Sample records for equation bie method

  1. Calculation of Moment Matrix Elements for Bilinear Quadrilaterals and Higher-Order Basis Functions

    DTIC Science & Technology

    2016-01-06

    methods are known as boundary integral equation (BIE) methods and the present study falls into this category. The numerical solution of the BIE is...iterated integrals. The inner integral involves the product of the free-space Green’s function for the Helmholtz equation multiplied by an appropriate...Website: http://www.wipl-d.com/ 5. Y. Zhang and T. K. Sarkar, Parallel Solution of Integral Equation -Based EM Problems in the Frequency Domain. New

  2. On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

    NASA Technical Reports Server (NTRS)

    Atluri, Satya N.; Shen, Shengping

    2002-01-01

    In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

  3. Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Liu, Y.; Rizzo, F.J.

    1997-08-01

    In this paper, the composite boundary integral equation (BIE) formulation is applied to scattering of elastic waves from thin shapes with small but {ital finite} thickness (open cracks or thin voids, thin inclusions, thin-layer interfaces, etc.), which are modeled with {ital two surfaces}. This composite BIE formulation, which is an extension of the Burton and Miller{close_quote}s formulation for acoustic waves, uses a linear combination of the conventional BIE and the hypersingular BIE. For thin shapes, the conventional BIE, as well as the hypersingular BIE, will degenerate (or nearly degenerate) if they are applied {ital individually} on the two surfaces. Themore » composite BIE formulation, however, will not degenerate for such problems, as demonstrated in this paper. Nearly singular and hypersingular integrals, which arise in problems involving thin shapes modeled with two surfaces, are transformed into sums of weakly singular integrals and nonsingular line integrals. Thus, no finer mesh is needed to compute these nearly singular integrals. Numerical examples of elastic waves scattered from penny-shaped cracks with varying openings are presented to demonstrate the effectiveness of the composite BIE formulation. {copyright} {ital 1997 Acoustical Society of America.}« less

  4. Methods for analysis of cracks in three-dimensional solids

    NASA Technical Reports Server (NTRS)

    Raju, I. S.; Newman, J. C., Jr.

    1984-01-01

    Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

  5. Acoustic coupled fluid-structure interactions using a unified fast multipole boundary element method.

    PubMed

    Wilkes, Daniel R; Duncan, Alec J

    2015-04-01

    This paper presents a numerical model for the acoustic coupled fluid-structure interaction (FSI) of a submerged finite elastic body using the fast multipole boundary element method (FMBEM). The Helmholtz and elastodynamic boundary integral equations (BIEs) are, respectively, employed to model the exterior fluid and interior solid domains, and the pressure and displacement unknowns are coupled between conforming meshes at the shared boundary interface to achieve the acoustic FSI. The low frequency FMBEM is applied to both BIEs to reduce the algorithmic complexity of the iterative solution from O(N(2)) to O(N(1.5)) operations per matrix-vector product for N boundary unknowns. Numerical examples are presented to demonstrate the algorithmic and memory complexity of the method, which are shown to be in good agreement with the theoretical estimates, while the solution accuracy is comparable to that achieved by a conventional finite element-boundary element FSI model.

  6. Error analysis regarding the calculation of nonlinear force-free field

    NASA Astrophysics Data System (ADS)

    Liu, S.; Zhang, H. Q.; Su, J. T.

    2012-02-01

    Magnetic field extrapolation is an alternative method to study chromospheric and coronal magnetic fields. In this paper, two semi-analytical solutions of force-free fields (Low and Lou in Astrophys. J. 352:343, 1990) have been used to study the errors of nonlinear force-free (NLFF) fields based on force-free factor α. Three NLFF fields are extrapolated by approximate vertical integration (AVI) Song et al. (Astrophys. J. 649:1084, 2006), boundary integral equation (BIE) Yan and Sakurai (Sol. Phys. 195:89, 2000) and optimization (Opt.) Wiegelmann (Sol. Phys. 219:87, 2004) methods. Compared with the first semi-analytical field, it is found that the mean values of absolute relative standard deviations (RSD) of α along field lines are about 0.96-1.19, 0.63-1.07 and 0.43-0.72 for AVI, BIE and Opt. fields, respectively. While for the second semi-analytical field, they are about 0.80-1.02, 0.67-1.34 and 0.33-0.55 for AVI, BIE and Opt. fields, respectively. As for the analytical field, the calculation error of <| RSD|> is about 0.1˜0.2. It is also found that RSD does not apparently depend on the length of field line. These provide the basic estimation on the deviation of extrapolated field obtained by proposed methods from the real force-free field.

  7. An integral equation formulation for rigid bodies in Stokes flow in three dimensions

    NASA Astrophysics Data System (ADS)

    Corona, Eduardo; Greengard, Leslie; Rachh, Manas; Veerapaneni, Shravan

    2017-03-01

    We present a new derivation of a boundary integral equation (BIE) for simulating the three-dimensional dynamics of arbitrarily-shaped rigid particles of genus zero immersed in a Stokes fluid, on which are prescribed forces and torques. Our method is based on a single-layer representation and leads to a simple second-kind integral equation. It avoids the use of auxiliary sources within each particle that play a role in some classical formulations. We use a spectrally accurate quadrature scheme to evaluate the corresponding layer potentials, so that only a small number of spatial discretization points per particle are required. The resulting discrete sums are computed in O (n) time, where n denotes the number of particles, using the fast multipole method (FMM). The particle positions and orientations are updated by a high-order time-stepping scheme. We illustrate the accuracy, conditioning and scaling of our solvers with several numerical examples.

  8. 15 CFR 310.1 - Background and purpose.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... Expositions (BIE) rules. The BIE is an international organization established by the Paris Convention of 1928... ratification of the Paris Convention by the U.S. Senate (114 Cong. Rec. 11012). 1 The BIE defines a General... detailed BIE classification criteria and regulations are contained in the Paris Convention of 1928, as...

  9. Lasing eigenvalue problems: the electromagnetic modelling of microlasers

    NASA Astrophysics Data System (ADS)

    Benson, Trevor; Nosich, Alexander; Smotrova, Elena; Balaban, Mikhail; Sewell, Phillip

    2007-02-01

    Comprehensive microcavity laser models should account for several physical mechanisms, e.g. carrier transport, heating and optical confinement, coupled by non-linear effects. Nevertheless, considerable useful information can still be obtained if all non-electromagnetic effects are neglected, often within an additional effective-index reduction to an equivalent 2D problem, and the optical modes viewed as solutions of Maxwell's equations. Integral equation (IE) formulations have many advantages over numerical techniques such as FDTD for the study of such microcavity laser problems. The most notable advantages of an IE approach are computational efficiency, the correct description of cavity boundaries without stair-step errors, and the direct solution of an eigenvalue problem rather than the spectral analysis of a transient signal. Boundary IE (BIE) formulations are more economic that volume IE (VIE) ones, because of their lower dimensionality, but they are only applicable to the constant cavity refractive index case. The Muller BIE, being free of 'defect' frequencies and having smooth or integrable kernels, provides a reliable tool for the modal analysis of microcavities. Whilst such an approach can readily identify complex-valued natural frequencies and Q-factors, the lasing condition is not addressed directly. We have thus suggested using a Muller BIE approach to solve a lasing eigenvalue problem (LEP), i.e. a linear eigenvalue solution in the form of two real-valued numbers (lasing wavelength and threshold information) when macroscopic gain is introduced into the cavity material within an active region. Such an approach yields clear insight into the lasing thresholds of individual cavities with uniform and non-uniform gain, cavities coupled as photonic molecules and cavities equipped with one or more quantum dots.

  10. A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

    NASA Technical Reports Server (NTRS)

    Homicz, G. F.; Moselle, J. R.

    1985-01-01

    A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

  11. Computational statistics using the Bayesian Inference Engine

    NASA Astrophysics Data System (ADS)

    Weinberg, Martin D.

    2013-09-01

    This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.

  12. Where You Look Matters for Body Perception: Preferred Gaze Location Contributes to the Body Inversion Effect

    PubMed Central

    McKean, Danielle L.; Tsao, Jack W.; Chan, Annie W.-Y.

