in the test network. We distinguish network preservation statistics by the type of the underlying network. Some preservation statistics are defined for a general network (defined by an adjacency matrix while others are only defined for a correlation network (constructed on the basis of pairwise correlations between numeric variables. Our applications show that the correlation structure facilitates the definition of particularly powerful module preservation statistics. We illustrate that evaluating module preservation is in general different from evaluating cluster preservation. We find that it is advantageous to aggregate multiple preservation statistics into summary preservation statistics. We illustrate the use of these methods in six gene co-expression network applications including 1 preservation of cholesterol biosynthesis pathway in mouse tissues, 2 comparison of human and chimpanzee brain networks, 3 preservation of selected KEGG pathways between human and chimpanzee brain networks, 4 sex differences in human cortical networks, 5 sex differences in mouse liver networks. While we find no evidence for sex specific modules in human cortical networks, we find that several human cortical modules are less preserved in chimpanzees. In particular, apoptosis genes are differentially co-expressed between humans and chimpanzees. Our simulation studies and applications show that module preservation statistics are useful for studying differences between the modular structure of networks. Data, R software and accompanying tutorials can be downloaded from the following webpage: http://www.genetics.ucla.edu/labs/horvath/CoexpressionNetwork/ModulePreservation.

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

Energy Technology Data Exchange (ETDEWEB)

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

2008-12-15

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

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

International Nuclear Information System (INIS)

Fenwick, John D.; Pardo-Montero, Juan

2010-01-01

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

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

Science.gov (United States)

Henclik, Sławomir

2018-03-01

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

Fertility preservation in Turner syndrome.

Science.gov (United States)

Grynberg, Michaël; Bidet, Maud; Benard, Julie; Poulain, Marine; Sonigo, Charlotte; Cédrin-Durnerin, Isabelle; Polak, Michel

2016-01-01

Premature ovarian insufficiency is a relatively rare condition that can appear early in life. In a non-negligible number of cases the ovarian dysfunction results from genetic diseases. Turner syndrome (TS), the most common sex chromosome abnormality in females, is associated with an inevitable premature exhaustion of the follicular stockpile. The possible or probable infertility is a major concern for TS patients and their parents, and physicians are often asked about possible options to preserve fertility. Unfortunately, there are no recommendations on fertility preservation in this group. The severely reduced follicle pool even during prepubertal life represents the major limit for fertility preservation and is the root of numerous questions regarding the competence of gametes or ovarian tissue crybanked. In addition, patients suffering from TS show higher than usual rates of spontaneous abortion, fetal anomaly, and maternal morbidity and mortality, which should be considered at the time of fertility preservation and before reutilization of the cryopreserved gametes. Apart from fulfillment of the desire of becoming genetic parents, TS patients may be potential candidates for egg donation, gestational surrogacy, and adoption. The present review discusses the different options for preserving female fertility in TS and the ethical questions raised by these approaches. Copyright © 2016 American Society for Reproductive Medicine. Published by Elsevier Inc. All rights reserved.

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

Science.gov (United States)

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

2017-04-01

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

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

Science.gov (United States)

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

2002-11-01

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

Numerical analysis

CERN Document Server

Brezinski, C

2012-01-01

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

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

Science.gov (United States)

Wu, Yang; Kelly, Damien P

2014-12-12

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

Privacy-Preserving Computation with Trusted Computing via Scramble-then-Compute

OpenAIRE

Dang Hung; Dinh Tien Tuan Anh; Chang Ee-Chien; Ooi Beng Chin

2017-01-01

We consider privacy-preserving computation of big data using trusted computing primitives with limited private memory. Simply ensuring that the data remains encrypted outside the trusted computing environment is insufficient to preserve data privacy, for data movement observed during computation could leak information. While it is possible to thwart such leakage using generic solution such as ORAM [42], designing efficient privacy-preserving algorithms is challenging. Besides computation effi...

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

Directory of Open Access Journals (Sweden)

Fukang Yin

2013-01-01

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

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

International Nuclear Information System (INIS)

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

2010-01-01

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

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

International Nuclear Information System (INIS)

Biddlecombe, C.S.

1978-07-01

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

Dry Preserving the Green Sea Urchin.

Science.gov (United States)

Stimson, Cheryl D.

1987-01-01

Describes a project for junior high and senior high school students designed to safely preserve hard-bodied marine invertebrates. Details the materials and procedures used in this technique. Stresses the use of non-toxic solutions and producing a lifelike specimen. (CW)

Application of ionizing radiation to preservation of mushrooms

International Nuclear Information System (INIS)

Smierzchalska, K.; Gubrynowicz, E.

1979-01-01

The influence of ionizing radiation on prolongation of preservation time and quality of mushrooms is discussed. Some numerical data are cited. The influence of ionizing radiation on growth rate and physiological processes is also presented. (A.S.)

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

NARCIS (Netherlands)

Veldman, A.E.P.

1973-01-01

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

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

International Nuclear Information System (INIS)

Jo, Jong Chull; Shin, Won Ky

1997-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

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

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

International Nuclear Information System (INIS)

Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem

2008-01-01

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

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

International Nuclear Information System (INIS)

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

2008-12-01

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

Numerical relativity

CERN Document Server

Shibata, Masaru

2016-01-01

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

Numerical analysis

CERN Document Server

Khabaza, I M

1960-01-01

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

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

International Nuclear Information System (INIS)

Abourida, B.; Hasnaoui, M.

2005-01-01

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

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

Science.gov (United States)

Felici, Helene Marie

1992-01-01

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

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

Czech Academy of Sciences Publication Activity Database

Papež, Jan; Liesen, J.; Strakoš, Z.

2014-01-01

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

[Antimicrobial Effects of Iodine-Polyvinyl Alcohol Ophthalmic and Eye Washing Solution (PA * IODO) with Special Reference to its Temperature, Concentration and Time and its Preservation Stability].

Science.gov (United States)

Hatano, Hiroshi; Sakamoto, Masako; Hayashi, Kazuo; Kamiya, Seigo

2015-08-01

Temperature, concentration and time are the three factors that affect the inactivation capacity of iodine antiseptics. We investigated the effect of these factors on the microbe inactivation of Iodine-Polyvinyl Alcohol ophthalmic and eye washing solution (PA * IODO), and also investigated the preservation conditions on stability of the inactivation activity of the PA * IODO. Test microbes were mixed with PA * IODO, varying the three factors. The live microbes were counted after each reaction. The effects of plugging and preservation temperature were investigated to determine the preserving stability. The inactivation capacity of PA * IODO tended to decrease in almost all microbes tested at 4 degrees C. Twenty times or less diluted PA * IODO killed almost all microbes completely. The time effect was more marked in viruses. Plugging and low-temperature made iodine concentration in diluted PA * IODO remain relatively high. The concentration of PA * IODO affected the inactivation ability more than the temperature and time, although all the three factors correlated positively to the inactivation. For preservation the diluted PA * IODO needed plugging and low temperature.

Comparison of the effects of ophthalmic solutions on human corneal epithelial cells using fluorescent dyes.

Science.gov (United States)

Xu, Manlong; Sivak, Jacob G; McCanna, David J

2013-11-01

To investigate the effect of differently preserved ophthalmic solutions on the viability and barrier function of human corneal epithelial cells (HCEC) using fluorescent dyes. HCEC monolayers were exposed to the ophthalmic solutions containing benzalkonium chloride (BAK), edetate disodium, polyquad, stabilized oxychloro complex (Purite), sodium perborate, or sorbic acid for 5 min, 15 min, and 1 h. At 24 h after exposure, the cultures were assessed for metabolic activity using alamarBlue. The enzyme activity, membrane integrity, and apoptosis were evaluated using confocal microscopy. Barrier function was assessed using sodium fluorescein. The metabolic assay showed that the BAK-preserved ophthalmic solutions significantly reduced cell viability after a 5-min exposure compared to the phosphate buffered saline treated control (POphthalmic solutions with new preservatives had varying time-dependent adverse effects on cell viability, and the preservative-free solution had the least effect on HCEC. Sodium fluorescein permeability showed that HCEC monolayers treated with BAK-preserved solutions were more permeable to sodium fluorescein than those treated by the other ophthalmic solutions (Psolutions had greater adverse effects on metabolic activity, enzyme activity, membrane integrity, cell viability, and barrier function than the solutions that were not preserved with BAK. Our study suggests that BAK-free especially, preservative-free ophthalmic solutions are safer alternatives to BAK-preserved ones.

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

International Nuclear Information System (INIS)

Woznicki, Z.I.

1994-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1994-12-31

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

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

International Nuclear Information System (INIS)

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

1996-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1996-07-01

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

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

Energy Technology Data Exchange (ETDEWEB)

Wu, Kailiang [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn [HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)

2017-01-01

The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.

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

Energy Technology Data Exchange (ETDEWEB)

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

1998-12-31

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1997-12-31

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

An Innovative Hyperbaric Hypothermic Machine Perfusion Protects the Liver from Experimental Preservation Injury

Directory of Open Access Journals (Sweden)

Ferdinando A. Giannone

2012-01-01

Full Text Available Purpose. Hypothermic machine perfusion systems seem more effective than the current static storage to prevent cold ischemic liver injury. Thus, we test an innovative hyperbaric hypothermic machine perfusion (HHMP, which combines hyperbaric oxygenation of the preservation solution and continuous perfusion of the graft. Methods. Rat livers were preserved with Celsior solution according to 4 different modalities: normobaric static preservation; hyperbaric static preservation at 2 atmosphere absolute (ATA; normobaric dynamic preservation, with continuous perfusion; hyperbaric dynamic preservation, with continuous perfusion at 2 ATA. After 24 h cold preservation, we assessed different parameters. Results. Compared to baseline, livers preserved with the current static storage showed severe ultrastructural damage, glycogen depletion and an increased oxidative stress. Normobaric perfused livers showed improved hepatocyte ultrastructure and ameliorated glycogen stores, but they still suffered a significant oxidative damage. The addition of hyperbaric oxygen produces an extra benefit by improving oxidative injury and by inducing endothelial NO synthase (eNOS gene expression. Conclusions. Preservation by means of the present innovative HHMP reduced the liver injury occurring after the current static cold storage by lowering glycogen depletion and oxidative damage. Interestingly, only the use of hyperbaric oxygen was associated to a blunted oxidative stress and an increased eNOS gene expression.

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

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

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

Lung preservation with Euro-Collins, University of Wisconsin, Wallwork, and low-potassium-dextran solution. Université++ Paris-Sud Lung Transplant Group.

Science.gov (United States)

Xiong, L; Mazmanian, M; Chapelier, A R; Reignier, J; Weiss, M; Dartevelle, P G; Hervé, P

1994-09-01

Using isolated rat lungs, we compared prevention of ischemia-reperfusion injury provided by flushing the lungs with modified Euro-Collins solution (EC), University of Wisconsin solution (UW), low-potassium-dextran solution (LPD), or Wallwork solution (WA). After 4 hours' and 6 hours' cold ischemia, reperfusion injury was assessed on the basis of changes in filtration coefficients (Kfc) and pressure-flow curves, characterized by the slope of the curves (incremental resistance) and the extrapolation of this slope to zero flow (pulmonary pressure intercept [Ppi]). After 4 hours, Kfc and Ppi were higher with EC than with UW, LPD, and WA, and the incremental resistance was higher with EC and UW. After 6 hours, Kfc and incremental resistance Ppi were higher with LPD than with WA. Because ischemia-reperfusion injury is associated with decreased endothelial synthesis of prostacyclin and nitric oxide, we tested whether the addition of prostacyclin or the nitric oxide precursor L-arginine to WA would improve preservation. The Kfc and Ppi were lower with both treatments. In conclusion, ischemia-reperfusion injury was best prevented by using WA. The favorable effect of prostacyclin or L-arginine emphasizes the role played by endothelial dysfunction in ischemia-reperfusion injury.

Preserving the memory of waste disposal centres for the future generations; Preserver la memoire des centre de stockage pour les generations futures

Energy Technology Data Exchange (ETDEWEB)

NONE

2006-07-01

Radioactive waste disposal and storage facilities are designed to be intrinsically safe (lowest possible impact) for a duration depending on the lifetime of wastes. The French national agency of waste management (ANDRA) wishes to preserve as long as possible the memory of its waste facilities taking into account a possible loss of this memory beyond the legal monitoring period. For this reason, the ANDRA has analyzed the means that have permitted the preservation of the historical heritage through the centuries. The conclusions show that it is possible to preserve with a good confidence a patrimony during long time scales providing some organizing and structuring of this memory (archiving on numerical media and on permanent paper). (J.S.)

Numerical solution of a flow inside a labyrinth seal

Directory of Open Access Journals (Sweden)

Šimák Jan

2012-04-01

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

Renormalization of period doubling in symmetric four-dimensional volume-preserving maps

International Nuclear Information System (INIS)

Mao, J.; Greene, J.M.