    2017-01-01

    The Body Inversion Effect (BIE; reduced visual discrimination performance for inverted compared to upright bodies) suggests that bodies are visually processed configurally; however, the specific importance of head posture information in the BIE has been indicated in reports of BIE reduction for whole bodies with fixed head position and for headless bodies. Through measurement of gaze patterns and investigation of the causal relation of fixation location to visual body discrimination performance, the present study reveals joint contributions of feature and configuration processing to visual body discrimination. Participants predominantly gazed at the (body-centric) upper body for upright bodies and the lower body for inverted bodies in the context of an experimental paradigm directly comparable to that of prior studies of the BIE. Subsequent manipulation of fixation location indicates that these preferential gaze locations causally contributed to the BIE for whole bodies largely due to the informative nature of gazing at or near the head. Also, a BIE was detected for both whole and headless bodies even when fixation location on the body was held constant, indicating a role of configural processing in body discrimination, though inclusion of the head posture information was still highly discriminative in the context of such processing. Interestingly, the impact of configuration (upright and inverted) to the BIE appears greater than that of differential preferred gaze locations. PMID:28085894

  13. 76 FR 9593 - New Agency Information Collection for Solicitation of Nominations for the Advisory Board for...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-02-18

    ... the Paperwork Reduction Act of 1995, the Bureau of Indian Education (BIE) is seeking comments on a... with Disabilities Education Improvement Act. The BIE is seeking approval from the Office of Management... requesting comment on the information the BIE may collect in the future for nominations by a separate Federal...

  14. Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

    NASA Astrophysics Data System (ADS)

    Lovell, Amy Elizabeth

    Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

  15. Annual Performance Report. FFY 2012. Revised Clarification April 30, 2014. APR Template-Part B.

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2014

    2014-01-01

    During school year (SY) 2012-2013, the Bureau of Indian Education (BIE) continued its efforts to improve the validity and reliability of data reporting. BIE data collections are dependent on school level entry (self-reporting) into the Native American Student Information System (NASIS) or into the BIE's Academic Report (formerly the BIEs…

  16. Annual Performance Report. Bureau of Indian Education FFY 2011. Revised Clarification, May 17, 2013. APR Template-Part B

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2013

    2013-01-01

    During SY 2011-2012, the Bureau of Indian Education (BIE) continued their efforts to improve the validity and reliability of data reporting. BIE data collections are dependent on school level entry (self-reporting) into the Native American Student Information System (NASIS) or into the BIE's Annual Report from the schools. In addition, data…

  17. Characterization of newly established bovine intestinal epithelial cell line.

    PubMed

    Miyazawa, Kohtaro; Hondo, Tetsuya; Kanaya, Takashi; Tanaka, Sachi; Takakura, Ikuro; Itani, Wataru; Rose, Michael T; Kitazawa, Haruki; Yamaguchi, Takahiro; Aso, Hisashi

    2010-01-01

    Membranous epithelial cells (M cells) of the follicle-associated epithelium in Peyer's patches have a high capacity for transcytosis of several viruses and microorganisms. Here, we report that we have successfully established a bovine intestinal epithelial cell line (BIE cells) and developed an in vitro M cell model. BIE cells have a cobblestone morphology and microvilli-like structures, and strongly express cell-to-cell junctional proteins and cytokeratin, which is a specific intermediate filament protein of epithelial cells. After co-culture with murine intestinal lymphocytes or treatment with supernatant from bovine PBMC cultured with IL-2, BIE cells acquired the ability of transcytosis. Therefore, BIE cells have typical characteristics of bovine intestinal epithelial cells and also have the ability to differentiate into an M cell like linage. In addition, our results indicate that contact between immune cells and epithelial cells may not be absolutely required for the differentiation of M cells. We think that BIE cells will be useful for studying the transport mechanisms of various pathogens and also the evaluation of drug delivery via M cells.

  18. 77 FR 14561 - Tribal Consultation Sessions-Administrative Organizational Assessment Draft Report...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-03-12

    ... DEPARTMENT OF THE INTERIOR Tribal Consultation Sessions--Administrative Organizational Assessment Draft Report, Organizational Streamlining of BIA and BIE, and BIE Topics AGENCY: Office of the Assistant...: the Administrative Organizational Assessment Draft Report on the organization of the AS-IA; ways to...

  19. Consent Agreement with the US Department of Interior (DOI), Bureau of Indian Affairs (BIA) and Bureau of Indian Education (BIE)

    EPA Pesticide Factsheets

    Consent Agreement between EPA and the Department of Interior (DOI), Bureau of Indian Affairs and Bureau of Indian Education (BIE) for violations of RCRA, CAA, TSCA, AHERA, and SDWA. These violations involve schools and public water systems.

  20. Comments on the paper by Zinoviev and Bies "On Acoustic Radiation by a Rigid Object in a Fluid Flow"

    NASA Technical Reports Server (NTRS)

    Farassat, F.

    2005-01-01

    In a recent paper by Zinoviev and Bies in this Journal, the authors have claimed that the well-known theoretical results of Curle and Ffowcs Williams and Hawkings (FW-H) are incorrect. This claim is categorically refuted below and serious errors are pointed out.

  1. A newly established bovine intestinal epithelial cell line is effective for in vitro screening of potential antiviral immunobiotic microorganisms for cattle.

    PubMed

    Chiba, Eriko; Villena, Julio; Hosoya, Shoichi; Takanashi, Naoya; Shimazu, Tomoyuki; Aso, Hisashi; Tohno, Masanori; Suda, Yoshihito; Kawai, Yasushi; Saito, Tadao; Miyazawa, Kenji; He, Fang; Kitazawa, Haruki

    2012-10-01

    We evaluated whether a bovine intestinal epithelial (BIE) cell line could serve as a useful in vitro model system for studying antiviral immune responses in bovine intestinal epithelial cells (IECs) and for the primary screening of immunobiotic microorganisms with antiviral protective capabilities. Immunofluorescent analyses revealed that toll-like receptor 3 (TLR3) was expressed in BIE cells, and the results of real-time quantitative PCR showed that these cells respond to stimulation with poly(I:C) by up-regulating pro-inflammatory cytokines and type I interferons. In addition, we demonstrated that BIE cells are useful for the primary screening of immunobiotic lactic acid bacteria strains which are able to beneficially modulate antiviral immune responses triggered by TLR3 activation in bovine IECs. The characterization of BIE cells performed in the present study represents an important step towards the establishment of a valuable bovine in vitro system that could be used for the development of immunomodulatory feed for bovine hosts. Copyright © 2011 Elsevier Ltd. All rights reserved.

  2. South Dakota School Principals' Preferred Leadership Styles for Leading Change to Face Poverty and Discrimination

    ERIC Educational Resources Information Center

    Soka, John Alex

    2011-01-01

    This quantitative research study identified perceptions regarding leadership styles of a sample of high school, middle school, and elementary school principals serving in South Dakota public and tribal/BIE (Bureau of Indian Education) schools in 2011. From 152 public school districts and 20 tribal/BIE schools, a sample of 148 school principals was…

  3. It's All in Your Head: Why Is the Body Inversion Effect Abolished for Headless Bodies?

    ERIC Educational Resources Information Center

    Yovel, Galit; Pelc, Tatiana; Lubetzky, Ida

    2010-01-01

    It has been recently argued that human bodies are processed by a specialized processing mechanism. Central evidence was that body inversion reduces recognition abilities (body inversion effect; BIE) as much as it does for faces, but more than for other objects. Here we showed that the BIE is markedly reduced for headless bodies and examined the…

  4. An Unsupervised Method for Uncovering Morphological Chains (Open Access, Publisher’s Version)

    DTIC Science & Technology

    2015-03-08

    Consortium. Marco Baroni, Johannes Matiasek, and Harald Trost. 2002. Unsupervised discovery of morphologically re- lated words based on orthographic and...Better word representations with re- cursive neural networks for morphology. In CoNLL, Sofia, Bulgaria. Mohamed Maamouri, Ann Bies, Hubert Jin, and Tim

  5. Annual Performance Report 2009-2010. Bureau of Indian Education. Submitted February 1, 2011. Revised Clarification, April 18, 2011. APR Template-Part B (4)

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2011

    2011-01-01

    During SY 2009-2010, the Bureau of Indian Education (BIE) continued their efforts to improve the validity and reliability of data reporting. BIE data collections are dependent on school level entry (self reporting) into the Native American Student Information System (NASIS) or into the Bureau's Annual Report from the schools. In addition,…

  6. Annual Performance Report 2010-2011. Bureau of Indian Education. Submitted February 1, 2012. Revised Clarification, April 17, 2012. APR Template-Part B (4)

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2012

    2012-01-01

    During SY 2010-2011, the Bureau of Indian Education (BIE) continued their efforts to improve the validity and reliability of data reporting. BIE data collections are dependent on school level entry (self-reporting) into the Native American Student Information System (NASIS) or into the Bureau's Annual Report from the schools. In addition,…

  7. Dynamic model of open shell structures buried in poroelastic soils

    NASA Astrophysics Data System (ADS)

    Bordón, J. D. R.; Aznárez, J. J.; Maeso, O.

    2017-08-01

    This paper is concerned with a three-dimensional time harmonic model of open shell structures buried in poroelastic soils. It combines the dual boundary element method (DBEM) for treating the soil and shell finite elements for modelling the structure, leading to a simple and efficient representation of buried open shell structures. A new fully regularised hypersingular boundary integral equation (HBIE) has been developed to this aim, which is then used to build the pair of dual BIEs necessary to formulate the DBEM for Biot poroelasticity. The new regularised HBIE is validated against a problem with analytical solution. The model is used in a wave diffraction problem in order to show its effectiveness. It offers excellent agreement for length to thickness ratios greater than 10, and relatively coarse meshes. The model is also applied to the calculation of impedances of bucket foundations. It is found that all impedances except the torsional one depend considerably on hydraulic conductivity within the typical frequency range of interest of offshore wind turbines.

  8. How Are They Now? Longer Term Effects of eCoaching through Online Bug-in-Ear Technology

    ERIC Educational Resources Information Center

    Rock, Marcia L.; Schumacker, Randall E.; Gregg, Madeleine; Howard, Pamela W.; Gable, Robert A.; Zigmond, Naomi

    2014-01-01

    In this study, using mixed methods, we investigated the longer term effects of eCoaching through advanced online bug-in-ear (BIE) technology. Quantitative data on five dependent variables were extracted from 14 participants' electronically archived video files at three points in time--Spring 1 (i.e., baseline, which was the first semester of…

  9. Kinetic isotope effects reveal early transition state of protein lysine methyltransferase SET8

    PubMed Central

    Linscott, Joshua A.; Kapilashrami, Kanishk; Wang, Zhen; Senevirathne, Chamara; Bothwell, Ian R.; Blum, Gil; Luo, Minkui

    2016-01-01

    Protein lysine methyltransferases (PKMTs) catalyze the methylation of protein substrates, and their dysregulation has been linked to many diseases, including cancer. Accumulated evidence suggests that the reaction path of PKMT-catalyzed methylation consists of the formation of a cofactor(cosubstrate)–PKMT–substrate complex, lysine deprotonation through dynamic water channels, and a nucleophilic substitution (SN2) transition state for transmethylation. However, the molecular characters of the proposed process remain to be elucidated experimentally. Here we developed a matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF-MS) method and corresponding mathematic matrix to determine precisely the ratios of isotopically methylated peptides. This approach may be generally applicable for examining the kinetic isotope effects (KIEs) of posttranslational modifying enzymes. Protein lysine methyltransferase SET8 is the sole PKMT to monomethylate histone 4 lysine 20 (H4K20) and its function has been implicated in normal cell cycle progression and cancer metastasis. We therefore implemented the MS-based method to measure KIEs and binding isotope effects (BIEs) of the cofactor S-adenosyl-l-methionine (SAM) for SET8-catalyzed H4K20 monomethylation. A primary intrinsic 13C KIE of 1.04, an inverse intrinsic α-secondary CD3 KIE of 0.90, and a small but statistically significant inverse CD3 BIE of 0.96, in combination with computational modeling, revealed that SET8-catalyzed methylation proceeds through an early, asymmetrical SN2 transition state with the C-N and C-S distances of 2.35–2.40 Å and 2.00–2.05 Å, respectively. This transition state is further supported by the KIEs, BIEs, and steady-state kinetics with the SAM analog Se-adenosyl-l-selenomethionine (SeAM) as a cofactor surrogate. The distinct transition states between protein methyltransferases present the opportunity to design selective transition-state analog inhibitors. PMID:27940912

  10. Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

    NASA Astrophysics Data System (ADS)

    Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

    2016-04-01

    The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

  11. Redox-Triggered Bonding-Induced Emission of Thiol-Functionalized Gold Nanoclusters for Luminescence Turn-On Detection of Molecular Oxygen.

    PubMed

    Ao, Hang; Feng, Hui; Zhao, Mengting; Zhao, Meizhi; Chen, Jianrong; Qian, Zhaosheng

    2017-11-22

    Most optical sensors for molecular oxygen were developed based on the quenching effect of the luminescence of oxygen-sensitive probes; however, the signal turn-off mode of these probes is undesirable to quantify and visualize molecular oxygen. Herein, we report a novel luminescence turn-on detection strategy for molecular oxygen via the specific oxygen-triggered bonding-induced emission of thiol-functionalized gold nanoclusters. Thiol-functionalized gold nanoclusters were prepared by a facile one-step synthesis, and as-prepared gold nanoclusters possess significant aggregation-induced emission (AIE) property. It is the first time to discover the oxygen-triggered bonding-induced emission (BIE) behavior of gold nanoclusters, which results in disulfide-linked covalent bonding assemblies with intensely red luminescence. This specific redox-triggered BIE is capable of quantitatively detecting dissolved oxygen in aqueous solution in a light-up manner, and trace amount of dissolved oxygen at ppb level is achieved based on this detection method. A facile and convenient test strip for oxygen detection was also developed to monitor molecular oxygen in a gas matrix. Covalent bonding-induced emission is proven to be a more efficient way to attain high brightness of AIEgens than a physical aggregation-induced emission process, and provides a more convenient and desirable detection method for molecular oxygen than the previous sensors.

  12. The Effects of Bug-in-Ear Coaching on Pre-Service Behavior Analysts' Use of Functional Communication Training.

    PubMed

    Artman-Meeker, Kathleen; Rosenberg, Nancy; Badgett, Natalie; Yang, Xueyan; Penney, Ashley

    2017-09-01

    Behavior analysts play an important role in supporting the behavior and learning of young children with disabilities in natural settings. However, there is very little research related specifically to developing the skills and competencies needed by pre-service behavior analysts. This study examined the effects of "bug-in-ear" (BIE) coaching on pre-service behavior analysts' implementation of functional communication training with pre-school children with autism in their classrooms. BIE coaching was associated with increases in the rate of functional communication training trials each intern initiated per session and in the fidelity with which interns implemented functional communication training. Adults created more intentional opportunities for children to communicate, and adults provided more systematic instruction around those opportunities.