1987-01-01

We have determined three maps (truncated at quadratic terms) that are fixed under the renormalization operator of pitchfork period doubling in symmetric four-dimensional volume-preserving maps. Each of these contains the previously known two-dimensional area-preserving map that is fixed under the period-doubling operator. One of these three fixed maps consists of two uncoupled two-dimensional (nonlinear) area-preserving fixed maps. The other two contain also the two-dimensional area-preserving fixed map coupled (in general) with a linear two-dimensional map. The renormalization calculation recovers all numerical results for the pitchfork period doubling in the symmetric four-dimensional volume-preserving maps, reported by Mao and Helleman [Phys. Rev. A 35, 1847 (1987)]. For a large class of nonsymmetric four-dimensional volume-preserving maps, we found that the fixed maps are the same as those for the symmetric maps

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

Science.gov (United States)

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

2017-01-01

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

Intraluminal polyethylene glycol stabilizes tight junctions and improves intestinal preservation in the rat.

Science.gov (United States)

Oltean, M; Joshi, M; Björkman, E; Oltean, S; Casselbrant, A; Herlenius, G; Olausson, M

2012-08-01

Rapidly progressing mucosal breakdown limits the intestinal preservation time below 10 h. Recent studies indicate that intraluminal solutions containing polyethylene glycol (PEG) alleviate preservation injury of intestines stored in UW-Viaspan. We investigated whether a low-sodium PEG solution is beneficial for intestines stored in histidine-tryptophane-ketoglutarate (HTK) preservation solution. Rat intestines used as control tissue (group 1) were perfused with HTK, groups 2 and 3 received either a customized PEG-3350 (group 2) or an electrolyte solution (group 3) intraluminally before cold storage. Tissue injury, brush-border maltase activity, zonula occludens-1 (ZO-1) and claudin-3 expression in the tight junctions (TJ) were analyzed after 8, 14 and 20 h. We measured epithelial resistance and permeability (Ussing chamber) after 8 and 14 h. Group 2 had superior morphology while maltase activity was similar in all groups. TJ proteins rapidly decreased and decolocalized in groups 1 3; these negative events were delayed in group 2, where colocalization persisted for about 14 h. Intestines in group 2 had higher epithelial resistance and lower permeability than the other groups. These results suggest that a customized PEG solution intraluminally reduces the intestinal preservation injury by improving several major epithelial characteristics without negatively affecting the brush-border enzymes or promoting edema. © Copyright 2012 The American Society of Transplantation and the American Society of Transplant Surgeons.

A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

Energy Technology Data Exchange (ETDEWEB)

Wang, Bin, E-mail: wangbinmaths@gmail.com [Department of Mathematics, Nanjing University, State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing 210093 (China); Wu, Xinyuan, E-mail: xywu@nju.edu.cn [Department of Mathematics, Nanjing University, State Key Laboratory for Novel Software Technology at Nanjing University, Nanjing 210093 (China)

2012-03-05

This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q{sup ″}(t)+Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=−∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=1/2 p{sup T}p+1/2 q{sup T}Mq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi–Pasta–Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method. -- Highlights: ► A novel high order energy-preserving integrator AAVF-GL is proposed. ► The important properties of the new integrator AAVF-GL are shown. ► Numerical experiment is carried out compared with AVF method etc. appeared recently.

Novel Slope Source Term Treatment for Preservation of Quiescent Steady States in Shallow Water Flows

Directory of Open Access Journals (Sweden)

Khawar Rehman

2016-10-01

Full Text Available This paper proposes a robust method for modeling shallow-water flows and near shore tsunami propagation, applicable for both simple and complex geometries with uneven beds. The novel aspect of the model includes the introduction of a new method for slope source terms treatment to preserve quiescent equilibrium over uneven topographies, applicable to both structured and unstructured mesh systems with equal accuracy. Our model is based on the Godunov-type finite volume numerical approximation. Second-order spatial and temporal accuracy is achieved through high resolution gradient reconstruction and the predictor-corrector method, respectively. The approximate Riemann solver of Harten, Lax, and van Leer with contact wave restoration (HLLC is used to compute fluxes. Comparisons of the model’s results with analytical, experimental, and published numerical solutions show that the proposed method is capable of accurately predicting experimental and real-time tsunami propagation/inundation, and dam-break flows over varying topographies.

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

Science.gov (United States)

Ghosh, Pradipto

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

New Poisson–Boltzmann type equations: one-dimensional solutions

International Nuclear Information System (INIS)

Lee, Chiun-Chang; Lee, Hijin; Hyon, YunKyong; Lin, Tai-Chia; Liu, Chun

2011-01-01

The Poisson–Boltzmann (PB) equation is conventionally used to model the equilibrium of bulk ionic species in different media and solvents. In this paper we study a new Poisson–Boltzmann type (PB n ) equation with a small dielectric parameter ε 2 and non-local nonlinearity which takes into consideration the preservation of the total amount of each individual ion. This equation can be derived from the original Poisson–Nernst–Planck system. Under Robin-type boundary conditions with various coefficient scales, we demonstrate the asymptotic behaviours of one-dimensional solutions of PB n equations as the parameter ε approaches zero. In particular, we show that in case of electroneutrality, i.e. α = β, solutions of 1D PB n equations have a similar asymptotic behaviour as those of 1D PB equations. However, as α ≠ β (non-electroneutrality), solutions of 1D PB n equations may have blow-up behaviour which cannot be found in 1D PB equations. Such a difference between 1D PB and PB n equations can also be verified by numerical simulations

Discrete convolution-operators and radioactive disintegration. [Numerical solution

Energy Technology Data Exchange (ETDEWEB)

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

1975-08-01

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

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)

Methods of numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1983-01-01

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

The preservative polyquaternium-1 increases cytoxicity and NF-kappaB linked inflammation in human corneal epithelial cells

Science.gov (United States)

Paimela, Tuomas; Ryhänen, Tuomas; Kauppinen, Anu; Marttila, Liisa; Salminen, Antero