  13. Hydroclimatic shifts recorded in peat archive from Rąbień mire (Central Poland) - better understanding of past climate changes using multidisciplinary approach

    NASA Astrophysics Data System (ADS)

    Słowiński, Michał; Marcisz, Katarzyna; Płóciennik, Mateusz; Obremska, Milena; Pawłowski, Dominik; Okupny, Daniel; Słowińska, Sandra; Borówka, Ryszard; Kittel, Piotr; Forysiak, Jacek; Michczyńska, Danuta J.; Lamentowicz, Mariusz

    2016-04-01

    Hydrological changes are main drivers of the processes occurring in the peatland ecosystem, e.g. organic matter accumulation and decomposition. Hydroclimatic changes in mires are caused by various non-climatic factors, such as hydroseral succession or land use changes. Central Europe, namely Poland, is characterized by a transitional climate with influence o both continental and Atlantic air masses, which makes a this region a very sensitive to climate change. Here we explore a potential of multidisciplinary approach in reconstruction of past climate change and particularly hydroclimatic conditions which control in Sphagnum peatland ecosystem. We reconstructed 3300 years (between 3,500 BC and 200 BC) history of development of Rąbień mire using several biotic proxies (pollen, plant macrofossils, testate amoebae, Cladocera, Chironomidae) and geochemistry. Study site - Rąbień mire (area 42 ha) is located in central Poland and it is protected nature reserve. The origin of the mire depression is connected with the development of the thermokarst basin isolated by dunes. Rąbień mire is limnogenic, i.e. formed by the process of terrestrialisation of a water body and thickness of biogenic deposits is 6.2 m (440 cm of lacustrine sediment and 180 cm of peat). Our results demonstrate the high potential of Rąbień peat record for reconstructing the palaeohydrological dynamics. The studied time interval is characterized by two pronounced dry periods: ~2,500 to ~1,700 cal. BC and ~800 to ~600 cal. BC, and two periods of significant increases in water table: ~1,100 to ~800 cal. BC and ~600 to ~250 cal. BC. The timing of the wet shift at 600 cal. BC corresponds to wet periods in different sites from Central and Eastern Europe. Our investigation reveals a complex pattern of proxies, what might be linked to the past atmospheric circulation patterns. Extreme hydroclimatic conditions most possibly had a direct impact on the functioning of peatland ecosystems. What has been observed in the within the peatland monitoring during the heat wave events in 2015 (Linje mire, Northern Poland). In our opinion, only reconstructions supported by the knowledge of current observations from peatland ecosystems may provide a better interpretation of past climate changes. The research was supported by the National Science Centre Poland (grants NN 306 27 6735 NN 306 034 040, No 2015/17/B/ST10/03430). This study is a contribution to the Virtual Institute of Integrated Climate and Landscape Evolution (ICLEA) of the Helmholtz Association. We acknowledge support from grant PSPB-013/2010 from Switzerland through the Swiss Contribution to the enlarged European Union.

  14. [Effects of blueberry on apoptosis and expression of Bcl-2 and Bax in HSC-T6].

    PubMed

    Lu, Shuang; Cheng, Mingliang; Yang, Demeng; Liu, Yang; Guan, Li; Wu, Jun

    2015-08-18

    To investigate the effects of blueberry on the apoptosis, expression of Bcl-2 and Bax in rat hepatic stellate cell (HSC-T6). 10% blueberry serum at low, middle and high dose, 10% Fu-Fang-Bie-Jia-Ruan-Gan tablet serum and 10% saline serum were prepared by method of serum pharmacology. Subcultured HSC-T6 was divided into saline serum control group, blueberry serum at low, middle, high dose and Fu-Fang-Bie-Jia-Ruan-Gan tablet serum group, and then was respectively incubated at different dose of 10% blueberry serum, 10% Fu-Fang-Bie-Jia-Ruan-Gan tablet serum and 10% saline serum for 72 hours.Apoptosis of HSC-T6 was detected using flow cytometry with annexin V FITC/PI double staining. The expression of Bcl-2 and Bax in HSC-T6 were examined using immunocytochemistry and Western blotting, respectively. There was no significant difference for HSC-T6 Bax protein expression in the low, middle and high dose blueberry serum groups, compared with saline serum control group, respectively.In the high-dose blueberry serum group HSC-T6 early and total apoptosis rate increased significantly compared with the saline serum control group (5.55% ± 0.98% vs 2.53% ± 0.46%, 7.01% ± 1.05% vs 2.96% ± 0.81%, both P<0.05); Bcl-2 protein expression was significantly decreased (A value, 82 ± 35 vs 51 ± 13, P<0.05); Bcl-2/Bax ratio was significantly decreased (0.26 ± 0.02 vs 0.46 ± 0.03, P<0.05); HSC-T6 early and total apoptosis rate, Bcl-2 expression and Bcl-2/Bax ratio in the low and the middle dose blueberry serum group showed no significant difference with the saline serum control group. Blueberry can induce HSC-T6 apoptosis by down-regulating Bcl-2 expression and decreasing the ratio of Bcl-2/Bax in HSC-T6 cells, so it may have potential interference effects on hepatic fibrosis.

  15. 76 FR 2349 - Office of Postsecondary Education; Overview Information; Business and International Education...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-01-13

    ... DEPARTMENT OF EDUCATION Office of Postsecondary Education; Overview Information; Business and International Education Program Notice inviting applications for new awards for fiscal year (FY) 2011. Catalog... Business and International Education (BIE) Program provides grants to enhance international business...

  16. 77 FR 70807 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-11-27

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  17. 77 FR 47873 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-08-10

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  18. 76 FR 40929 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-07-12

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  19. 75 FR 50780 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-08-17

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  20. Cyclophilin A is a new M cell marker of bovine intestinal epithelium.

    PubMed

    Hondo, Tetsuya; Someya, Shunsuke; Nagasawa, Yuya; Terada, Shunsuke; Watanabe, Hitoshi; Chen, Xiangning; Watanabe, Kouichi; Ohwada, Shyuichi; Kitazawa, Haruki; Rose, Michael T; Nochi, Tomonori; Aso, Hisashi

    2016-06-01

    Microfold (M) cells in the follicle-associated epithelium (FAE) of Peyer's patches contribute to the mucosal immune response by the transcytosis of microorganisms. The mechanism by which M cells take up microorganisms, and the functional proteins by which they do this, are not clear. In order to explore one such protein, we developed a 2H5-F3 monoclonal antibody (2H5-F3 mAb) through its binding to bovine M cells, and identified the antibody reactive molecule as cyclophilin A (Cyp-A). The localization patterns of Cyp-A were very similar to the localization pattern of cytokeratin (CK) 18-positive M cells. Cyp-A was identified at the luminal surface of CK18-positive M cells in bovine jejunal and ileal FAE. The membranous localization of Cyp-A in the bovine intestinal cell line (BIE cells) increased as cells differentiated toward M cells, as determined by flow cytometry analysis. Additionally, BIE cells released Cyp-A to the extracellular space and the differentiation of BIE cells to M cells increased the secretion of Cyp-A, as determined by western blotting. Accordingly, Cyp-A may be localized in M cells in the small intestinal epithelium of cattle. The rise of the membranous localization and secretion of Cyp-A by differentiation toward M cells indicates that Cyp-A has an important role in the function of M cells. While Cyp-A of the M cell membrane may contribute to the uptake of viruses with peptidyl-prolyl cis-trans isomerase activity, in the extracellular space Cyp-A may work as a chemokine and contribute to the distribution of immuno-competent cells.

  1. Settlement with the Department of the Interior (DOI) to Resolve Violations at Schools in Indian Country

    EPA Pesticide Factsheets

    Consent Agreement with the DOI, BIA and Bureau of Indian Education (BIE) on alleged violations at schools and public water systems owned, operated or the responsibility of DOI. Violations occurred under the CAA, CWA, SDWA, TSCA, ADHERA.

  2. 76 FR 17965 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-03-31

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... Individuals with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  3. 75 FR 82410 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-12-30

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... Individuals with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  4. 77 FR 16062 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-03-19

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... Individuals with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  5. 77 FR 28897 - Advisory Board for Exceptional Children

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-05-16

    ... DEPARTMENT OF THE INTERIOR Bureau of Indian Affairs Advisory Board for Exceptional Children AGENCY... (BIE) is announcing that the Advisory Board for Exceptional Children (Advisory Board) will hold its... Individuals with Disabilities Education Act of 2004 (IDEA) for Indian children with disabilities. DATES: The...

  6. Mediation of donor–acceptor distance in an enzymatic methyl transfer reaction

    PubMed Central

    Zhang, Jianyu; Kulik, Heather J.; Martinez, Todd J.; Klinman, Judith P.

    2015-01-01

    Enzymatic methyl transfer, catalyzed by catechol-O-methyltransferase (COMT), is investigated using binding isotope effects (BIEs), time-resolved fluorescence lifetimes, Stokes shifts, and extended graphics processing unit (GPU)-based quantum mechanics/molecular mechanics (QM/MM) approaches. The WT enzyme is compared with mutants at Tyr68, a conserved residue that is located behind the reactive sulfur of cofactor. Small (>1) BIEs are observed for an S-adenosylmethionine (AdoMet)-binary and abortive ternary complex containing 8-hydroxyquinoline, and contrast with previously reported inverse (<1) kinetic isotope effects (KIEs). Extended GPU-based computational studies of a ternary complex containing catecholate show a clear trend in ground state structures, from noncanonical bond lengths for WT toward solution values with mutants. Structural and dynamical differences that are sensitive to Tyr68 have also been detected using time-resolved Stokes shift measurements and molecular dynamics. These experimental and computational results are discussed in the context of active site compaction that requires an ionization of substrate within the enzyme ternary complex. PMID:26080432

  7. Methodology of Estimation of Methane Emissions from Coal Mines in Poland

    NASA Astrophysics Data System (ADS)

    Patyńska, Renata

    2014-03-01

    Based on a literature review concerning methane emissions in Poland, it was stated in 2009 that the National Greenhouse Inventory 2007 [13] was published. It was prepared firstly to meet Poland's obligations resulting from point 3.1 Decision no. 280/2004/WE of the European Parliament and of the Council of 11 February 2004, concerning a mechanism for monitoring community greenhouse gas emissions and for implementing the Kyoto Protocol and secondly, for the United Nations Framework Convention on Climate Change (UNFCCC) and Kyoto Protocol. The National Greenhouse Inventory states that there are no detailed data concerning methane emissions in collieries in the Polish mining industry. That is why the methane emission in the methane coal mines of Górnośląskie Zagłębie Węglowe - GZW (Upper Silesian Coal Basin - USCB) in Poland was meticulously studied and evaluated. The applied methodology for estimating methane emission from the GZW coal mining system was used for the four basic sources of its emission. Methane emission during the mining and post-mining process. Such an approach resulted from the IPCC guidelines of 2006 [10]. Updating the proposed methods (IPCC2006) of estimating the methane emissions of hard coal mines (active and abandoned ones) in Poland, assumes that the methane emission factor (EF) is calculated based on methane coal mine output and actual values of absolute methane content. The result of verifying the method of estimating methane emission during the mining process for Polish coal mines is the equation of methane emission factor EF.

  8. Federal Grants Drive STEM Curricula at SIPI

    ERIC Educational Resources Information Center

    Tribal College Journal of American Indian Higher Education, 2016

    2016-01-01

    First established in 1971, Southwestern Indian Polytechnic Institute (SIPI) in Albuquerque, New Mexico, is one of two tribal colleges that the Bureau of Indian Education (BIE) operates and funds. SIPI offers a variety of certificate and two-year associate's degree programs, but its primary curricular focus remains the science, technology,…

  9. The impact of kura clover living mulch on nitrous oxide emissions in a corn/soybean system

    USDA-ARS?s Scientific Manuscript database

    Nitrous oxide (N2O) is a potent greenhouse gas and the dominant ozone depleting substance. Produced primarily in agricultural soils, efforts to reduce N2O emissions are underway, but mitigation results thus far have been inconsistent. The leguminous perennial kura clover (Trifolium ambiguum M. Bie...

  10. 25 CFR 36.97 - What basic requirements must a program's health services meet?

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ... the BIE and the Indian Health Service or between a tribally-operated homeliving program and the Indian Health Service or tribal health program. (b) A homeliving program must have written procedures for... MINIMUM ACADEMIC STANDARDS FOR THE BASIC EDUCATION OF INDIAN CHILDREN AND NATIONAL CRITERIA FOR DORMITORY...

  11. Bilingual Intercultural Education in Indigenous Schools: An Ethnography of Teacher Interpretations of Government Policy

    ERIC Educational Resources Information Center

    Valdiviezo, Laura

    2009-01-01

    This paper explores how teachers' beliefs and practices create spaces for the contestation and innovation of bilingual intercultural education (BIE) policy, a policy of indigenous culture and language revitalization in Peru. Based on ethnographic research, there are two central arguments developed throughout this paper. First, the author argues…

  12. Indigenous Worldviews in Intercultural Education: Teachers' Construction of Interculturalism in a Bilingual Quechua-Spanish Program

    ERIC Educational Resources Information Center

    Valdiviezo, Laura Alicia

    2010-01-01

    This paper examines teachers' implementation of a bilingual intercultural education (BIE) program in Peru. This program is inspired by global policies that promote cultural pluralism and educational access to marginalized indigenous populations. Broadly addressed in policy in Andean countries, interculturalism in Peru has remained a core…

  13. The 13th Annual Legislative Summit (Washington, DC, 2010). Briefing Papers

    ERIC Educational Resources Information Center

    National Indian Education Association, 2010

    2010-01-01

    This volume contains briefing papers presented at the 13th Annual National Indian Education Association (NIEA) Legislative Summit held in Washington, DC. The following papers are included: (1) NIEA Appropriations Priorities for FY11; (2) The President's Budget Request for Fiscal Year 2011 for Native Education; (3) BIE Race to the Top; (4)…

  14. 76 FR 15334 - Information Collection for IDEIA Part B and C Child Count; Comment Request

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-03-21

    ... C. In IDEIA Part B--Assistance for Education of All Children with Disabilities, 20 U.S.C. 1411(h)(4... Child Count; Comment Request AGENCY: Bureau of Indian Affairs, Interior. ACTION: Notice of Submission to... of Indian Education (BIE), U.S. Department of the Interior (Interior) is submitting a proposed...

  15. Soil erosion and nutrient runoff in corn silage production with kura clover living mulch and winter rye

    USDA-ARS?s Scientific Manuscript database

    Corn (Zea mays L.) harvested for silage is a productive forage crop, but one that can exacerbate soil loss, surface water runoff, and nonpoint source nutrient pollution from agricultural fields. The objective of this research was to compare the effects of using Kura clover (Trifolium ambiguum M. Bie...

  16. [Intervention effects of Dan-fang capsule in rats with hepatic fibrosis].

    PubMed

    Hu, X H; Wu, J; Lu, S

    2017-09-19

    Objective: To investigate the interventional effect of Dan-fang capsule on liver fibrosis in rats. Methods: Sixty one-week aged male healthy SD rats [weight (180±20) g] were randomly divided into normal control group (group A), hepatic fibrosis model group (group B), Fu-Fang-Bie-Jia-Ruan-Gan tablet group (group C), Dan-fang capsule groups at high, middle and low dose group (group D, E, F, respectively). Except for the normal control group, hepatic fibrosis was induced in other groups by intraperitoneal injection of porcine serum.Simultaneously, rats in Dan-fang capsule groups were administered by gavage with Dan-fang capsule at doses of 4.32, 2.16, 0.54 g/kg, respectively.Rats in Fu-Fang-Bie-Jia-Ruan-Gan tablet group were orally administered by gavage with Fu-Fang-Bie-Jia-Ruan-Gan tablet (0.54 g/kg) every day and the normal control group received saline alone.All rats were killed at the end of the 12th week. Serum alanine aminotransferase (ALT), aspartate aminotransferase (AST) and PⅢnp clia (PⅢNP) were measured in the groups.Pathology changes of hepatic tissue were evaluated by hematoxylin-eosin (HE) and Masson staining.The proteinic expressions of alpha-smooth muscle actin (α-SMA), collagen-Ⅰ (COL-Ⅰ) and collagen-Ⅲ (COL-Ⅲ) were observed with the method of immunohistochemistry.Analysis of variance was applied when data were compared among groups. Results: Compared with those in the group A, the levels of ALT, AST and PⅢNP in serum and the expressions of α-SMA, COL-Ⅰ and COL-Ⅲ in liver tissues were significantly higher in group B [(68.3±3.4) vs (51.5±6.3) U/L, (205±52) vs (135±24) U/L, (3.1±1.4) vs (1.6±0.6) μg/L and 0.35±0.02 vs 0.13±0.02, 0.37±0.02 vs 0.13±0.02, 0.43±0.13 vs 0.13±0.01, t =17.020, 71.053, 1.552, 0.214, 0.241, 0.292, all P <0.01], and the degree of liver fibrosis significantly increased in group B than that in group A. Compared with those in group B, the levels of ALT, AST, PⅢNP and the expressions of α-SMA, COL-Ⅰ, COL-Ⅲ were all significantly lower in group D, E and F ( t =-58.232--0.104, all P <0.01). The degree of liver fibrosis significantly reduced in group D, E and F than that in group B ( Z =3.82, 3.76, 3.90, all P <0.05). Conclusion: Dan-fang capsule has certain preventive effect on liver fibrosis that caused by porcine serum in rats.