2012-01-01

Purpose In numerous clinical and experimental studies, preservatives present in eye drops have had detrimental effects on ocular epithelial cells. The aim of this study was to compare the cytotoxic and inflammatory effects of the preservative polyquaternium-1 (PQ-1) containing Travatan (travoprost 0.004%) and Systane Ultra eye drops with benzalkonium chloride (BAK) alone or BAK-preserved Xalatan (0.005% latanoprost) eye drops in HCE-2 human corneal epithelial cell culture. Methods HCE-2 cells were exposed to the commercial eye drops Travatan, Systane Ultra, Xalatan, and the preservative BAK. Cell viability was determined using colorimetric MTT (3-(4,5-dimethyldiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay and by release of lactate dehydrogenase (LDH). Induction of apoptosis was measured with a using a colorimetric caspase-3 assay kit. DNA binding of the nuclear factor kappa B (NF-κB) transcription factor, and productions of the proinflammatory cytokines, interleukins IL-6 and IL-8, were determined using an enzyme-linked immunosorbent assay (ELISA) method. Results Cell viability, as measured by the MTT assay, declined by up to 50% after exposure to Travatan or Systane Ultra solutions which contain 0.001% PQ-1. BAK at 0.02% rather than at 0.001% concentration evoked total cell death signs on HCE-2 cells. In addition, cell membrane permeability, as measured by LDH release, was elevated by sixfold with Travatan and by a maximum threefold with Systane Ultra. Interestingly, Travatan and Systane Ultra activated NF-κB and elevated the secretion of inflammation markers IL-6 by 3 to eightfold and IL-8 by 1.5 to 3.5 fold, respectively, as analyzed with ELISA. Conclusions Eye drops containing PQ-1 evoke cytotoxicity and enhance the NF-κB driven inflammation reaction in cultured HCE-2 cells. Our results indicate that these harmful effects of ocular solutions preserved with PQ-1 should be further evaluated in vitro and in vivo. PMID:22605930

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

KAUST Repository

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

2012-01-01

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

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

NARCIS (Netherlands)

Lucas, P.; Van Zuijlen, A.H.; Bijl, H.

2009-01-01

Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This

On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

International Nuclear Information System (INIS)

Mieussens, Luc

2013-01-01

The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme

Survey of a numerical procedure for the solution of hyperbolic systems of three dimensional fluid flow

International Nuclear Information System (INIS)

Graf, U.

1986-01-01

A combination of several numerical methods is used to construct a procedure for effective calculation of complex three-dimensional fluid flow problems. The split coefficient matrix (SCM) method is used so that the differenced equations of the hyperbolic system do not disturb correct signal propagation. The semi-discretisation of the equations of the SCM method is done with the asymmetric, separated region, weighted residual (ASWR) method to give accurate solutions on a relatively coarse mesh. For the resulting system of ordinary differential equations, a general-purpose ordinary differential equation solver is used in conjunction with a method of fractional steps for an economic solution of the large system of linear equations. (orig.) [de

A numerical model for the determination of periodic solutions of pipes subjected to non-conservative loads

International Nuclear Information System (INIS)

Velloso, P.A.; Galeao, A.C.

1989-05-01

This paper deals with nonlinear vibrations of pipes subjected to non-conservative loads. Periodic solutions of these problems are determined using a variational approach based on Hamilton's Principle combined with a Fourier series expansion to describe the displacement field time dependence. A finite element model which utilizes Hemite's cubic interpolation for both axial and transversal displacement amplitudes is used. This model is applied to the problem of a pipe subjected to a tangential and a normal follower force. The numerical results obtained with this model are compared with the corespondent solutions determined using a total lagrangian description for the Principle of Virtual Work, coupled with Newmark's step-by-step integration procedure. It is shown that for small to moderate displacement amplitudes the one-term Fourier series approximation compares fairly well with the predicted solution. For large displacements as least a two-term approximation should be utilized [pt

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

Science.gov (United States)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Image storage and permanence considerations in the long-term preservation of photographic images - update 2010

International Nuclear Information System (INIS)

LaBarca, Joseph E

2010-01-01

Archivists and consumers, alike, need to become aware of long-term storage and preservation issues that relate to the preservation of the data behind digital photographic images. The more obvious issues, such as accidental or catastrophic data loss and hardware format evolution, are only now being recognized in the archiving community. Consumers need to be alerted to these issues and be prepared to develop preservation strategies as well. However, longer-term issues beyond routine backup and migration of data need to be considered. The very basic solution of preservation via hardcopy images stored in shoeboxes or albums is one option, but this raises a fundamental question regarding image preservation that transcends even the more complex solutions-the long-term stability of the chosen media, whether digital or analog. This paper discusses archiving and preservation as it relates to images, and the data behind those images, along with historical perspectives and an overview of possible longer-term preservation strategies. The importance of image permanence standards, as they relate to overall selection of preservation strategies, will also be discussed.

Usefulness of radionuclide scintiphotography to evaluate preserved kidney viability

International Nuclear Information System (INIS)

Sato, Koshi; Yokota, Kazuhiko; Uchida, Hisanori

1987-01-01

GAMMA imaging of the renal cortical microcirculation is a safe and non-invasive method for assessment of kidney viability before transplantation. We used trifluoperazine (TFP), urokinase and verapamil from 24 to 120 hour kidney preservation in dogs. For these preserved kidneys, we used radionuuclide scintiphotography to evaluate kidney viability. After preservation, these kidneys were perfused with technitium -99m labeled microspheres, and imaging of the renal vasculature was obtained by scintigraphy. The distribution of the microspheres was assessed visually and by computer analysis. Modified Collins' solution perfused kidneys show very poor cortical uptake with marked increase in uptake in the hilar region after preservation. In contrast, cortical flow remained relatively well preserved in kidneys perfused and preserved by use of modified Collins' solotion with TFP, urokinase and urokinase + verapamil. There was a direct correlation between these results and the capacity of kidneys treated in the same fashion to sustain life after retransplantation into the original host. (author)

Numerical Solution of a Fractional Order Model of HIV Infection of CD4+T Cells Using Müntz-Legendre Polynomials

Directory of Open Access Journals (Sweden)

Mojtaba Rasouli Gandomani

2016-06-01

Full Text Available In this paper, the model of HIV infection of CD4+ T cells is considered as a system of fractional differential equations. Then, a numerical method by using collocation method based on the Müntz-Legendre polynomials to approximate solution of the model is presented. The application of the proposed numerical method causes fractional differential equations system to convert into the algebraic equations system. The new system can be solved by one of the existing methods. Finally, we compare the result of this numerical method with the result of the methods have already been presented in the literature.

Numerical Algorithm for Delta of Asian Option

Directory of Open Access Journals (Sweden)

Boxiang Zhang

2015-01-01

Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.

Soft-Bodied Fossils Are Not Simply Rotten Carcasses - Toward a Holistic Understanding of Exceptional Fossil Preservation: Exceptional Fossil Preservation Is Complex and Involves the Interplay of Numerous Biological and Geological Processes.