  17. AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

    NASA Astrophysics Data System (ADS)

    Lu, Benzhuo; Cheng, Xiaolin; Huang, Jingfang; McCammon, J. Andrew

    2010-06-01

    A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Program summaryProgram title: AFMPB: Adaptive fast multipole Poisson-Boltzmann solver Catalogue identifier: AEGB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL 2.0 No. of lines in distributed program, including test data, etc.: 453 649 No. of bytes in distributed program, including test data, etc.: 8 764 754 Distribution format: tar.gz Programming language: Fortran Computer: Any Operating system: Any RAM: Depends on the size of the discretized biomolecular system Classification: 3 External routines: Pre- and post-processing tools are required for generating the boundary elements and for visualization. Users can use MSMS ( http://www.scripps.edu/~sanner/html/msms_home.html) for pre-processing, and VMD ( http://www.ks.uiuc.edu/Research/vmd/) for visualization. Sub-programs included: An iterative Krylov subspace solvers package from SPARSKIT by Yousef Saad ( http://www-users.cs.umn.edu/~saad/software/SPARSKIT/sparskit.html), and the fast multipole methods subroutines from FMMSuite ( http://www.fastmultipole.org/). Nature of problem: Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Solution method: A novel node-patch scheme is used to discretize the well-conditioned boundary integral equation formulation of the linearized Poisson-Boltzmann equation. Various Krylov subspace solvers can be subsequently applied to solve the resulting linear system, with a bounded number of iterations independent of the number of discretized unknowns. The matrix-vector multiplication at each iteration is accelerated by the adaptive new versions of fast multipole methods. The AFMPB solver requires other stand-alone pre-processing tools for boundary mesh generation, post-processing tools for data analysis and visualization, and can be conveniently coupled with different time stepping methods for dynamics simulation. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/~lubz/afmpb.html and http://mccammon.ucsd.edu/ for updates and changes. Running time: The running time varies with the number of discretized elements ( N) in the system and their distributions. In most cases, it scales linearly as a function of N.

  18. Increasing the quality and germination gymnosperms by photonics methods

    NASA Astrophysics Data System (ADS)

    Iakovlev, Alexey; Durova, Anastasia; Kascheev, Sergey; Grishkanich, Aleksandr; Mak, Andrey; Ruzankina, Julia

    2017-02-01

    The research of seed sowing qualities demonstrates the considerable influence of laser irradiation on seeds of different species that are essential for the forestry of Russian Federation. For experiment, we used seeds of Spruce fir (Pícea ábies) and Siberian larch (Lárix sibírica). The seeds were exposed to radiation of the following wavelengths: 405 nm 500 mW, 450 nm 3000 mW, 532 nm 550 mW, 640 nm 1000 mW. The results show that laser exposure of seeds has positive impact on growth rate, technical germination ability, root formation, and more over on establishment and root formation while grafting. In experiments is obtained increasing germination by 15% and the germination time to 10%.

  19. Bureau of Indian Education (BIE), Albuquerque Service Center (ASC) Dispute Resolution in Special Education through Mediation. Parent/School and Mediator's Manual. Revised

    ERIC Educational Resources Information Center

    Copenhaver, John

    2007-01-01

    Parents and school staff usually agree upon issues regarding evaluation, eligibility, program, and placement of students with disabilities. However, there are times when disagreement occurs. Disagreements and conflict are often inevitable, but they need not produce negative results. Mediation in special education is a process to assist parents and…

  20. The Swift Trust Partnership: A Project Management Exercise Investigating the Effects of Trust and Distrust in Outsourcing Relationships

    ERIC Educational Resources Information Center

    Adler, Terry R.

    2005-01-01

    The Swift Trust exercise provides instructors with the opportunity to discuss the issues of managing trust and distrust perceptions in a team-based design. Lewicki, McAllister, and Bies's (1998) framework is used to allow students to experience the difficulties of deriving a common set of contract requirements based on team dynamics and…

  1. Examining the Perceptions of Parental Involvement in Schools: Implications for Changing Roles for School Leaders from the Voices of the Community

    ERIC Educational Resources Information Center

    Jojola, Tracia Keri

    2011-01-01

    Research studies have demonstrated that effective parental involvement correlates with positive academic success. This study sought to gain more insight into the perceptions of parents and caregivers of Navajo children enrolled in a K-12 tribally controlled, public, charter, or Bureau of Indian Education (BIE) operated schools. By completing a…

  2. Evaluation of Flammability of Footwear Upper Materials. Patent and Regular Shoe Upper Leather vs. Porvair and Clarino Poromerics

    DTIC Science & Technology

    1984-09-01

    leather is thus designated ŗ-ounce leather." -ll specimens, except the UL, had high-gloss polyurethane finishes. The UL ’eLi wr contained a...ITT Research Institute, October 1965, p. 18. 4.4 %d :i.bie 2. Comparativ ~e heat transfer values of shoe uppe materials vs. shoe upper materials with

  3. Intercultural bilingual education in Nicaragua: Contextualisation for improving the quality of education

    NASA Astrophysics Data System (ADS)

    Valiente Catter, Teresa

    2011-12-01

    For the past 35 years, various models of intercultural bilingual education (IBE) have been implemented in Latin American schools and adult education. While Spanish is the official language in Nicaragua, many indigenous languages, such as Miskito and Sumo-Mayangna, are also spoken - especially in the Atlantic coastal region. The Nicaraguan Ministry of Education, Culture and Sport recognises the need for a flexible curriculum that reflects individual local and regional linguistic and socio-cultural characteristics, through the use of mother tongue and second language learning. The contextualisation model applied in the Atlantic coastal region of Nicaragua is therefore based on the use of a languages strategy in preparing textbooks and basic technical materials with an IBE approach, as part of the process of improving the quality of education. Thus intercultural communication is enhanced, and the need to strengthen the systematic teaching of languages, differentiating between mother tongue, second language and foreign language, is recognised. As well as explaining the contextualisation process in detail, this article discusses the conceptual differences between intercultural bilingual education (IBE) and bilingual intercultural education (BIE). The paper concludes with several recommendations for the further development of BIE in Latin America.

  4. Bureau of Indian Education (BIE), Albuquerque Service Center (ASC) Due Process Hearing Officer Manual. Resolution Session and Due Process Hearing Procedures in Special Education. Revised

    ERIC Educational Resources Information Center

    Copenhaver, John

    2007-01-01

    Due process is a set of procedures that seeks to ensure fairness of education decisions and accountability, for both parents and educational professionals. The due process hearing provides a forum where disagreements about the identification, evaluation, educational placement, and provision of a free appropriate public education for students with…

  5. U.S. Department of the Interior, Bureau of Indian Education State Performance Plan. SPP Template-Part B. Revised May 17, 2013

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2013

    2013-01-01

    The Bureau of Indian Education (BIE) funds schools located on 63 reservations in 23 states across the nation. Of the 183 schools, 59 are Bureau operated and 124 are tribally controlled. One-hundred and sixteen schools provide instructional programs, 55 provide instructional as well as boarding services and 12 peripheral dormitories provide only…

  6. Bureau of Indian Affairs, Bureau of Indian Education State Performance Plan. Submitted February 1, 2011 (Resubmitted April 18, 2011). SPP Template-Part B

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2011

    2011-01-01

    The Bureau of Indian Education (BIE) funds schools located on 63 reservations in 23 states across the nation. Of the 183 schools, 59 are Bureau operated and 124 are tribally controlled. One-hundred and sixteen schools provide instructional programs, 55 provide instructional as well as boarding services and 12 peripheral dormitories provide only…

  7. Characteristics of Public School Districts in the United States: Results From the 2007-08 Schools and Staffing Survey. First Look. NCES 2009-320

    ERIC Educational Resources Information Center

    Aritomi, Paola; Coopersmith, Jared; Gruber, Kerry

    2009-01-01

    This report presents selected findings from the school district data file of the 2007-08 Schools and Staffing Survey (SASS). SASS is a nationally representative sample survey of public, private, and Bureau of Indian Education-funded (BIE) K-12 schools, principals, and teachers in the 50 states and the District of Columbia. The public school sample…

  8. U.S. Department of the Interior, Bureau of Indian Education State Performance Plan. Submitted February 1, 2012 (Re-Submitted April 17, 2012). SPP Template-Part B

    ERIC Educational Resources Information Center

    Bureau of Indian Education, 2012

    2012-01-01

    The Bureau of Indian Education (BIE) funds schools located on 63 reservations in 23 states across the nation. Of the 183 schools, 59 are Bureau operated and 124 are tribally controlled. One-hundred and sixteen schools provide instructional programs, 55 provide instructional as well as boarding services and 12 peripheral dormitories provide only…

  9. A Systems Biology-Based Investigation into the Pharmacological Mechanisms of Sheng-ma-bie-jia-tang Acting on Systemic Lupus Erythematosus by Multi-Level Data Integration.