Science.gov (United States)

Parry, Luke A; Smithwick, Fiann; Nordén, Klara K; Saitta, Evan T; Lozano-Fernandez, Jesus; Tanner, Alastair R; Caron, Jean-Bernard; Edgecombe, Gregory D; Briggs, Derek E G; Vinther, Jakob

2018-01-01

Exceptionally preserved fossils are the product of complex interplays of biological and geological processes including burial, autolysis and microbial decay, authigenic mineralization, diagenesis, metamorphism, and finally weathering and exhumation. Determining which tissues are preserved and how biases affect their preservation pathways is important for interpreting fossils in phylogenetic, ecological, and evolutionary frameworks. Although laboratory decay experiments reveal important aspects of fossilization, applying the results directly to the interpretation of exceptionally preserved fossils may overlook the impact of other key processes that remove or preserve morphological information. Investigations of fossils preserving non-biomineralized tissues suggest that certain structures that are decay resistant (e.g., the notochord) are rarely preserved (even where carbonaceous components survive), and decay-prone structures (e.g., nervous systems) can fossilize, albeit rarely. As we review here, decay resistance is an imperfect indicator of fossilization potential, and a suite of biological and geological processes account for the features preserved in exceptional fossils. © 2017 The Authors. BioEssays Published by WILEY Periodicals, Inc.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

Science.gov (United States)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

Energy Technology Data Exchange (ETDEWEB)

Paster, Amir, E-mail: paster@tau.ac.il [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978 (Israel); Bolster, Diogo [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); Benson, David A. [Hydrologic Science and Engineering, Colorado School of Mines, Golden, CO, 80401 (United States)

2014-04-15

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.

Numerical investigations of solute transport in bimodal porous media under dynamic boundary conditions

Science.gov (United States)

Cremer, Clemens; Neuweiler, Insa; Bechtold, Michel; Vanderborght, Jan

2016-04-01

Quantification of flow and solute transport in the shallow subsurface adjacent to the atmosphere is decisive to prevent groundwater pollution and conserve groundwater quality, to develop successful remediation strategies and to understand nutrient cycling. In nature, due to erratic precipitation-evaporation patterns, soil moisture content and related hydraulic conductivity in the vadose zone are not only variable in space but also in time. Flow directions and flow paths locally change between precipitation and evaporation periods. This makes the identification and description of solute transport processes in the vadose zone a complex problem. Recent studies (Lehmann and Or, 2009; Bechtold et al., 2011a) focused on the investigation of upward transport of solutes during evaporation in heterogeneous soil columns, where heterogeneity was introduced by a sharp vertical material interface between two types of sand. Lateral solute transport through the interface in both (lateral) directions was observed at different depths of the investigated soil columns. Following recent approaches, we conduct two-dimensional numerical simulations in a similar setup which is composed of two sands with a sharp vertical material interface. The investigation is broadened from the sole evaporation to combined precipitation-evaporation cycles in order to quantify transport processes resulting from the combined effects of heterogeneous soil structure and dynamic flow conditions. Simulations are performed with a coupled finite volume and random walk particle tracking algorithm (Ippisch et al., 2006; Bechtold et al., 2011b). By comparing scenarios with cyclic boundary conditions and stationary counterparts with the same net flow rate, we found that duration and intensity of precipitation and evaporation periods potentially have an influence on lateral redistribution of solutes and thus leaching rates. Whether or not dynamic boundary conditions lead to significant deviations in the transport

A structure preserving Lanczos algorithm for computing the optical absorption spectrum

Energy Technology Data Exchange (ETDEWEB)

Shao, Meiyue [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Jornada, Felipe H. da [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Div.; Lin, Lin [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Yang, Chao [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.; Deslippe, Jack [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Louie, Steven G. [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Div.

2016-11-16

We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

Influence of pH on extracellular matrix preservation during lung decellularization.

Science.gov (United States)

Tsuchiya, Tomoshi; Balestrini, Jenna L; Mendez, Julio; Calle, Elizabeth A; Zhao, Liping; Niklason, Laura E

2014-12-01

The creation of decellularized organs for use in regenerative medicine requires the preservation of the organ extracellular matrix (ECM) as a means to provide critical cues for differentiation and migration of cells that are seeded onto the organ scaffold. The purpose of this study was to assess the influence of varying pH levels on the preservation of key ECM components during the decellularization of rat lungs. Herein, we show that the pH of the 3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate (CHAPS)-based decellularization solution influences ECM retention, cell removal, and also the potential for host response upon implantation of acellular lung tissue. The preservation of ECM components, including elastin, fibronectin, and laminin, were better retained in the lower pH conditions that were tested (pH ranges tested: 8, 10, 12); glycosaminoglycans were preserved to a higher extent in the lower pH groups as well. The DNA content following decellularization of the rat lung was inversely correlated with the pH of the decellularization solution. Despite detectible levels of cyotoskeletal proteins and significant residual DNA, tissues decellularized at pH 8 demonstrated the greatest tissue architecture maintenance and the least induction of host response of all acellular conditions. These results highlight the effect of pH on the results obtained by organ decellularization and suggest that altering the pH of the solutions used for decellularization may influence the ability of cells to properly differentiate and home to appropriate locations within the scaffold, based on the preservation of key ECM components and implantation results.

Penalty methods for the numerical solution of American multi-asset option problems

Science.gov (United States)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

Numerical solution of stiff systems of ordinary differential equations with applications to electronic circuits

Science.gov (United States)

Rosenbaum, J. S.

1971-01-01

Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

Science.gov (United States)

Luo, Xiao-Ping; Wang, Cun-Hai; Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

2018-06-01

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

Archiving Software Systems: Approaches to Preserve Computational Capabilities

Science.gov (United States)

King, T. A.

2014-12-01

A great deal of effort is made to preserve scientific data. Not only because data is knowledge, but it is often costly to acquire and is sometimes collected under unique circumstances. Another part of the science enterprise is the development of software to process and analyze the data. Developed software is also a large investment and worthy of preservation. However, the long term preservation of software presents some challenges. Software often requires a specific technology stack to operate. This can include software, operating systems and hardware dependencies. One past approach to preserve computational capabilities is to maintain ancient hardware long past its typical viability. On an archive horizon of 100 years, this is not feasible. Another approach to preserve computational capabilities is to archive source code. While this can preserve details of the implementation and algorithms, it may not be possible to reproduce the technology stack needed to compile and run the resulting applications. This future forward dilemma has a solution. Technology used to create clouds and process big data can also be used to archive and preserve computational capabilities. We explore how basic hardware, virtual machines, containers and appropriate metadata can be used to preserve computational capabilities and to archive functional software systems. In conjunction with data archives, this provides scientist with both the data and capability to reproduce the processing and analysis used to generate past scientific results.

On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

Energy Technology Data Exchange (ETDEWEB)

Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo; Aloy, Miguel-Ángel [Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/Dr. Moliner 50, E-46100 Burjassot (Spain); Müller, Ewald, E-mail: tomasz.rembiasz@uv.es [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)

2017-06-01

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.

Numerical discrepancy between serial and MPI parallel computations

Directory of Open Access Journals (Sweden)

Sang Bong Lee

2016-09-01

Full Text Available Numerical simulations of 1D Burgers equation and 2D sloshing problem were carried out to study numerical discrepancy between serial and parallel computations. The numerical domain was decomposed into 2 and 4 subdomains for parallel computations with message passing interface. The numerical solution of Burgers equation disclosed that fully explicit boundary conditions used on subdomains of parallel computation was responsible for the numerical discrepancy of transient solution between serial and parallel computations. Two dimensional sloshing problems in a rectangular domain were solved using OpenFOAM. After a lapse of initial transient time sloshing patterns of water were significantly different in serial and parallel computations although the same numerical conditions were given. Based on the histograms of pressure measured at two points near the wall the statistical characteristics of numerical solution was not affected by the number of subdomains as much as the transient solution was dependent on the number of subdomains.

Derivation Method for the Foundation Boundaries of Hydraulic Numerical Simulation Models Based on the Elastic Boussinesq Solution

Directory of Open Access Journals (Sweden)

Jintao Song

2015-01-01

Full Text Available The foundation boundaries of numerical simulation models of hydraulic structures dominated by a vertical load are investigated. The method used is based on the stress formula for fundamental solutions to semi-infinite space body elastic mechanics under a vertical concentrated force. The limit method is introduced into the original formula, which is then partitioned and analyzed according to the direction of the depth extension of the foundation. The point load will be changed to a linear load with a length of 2a. Inverse proportion function assumptions are proposed at parameter a and depth l of the calculation points to solve the singularity questions of elastic stress in a semi-infinite space near the ground. Compared with the original formula, changing the point load to a linear load with a length of 2a is more reasonable. Finally, the boundary depth criterion of a hydraulic numerical simulation model is derived and applied to determine the depth boundary formula for gravity dam numerical simulations.

Material properties that predict preservative uptake for silicone hydrogel contact lenses.

Science.gov (United States)

Green, J Angelo; Phillips, K Scott; Hitchins, Victoria M; Lucas, Anne D; Shoff, Megan E; Hutter, Joseph C; Rorer, Eva M; Eydelman, Malvina B

2012-11-01

To assess material properties that affect preservative uptake by silicone hydrogel lenses. We evaluated the water content (using differential scanning calorimetry), effective pore size (using probe penetration), and preservative uptake (using high-performance liquid chromatography with spectrophotometric detection) of silicone and conventional hydrogel soft contact lenses. Lenses grouped similarly based on freezable water content as they did based on total water content. Evaluation of the effective pore size highlighted potential differences between the surface-treated and non-surface-treated materials. The water content of the lens materials and ionic charge are associated with the degree of preservative uptake. The current grouping system for testing contact lens-solution interactions separates all silicone hydrogels from conventional hydrogel contact lenses. However, not all silicone hydrogel lenses interact similarly with the same contact lens solution. Based upon the results of our research, we propose that the same material characteristics used to group conventional hydrogel lenses, water content and ionic charge, can also be used to predict uptake of hydrophilic preservatives for silicone hydrogel lenses. In addition, the hydrophobicity of silicone hydrogel contact lenses, although not investigated here, is a unique contact lens material property that should be evaluated for the uptake of relatively hydrophobic preservatives and tear components.

Numerical linear algebra with applications using Matlab

CERN Document Server

Ford, William

2014-01-01

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for

Energy preserving integration of bi-Hamiltonian partial differential equations

NARCIS (Netherlands)

Karasozen, B.; Simsek, G.

2013-01-01

The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the

A compositional multiphase model for groundwater contamination by petroleum products: 2. Numerical solution

Science.gov (United States)

Baehr, Arthur L.; Corapcioglu, M. Yavuz

1987-01-01

In this paper we develop a numerical solution to equations developed in part 1 (M. Y. Corapcioglu and A. L. Baehr, this issue) to predict the fate of an immiscible organic contaminant such as gasoline in the unsaturated zone subsequent to plume establishment. This solution, obtained by using a finite difference scheme and a method of forward projection to evaluate nonlinear coefficients, provides estimates of the flux of solubilized hydrocarbon constituents to groundwater from the portion of a spill which remains trapped in a soil after routine remedial efforts to recover the product have ceased. The procedure was used to solve the one-dimensional (vertical) form of the system of nonlinear partial differential equations defining the transport for each constituent of the product. Additionally, a homogeneous, isothermal soil with constant water content was assumed. An equilibrium assumption partitions the constituents between air, water, adsorbed, and immiscible phases. Free oxygen transport in the soil was also simulated to provide an upper bound estimate of aerobic biodgradation rates. Results are presented for a hypothetical gasoline consisting of eight groups of hydrocarbon constituents. Rates at which hydrocarbon mass is removed from the soil, entering either the atmosphere or groundwater, or is biodegraded are presented. A significant sensitivity to model parameters, particularly the parameters characterizing diffusive vapor transport, was discovered. We conclude that hydrocarbon solute composition in groundwater beneath a gasoline contaminated soil would be heavily weighted toward aromatic constituents like benzene, toluene, and xylene.

Pulmonary preservation studies: effects on endothelial function and pulmonary adenine nucleotides.