    PubMed

    Huang, Lin; Lv, Qi; Liu, Fenfen; Shi, Tieliu; Wen, Chengping

    2015-11-12

    Sheng-ma-bie-jia-tang (SMBJT) is a Traditional Chinese Medicine (TCM) formula that is widely used for the treatment of Systemic Lupus Erythematosus (SLE) in China. However, molecular mechanism behind this formula remains unknown. Here, we systematically analyzed targets of the ingredients in SMBJT to evaluate its potential molecular mechanism. First, we collected 1,267 targets from our previously published database, the Traditional Chinese Medicine Integrated Database (TCMID). Next, we conducted gene ontology and pathway enrichment analyses for these targets and determined that they were enriched in metabolism (amino acids, fatty acids, etc.) and signaling pathways (chemokines, Toll-like receptors, adipocytokines, etc.). 96 targets, which are known SLE disease proteins, were identified as essential targets and the rest 1,171 targets were defined as common targets of this formula. The essential targets directly interacted with SLE disease proteins. Besides, some common targets also had essential connections to both key targets and SLE disease proteins in enriched signaling pathway, e.g. toll-like receptor signaling pathway. We also found distinct function of essential and common targets in immune system processes. This multi-level approach to deciphering the underlying mechanism of SMBJT treatment of SLE details a new perspective that will further our understanding of TCM formulas.

  10. Testimony of Quinton Roman Nose, Treasurer National Indian Education Association before the Senate Committee on Indian Affairs Oversight Hearing on Does Indian School Safety Get a Passing Grade?

    ERIC Educational Resources Information Center

    Roman Nose, Quinton

    2010-01-01

    In this testimony, Quinton Roman Nose talks on behalf of the National Indian Education Association about the shocking disparity in the safety of Bureau of Indian Education (BIE) schools. NIEA advocates for the unique educational and culturally related academic needs of Native students, working to ensure that the federal government upholds its…

  11. The Effect of the Use of the Ohio Baldrige Initiative Training in the Pilot Districts on the Sustained Use of Quality Tools by Classroom Teachers

    ERIC Educational Resources Information Center

    Schmidbauer, Hollace J.

    2010-01-01

    In the late 1990s, teachers in five pilot districts in Ohio were trained during the Baldrige in Education Initiative (BiE IN). Training included Baldrige's theory, quality process and quality tools. The study was a follow-up to determine the effect of the use of the Ohio Baldrige Initiative training in the pilot districts (and other early…

  12. Characteristics of Public, Private, and Bureau of Indian Education Elementary and Secondary School Principals in the United States: Results from the 2007-08 Schools and Staffing Survey. First Look. NCES 2009-323

    ERIC Educational Resources Information Center

    Battle, Danielle; Gruber, Kerry

    2009-01-01

    This report presents selected findings from the school principal data files of the 2007-08 Schools and Staffing Survey (SASS). SASS is a nationally representative sample survey of public, private, and Bureau of Indian Education-funded (BIE) K-12 schools, principals, and teachers in the 50 states and the District of Columbia. The public school…

  13. Characteristics of Public, Private, and Bureau of Indian Education Elementary and Secondary School Teachers in the United States: Results From the 2007-08 Schools and Staffing Survey. First Look. NCES 2009-324

    ERIC Educational Resources Information Center

    Coopersmith, Jared

    2009-01-01

    This report presents selected findings from the school teacher data files of the 2007-08 Schools and Staffing Survey (SASS). SASS is a nationally representative sample survey of public, private, and Bureau of Indian Education-funded (BIE) K-12 schools, principals, and teachers in the 50 states and the District of Columbia. The public school…

  14. A dust spectral energy distribution model with hierarchical Bayesian inference - I. Formalism and benchmarking

    NASA Astrophysics Data System (ADS)

    Galliano, Frédéric

    2018-05-01

    This article presents a new dust spectral energy distribution (SED) model, named HerBIE, aimed at eliminating the noise-induced correlations and large scatter obtained when performing least-squares fits. The originality of this code is to apply the hierarchical Bayesian approach to full dust models, including realistic optical properties, stochastic heating, and the mixing of physical conditions in the observed regions. We test the performances of our model by applying it to synthetic observations. We explore the impact on the recovered parameters of several effects: signal-to-noise ratio, SED shape, sample size, the presence of intrinsic correlations, the wavelength coverage, and the use of different SED model components. We show that this method is very efficient: the recovered parameters are consistently distributed around their true values. We do not find any clear bias, even for the most degenerate parameters, or with extreme signal-to-noise ratios.

  15. Characteristics of Public, Private, and Bureau of Indian Education Elementary and Secondary Schools in the United States: Results From the 2007-08 Schools and Staffing Survey. First Look. NCES 2009-321

    ERIC Educational Resources Information Center

    Keigher, Ashley

    2009-01-01

    This report presents selected findings from the school data files of the 2007-08 Schools and Staffing Survey (SASS). SASS is a nationally representative sample survey of public, private, and Bureau of Indian Education-funded (BIE) K-12 schools, principals, and teachers in the 50 states and the District of Columbia. The 2007-08 SASS sample is a…

  16. Recognizing 3 D Objects from 2D Images Using Structural Knowledge Base of Genetic Views

    DTIC Science & Technology

    1988-08-31

    technical report. [BIE85] I. Biederman , "Human image understanding: Recent research and a theory", Computer Vision, Graphics, and Image Processing, vol...model bases", Technical Report 87-85, COINS Dept, University of Massachusetts, Amherst, MA 01003, August 1987 . [BUR87b) Burns, J. B. and L. J. Kitchen...34Recognition in 2D images of 3D objects from large model bases using prediction hierarchies", Proc. IJCAI-10, 1987 . [BUR891 J. B. Burns, forthcoming

  17. Definite Project Report for Section 14. Emergency Streambank Protection, Sangamon River Sewage Treatment Facility, Riverton, Illinois. Revision.

    DTIC Science & Technology

    1987-12-01

    Ffld. I-r &I6a ac rXpE~cjAi.Ly Pf~cgEt CiefkBIE bWb&S P-e1* I(j01Wjt SlAUEi. £jtFrc/gPAEA TAE -e.. &~C P.coy MSfi/.Cr ST~ftvh1 C0R* lID~ lA RuDf AS*fb...severe property and economia losses and a potential for environmental Impacts which could be substantially worse than the temporary Impaot to the

  18. Sunlight-induced self-healing of a microcapsule-type protective coating.

    PubMed

    Song, Young-Kyu; Jo, Ye-Hyun; Lim, Ye-Ji; Cho, Sung-Youl; Yu, Hwan-Chul; Ryu, Byung-Cheol; Lee, Sang-In; Chung, Chan-Moon

    2013-02-01

    Photopolymerization behavior of a methacryloxypropyl-terminated polydimethylsiloxane (MAT-PDMS) healing agent was investigated in the presence of benzoin isobutyl ether (BIE) photoinitiator by Fourier transform infrared (FT-IR) spectroscopy. MAT-PDMS and BIE were microencapsulated with urea-formaldehyde polymer. The surface and shell morphology of the microcapsules was investigated by scanning electron microscopy (SEM). Mean diameter and size distribution of the microcapsules could be controlled by agitation rate. A coating matrix formulation was prepared by sol-gel reaction of tetraethyl orthosilicate (TEOS) in the presence of a polysiloxane and by subsequent addition of an adhesion promoter. The formulation and microcapsules were mixed to give a self-healing coating formulation, which was then sprayed to surface of cellulose-fiber-reinforced-cement (CRC) board or mortar. Contact angle measurements showed that both the polymerized MAT-PDMS and the prepared coating matrix are hydrophobic, and the coating matrix has good wettability with MAT-PDMS. It was confirmed by optical microscopy and SEM that, when the self-healing coating is damaged, the healing agent is released from ruptured microcapsules and fills the damaged region. The self-healing coating was evaluated as protective coating for mortar, and it was demonstrated by water permeability and chloride ion penetration tests that our system has sunlight-induced self-healing capability. Our self-healing coating is the first example of capsule-type photoinduced self-healing system, and offers the advantages of catalyst-free, environmentally friendly, inexpensive, practical healing.