Science.gov (United States)

Paik, Hyo Chae; Hoffmann, Steven C; Egan, Thomas M

2003-02-27

Lung transplantation is an effective therapy plagued by a high incidence of early graft dysfunction, in part because of reperfusion injury. The optimal preservation solution for lung transplantation is unknown. We performed experiments using an isolated perfused rat lung model to test the effect of lung preservation with three solutions commonly used in clinical practice. Lungs were retrieved from Sprague-Dawley rats and flushed with one of three solutions: modified Euro-Collins (MEC), University of Wisconsin (UW), or low potassium dextran and glucose (LPDG), then stored cold for varying periods before reperfusion with Earle's balanced salt solution using the isolated perfused rat lung model. Outcome measures were capillary filtration coefficient (Kfc), wet-to-dry weight ratio, and lung tissue levels of adenine nucleotides and cyclic AMP. All lungs functioned well after 4 hr of storage. By 6 hr, UW-flushed lungs had a lower Kfc than LPDG-flushed lungs. After 8 hr of storage, only UW-flushed lungs had a measurable Kfc. Adenine nucleotide levels were higher in UW-flushed lungs after prolonged storage. Cyclic AMP levels correlated with Kfc in all groups. Early changes in endothelial permeability seemed to be better attenuated in lungs flushed with UW compared with LPDG or MEC; this was associated with higher amounts of adenine nucleotides. MEC-flushed lungs failed earlier than LPDG-flushed or UW-flushed lungs. The content of the solution may be more important for lung preservation than whether the ionic composition is intracellular or extracellular.

Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion—advection equation with variable coefficients

International Nuclear Information System (INIS)

Kumar, Vikas; Gupta, R. K.; Jiwari, Ram

2014-01-01

In this paper, the variable-coefficient diffusion—advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (G'/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions

Optimization of preservation activities and preservation engineering (1)

International Nuclear Information System (INIS)

Aoki, Takayuki; Mimaki, Hidehito; Oda, Mitsuyuki

2004-01-01

In order to deal with the optimization of preservation activities and 'preservation engineering' which makes it possible, the relation between general society and preservation, the content and the structure of preservation activities, and the viewpoint and the approach of the optimization of the preventive preservation are described. The optimization of the preventive preservation is shown respectively in the four stages of planning, implementation, result evaluation and countermeasure. (K. Kato)

A Global Optimizing Policy for Decaying Items with Ramp-Type Demand Rate under Two-Level Trade Credit Financing Taking Account of Preservation Technology

Directory of Open Access Journals (Sweden)

S. R. Singh

2013-01-01

Full Text Available An inventory system for deteriorating items, with ramp-type demand rate, under two-level trade credit policy taking account of preservation technology is considered. The objective of this study is to develop a deteriorating inventory policy when the supplier provides to the retailer a permissible delay in payments, and during this credit period, the retailer accumulates the revenue and earns interest on that revenue; also the retailer invests on the preservation technology to reduce the rate of product deterioration. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples draw attention to the obtained results, and the sensitivity analysis of the optimal solution with respect to leading parameters of the system is carried out.

Benchmark numerical solutions for radiative heat transfer in two-dimensional medium with graded index distribution

Energy Technology Data Exchange (ETDEWEB)

Liu, L.H. [School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001 (China)]. E-mail: lhliu@hit.edu.cn

2006-11-15

In graded index media, the ray goes along a curved path determined by Fermat principle. Generally, the curved ray trajectory in graded index media is a complex implicit function, and the curved ray tracing is very difficult and complex. Only for some special refractive index distributions, the curved ray trajectory can be expressed as a simple explicit function. Two important examples are the layered and the radial graded index distributions. In this paper, the radiative heat transfer problems in two-dimensional square semitransparent with layered and radial graded index distributions are analyzed. After deduction of the ray trajectory, the radiative heat transfer problems are solved by using the Monte Carlo curved ray-tracing method. Some numerical solutions of dimensionless net radiative heat flux and medium temperature are tabulated as the benchmark solutions for the future development of approximation techniques for multi-dimensional radiative heat transfer in graded index media.

Fourier Magnitude-Based Privacy-Preserving Clustering on Time-Series Data

Science.gov (United States)

Kim, Hea-Suk; Moon, Yang-Sae

Privacy-preserving clustering (PPC in short) is important in publishing sensitive time-series data. Previous PPC solutions, however, have a problem of not preserving distance orders or incurring privacy breach. To solve this problem, we propose a new PPC approach that exploits Fourier magnitudes of time-series. Our magnitude-based method does not cause privacy breach even though its techniques or related parameters are publicly revealed. Using magnitudes only, however, incurs the distance order problem, and we thus present magnitude selection strategies to preserve as many Euclidean distance orders as possible. Through extensive experiments, we showcase the superiority of our magnitude-based approach.

Infiltration analysis for Abadia de Goias repository: numerical solution; Analise de infiltracao para o repositorio de Abadia de Goias: solucao numerica

Energy Technology Data Exchange (ETDEWEB)

Martin Alves, Antonio S. de [NUCLEN, Rio de Janeiro, RJ (Brazil); Passos, Aline M.M. dos [Universidade Federal Fluminense, Niteroi, RJ (Brazil)

1997-12-01

The safety analysis of a structure known as repository for medium activity wastes leads to investigating the physical phenomena connected to the water infiltration. This work shows succinctly an engineering approach to obtain numerical results for the model differential equations. One of these equations, related to the two-phase flow within the structure, is a nonlinear Riccati type, whose solution is only known for certain cases. For safety analysis and design purposes, the solution for the case of variable parameters is also advantageous when one aims some accident scenarios analysis. The utilization of numerical techniques allowed excellent results applied for the design of the Abadia de Goias repository. The case treated in this paper was one of those applied to the safety assessment of this repository. (author). 7 refs., 4 figs., 7 tabs.

Performance analysis of numeric solutions applied to biokinetics of radionuclides; Analise de desempenho de solucoes numericas aplicadas a biocinetica de radionuclideos

Energy Technology Data Exchange (ETDEWEB)

Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva, E-mail: dani@ime.usp.br, E-mail: joyce@ime.usp.br [Universidade de Sao Paulo (IME/USP), SP (Brazil). Instituto de Matematica e Estatistica; Todo, Alberto Saburo; Rodrigues Junior, Orlando, E-mail: astodo@ipen.br, E-mail: rodrijr@ipen.br [Instituto de Pesquisas Energeticas Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)

2013-07-01

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

Explicit strong stability preserving multistep Runge–Kutta methods

KAUST Repository

Bresten, Christopher; Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel; Ketcheson, David I.; Né meth, Adrian

2015-01-01

High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.

Explicit strong stability preserving multistep Runge–Kutta methods

KAUST Repository

Bresten, Christopher

2015-10-15

High-order spatial discretizations of hyperbolic PDEs are often designed to have strong stability properties, such as monotonicity. We study explicit multistep Runge-Kutta strong stability preserving (SSP) time integration methods for use with such discretizations. We prove an upper bound on the SSP coefficient of explicit multistep Runge-Kutta methods of order two and above. Numerical optimization is used to find optimized explicit methods of up to five steps, eight stages, and tenth order. These methods are tested on the linear advection and nonlinear Buckley-Leverett equations, and the results for the observed total variation diminishing and/or positivity preserving time-step are presented.

A New Numerical Algorithm for Two-Point Boundary Value Problems

OpenAIRE

Guo, Lihua; Wu, Boying; Zhang, Dazhi

2014-01-01

We present a new numerical algorithm for two-point boundary value problems. We first present the exact solution in the form of series and then prove that the n-term numerical solution converges uniformly to the exact solution. Furthermore, we establish the numerical stability and error analysis. The numerical results show the effectiveness of the proposed algorithm.

Comparison of different soil water extraction systems for the prognoses of solute transport at the field scale using numerical simulations, field and lysimeter experiments

Energy Technology Data Exchange (ETDEWEB)

Weihermueller, L

2005-07-01

To date, the understanding of processes, factors, and interactions that influence the amount of extracted water and the solute composition sampled with suction cups is limited. But this information is required for process description of solute transport in natural soils. Improved system understanding can lead to a low cost and easy to install water sampling system which can help to predict solute transport in natural soils for the benefit of environmental protection. The main objectives of this work were to perform numerical simulations with different boundary conditions and to implement the findings in the interpretation of the lysimeter and field experiments. In a first part of this thesis, theoretical considerations on the processes affecting the spatial influence of a suction cup in soil and changes in solute transport initiated by the suction cups are presented, including testing and validation of available model and experimental approaches. In the second part, a detailed experimental study was conducted to obtain data for the comparison of the different soil water sampling systems. Finally, the numerical experiments of the suction cup influence were used for the interpretation of the experimental data. The main goals are summarized as follows: - Characterization of the suction cup activity domain (SCAD), suction cup extraction domain (SCED) and suction cup sampling area (SCSA) of active suction cups (definitions are given in Chapter 6). - Determination of the boundary conditions and soil properties [e.g. infiltration, applied suction, duration of water extraction, soil hydraulic properties and soil heterogeneity] affecting the activity domain, extraction domain and sampling area of a suction cup. - Identification of processes that change the travel time and travel time variance of solutes extracted by suction cups. - Validation of the numerically derived data with analytical and experimental data from literature. - Comparison of the experimental data obtained

An Efficient and Robust Numerical Solution of the Full-Order Multiscale Model of Lithium-Ion Battery

Directory of Open Access Journals (Sweden)

Michal Beneš

2018-01-01

Full Text Available We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the finite difference discretization of the diffusion equations combined with an original iterative scheme for solving the integral formulation of the laws of electrochemical interactions. We demonstrate that our implementation is fast and stable over the expected lifetime of the cell. In contrast to some simplified models, it provides physically consistent results for a wide range of applied currents including high loads. The algorithm forms a solid basis for simulations of cells and battery packs in hybrid electric vehicles, with possible straightforward extensions by aging and heat effects.

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

International Nuclear Information System (INIS)

Adam, Gh.

1978-05-01

A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)

Mathematical and numerical analysis of systems of compressible hydrodynamics and photonics with polar coordinates

International Nuclear Information System (INIS)

Meltz, Bertrand

2015-01-01

This thesis deals with the mathematical and numerical analysis of the systems of compressible hydrodynamics and radiative transfer. More precisely, we study the derivation of numerical methods with 2D polar coordinates (one for the radius, one for the angle) where equations are discretized on regular polar grids. On one hand, these methods are well-suited for the simulation of flows with polar symmetries since they preserve these symmetries by construction. On the other hand, such coordinates systems introduce geometrical singularities as well as geometrical source terms which must be carefully treated. The first part of this document is devoted to the study of hydrodynamics equations, or Euler equations. We propose a new class of arbitrary high-order numerical schemes in both space and time and rely on directional splitting methods for the resolution of 2D equations. Each sub-system is solved using a Lagrange+Remap solver. We study the influence of the r=0 geometrical singularities of the cylindrical and spherical coordinates systems on the precision of the 2D numerical solutions. The second part of this document is devoted to the study of radiative transfer equations. In these equations, the unknowns depend on a large number of variables and a stiff source term is involved. The main difficulty consists in capturing the correct asymptotic behavior on coarse grids. We first construct a class of models where the radiative intensity is projected on a truncated spherical harmonics basis in order to lower the number of mathematical dimensions. Then we propose an Asymptotic Preserving scheme built in polar coordinates and we show that the scheme capture the correct diffusion limit in the radial direction as well as in the polar direction. (author) [fr

Solution of large nonlinear time-dependent problems using reduced coordinates

International Nuclear Information System (INIS)

Mish, K.D.

1987-01-01

This research is concerned with the idea of reducing a large time-dependent problem, such as one obtained from a finite-element discretization, down to a more manageable size while preserving the most-important physical behavior of the solution. This reduction process is motivated by the concept of a projection operator on a Hilbert Space, and leads to the Lanczos Algorithm for generation of approximate eigenvectors of a large symmetric matrix. The Lanczos Algorithm is then used to develop a reduced form of the spatial component of a time-dependent problem. The solution of the remaining temporal part of the problem is considered from the standpoint of numerical-integration schemes in the time domain. All of these theoretical results are combined to motivate the proposed reduced coordinate algorithm. This algorithm is then developed, discussed, and compared to related methods from the mechanics literature. The proposed reduced coordinate method is then applied to the solution of some representative problems in mechanics. The results of these problems are discussed, conclusions are drawn, and suggestions are made for related future research

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

Science.gov (United States)

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

Long-time correlations of periodic, area-preserving maps

International Nuclear Information System (INIS)

Meiss, J.D.; Cary, J.R.; Grebogi, C.; Crawford, J.D.; Kaufman, A.N.; Abarbanel, H.D.I.

1982-04-01

A simple analytical decay law for correlation functions of periodic, area-preserving maps is obtained. This law is compared with numerical experiments on the standard map. The agreement between experiment and theory is good when islands are absent, but poor when islands are present. When islands are present, the correlations have a long, slowly decaying tail

Optimization of preservation activities and preservation engineering (2)

International Nuclear Information System (INIS)

Aoki, Takayuki; Mimaki, Hidehito; Oda, Mitsuyuki

2004-01-01

In order to deal with the optimization of preservation activities and 'preservation engineering' which makes it possible, the viewpoint and the approach of the optimization of the ex post facto preservation and the content to be possessed in 'preservation engineering' are described. The optimization of the ex post facto preservation is shown respectively in the four stages of planning, implementation, result evaluation and countermeasure. (K. Kato)