  19. New insights into galaxy structure from GALPHAT- I. Motivation, methodology and benchmarks for Sérsic models

    NASA Astrophysics Data System (ADS)

    Yoon, Ilsang; Weinberg, Martin D.; Katz, Neal

    2011-06-01

    We introduce a new galaxy image decomposition tool, GALPHAT (GALaxy PHotometric ATtributes), which is a front-end application of the Bayesian Inference Engine (BIE), a parallel Markov chain Monte Carlo package, to provide full posterior probability distributions and reliable confidence intervals for all model parameters. The BIE relies on GALPHAT to compute the likelihood function. GALPHAT generates scale-free cumulative image tables for the desired model family with precise error control. Interpolation of this table yields accurate pixellated images with any centre, scale and inclination angle. GALPHAT then rotates the image by position angle using a Fourier shift theorem, yielding high-speed, accurate likelihood computation. We benchmark this approach using an ensemble of simulated Sérsic model galaxies over a wide range of observational conditions: the signal-to-noise ratio S/N, the ratio of galaxy size to the point spread function (PSF) and the image size, and errors in the assumed PSF; and a range of structural parameters: the half-light radius re and the Sérsic index n. We characterize the strength of parameter covariance in the Sérsic model, which increases with S/N and n, and the results strongly motivate the need for the full posterior probability distribution in galaxy morphology analyses and later inferences. The test results for simulated galaxies successfully demonstrate that, with a careful choice of Markov chain Monte Carlo algorithms and fast model image generation, GALPHAT is a powerful analysis tool for reliably inferring morphological parameters from a large ensemble of galaxies over a wide range of different observational conditions.

  20. Rational Design of Bi Nanoparticles for Efficient Electrochemical CO 2 Reduction: The Elucidation of Size and Surface Condition Effects

    DOE PAGES

    Zhang, Zhiyong; Chi, Miaofang; Veith, Gabriel M.; ...

    2016-08-08

    Here we report an efficient electrochemical conversion of CO 2 to CO on surface-activated bismuth nanoparticles (NPs) in acetonitrile (MeCN) under ambient conditions, with the assistance of 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([bmim][OTf]). Through the comparison between electrodeposited Bi films (Bi-ED) and different types of Bi NPs, we, for the first time, demonstrate the effects of catalyst’s size and surface condition on organic phase electrochemical CO 2 reduction. Our study reveals that the surface inhibiting layer (hydrophobic surfactants and Bi 3+ species) formed during the synthesis and purification process hinders the CO 2 reduction, leading to a 20% drop in Faradaic efficiency formore » CO evolution (FE CO). Bi particle size showed a significant effect on FE CO when the surface of Bi was air-oxidized, but this effect of size on FE CO became negligible on surface-activated Bi NPs. After the surface activation (hydrazine treatment) that effectively removed the native inhibiting layer, activated 36-nm Bi NPs exhibited an almost-quantitative conversion of CO 2 to CO (96.1% FE CO), and a mass activity for CO evolution (MA CO) of 15.6 mA mg –1, which is three-fold higher than the conventional Bi-ED, at ₋2.0 V (vs Ag/AgCl). Ultimately, this work elucidates the importance of the surface activation for an efficient electrochemical CO 2 conversion on metal NPs and paves the way for understanding the CO 2 electrochemical reduction mechanism in nonaqueous media.« less

  1. Reader Training for the Restaging of Biochemically Recurrent Prostate Cancer Using 18F-Fluciclovine PET/CT.

    PubMed

    Miller, Matthew P; Kostakoglu, Lale; Pryma, Daniel; Yu, Jian Qin; Chau, Albert; Perlman, Eric; Clarke, Bonnie; Rosen, Donald; Ward, Penelope

    2017-10-01

    18 F-Fluciclovine is a novel PET/CT tracer. This blinded image evaluation (BIE) sought to demonstrate that, after limited training, readers naïve to 18 F-fluciclovine could interpret 18 F-fluciclovine images from subjects with biochemically recurrent prostate cancer with acceptable diagnostic performance and reproducibility. The primary objectives were to establish individual readers' diagnostic performance and the overall interpretation (2/3 reader concordance) compared with standard-of-truth data (histopathology or clinical follow-up) and to evaluate interreader reproducibility. Secondary objectives included comparison to the expert reader and assessment of intrareader reproducibility. Methods: 18 F-Fluciclovine PET/CT images ( n = 121) and corresponding standard-of-truth data were collected from 110 subjects at Emory University using a single-time-point static acquisition starting 5 min after injection of approximately 370 MBq of 18 F-fluciclovine. Three readers were trained using standardized interpretation methodology and subsequently evaluated the images in a blinded manner. Analyses were conducted at the lesion, region (prostate, including bed and seminal vesicle, or extraprostatic, including all lymph nodes, bone, or soft-tissue metastasis), and subject level. Results: Lesion-level overall positive predictive value was 70.5%. The readers' positive predictive value and negative predictive value were broadly consistent with each other and with the onsite read. Sensitivity was highest for readers 1 and 2 (68.5% and 63.9%, respectively) whereas specificity was highest for reader 3 (83.6%). Overall, prostate-level sensitivity was high (91.4%), but specificity was moderate (48.7%). Interreader agreement was 94.7%, 74.4%, and 70.3% for the lesion, prostate, and extraprostatic levels, respectively, with associated Fleiss' κ-values of 0.54, 0.50, and 0.57. Intrareader agreement was 97.8%, 96.9%, and 99.1% at the lesion level; 100%, 100%, and 91.7% in the prostate region; and 83.3%, 75.0%, and 83.3% in the extraprostatic region for readers 1, 2, and 3, respectively. Concordance between the BIE and the onsite reader exceeded 75% for each reader at the lesion, region, and subject levels. Conclusion: Specific training in the use of standardized interpretation methodology for assessment of 18 F-fluciclovine PET/CT images enables naïve readers to achieve acceptable diagnostic performance and reproducibility when staging recurrent prostate cancer. © 2017 by the Society of Nuclear Medicine and Molecular Imaging.

  2. The Clifford Deformation of the Hermite Semigroup

    NASA Astrophysics Data System (ADS)

    De Bie, Hendrik; Örsted, Bent; Somberg, Petr; Souček, Vladimir

    2013-02-01

    This paper is a continuation of the paper [De Bie H., Örsted B., Somberg P., Souček V., Trans. Amer. Math. Soc. 364 (2012), 3875-3902], investigating a natural radial deformation of the Fourier transform in the setting of Clifford analysis. At the same time, it gives extensions of many results obtained in [Ben Saïd S., Kobayashi T., Örsted B., Compos. Math. 148 (2012), 1265-1336]. We establish the analogues of Bochner's formula and the Heisenberg uncertainty relation in the framework of the (holomorphic) Hermite semigroup, and also give a detailed analytic treatment of the series expansion of the associated integral transform.

  3. The bats of Wyoming

    USGS Publications Warehouse

    Bogan, Michael A.; Cryan, Paul M.; Choate, Jerry R.

    2000-01-01

    We examined 1280 bats of 12 species submitted to the Wyoming State Veterinary Laboratory (WSVL) for ra­bies testing between 1981 and 1992. The most abundant species in the sample was Myotis lucifugus, followed by Epte­sicus fuscus, Lasionycteris noetivagans, M. ciliolabrum, and M. volans. Using the WSVL sample and additional museum specimens, we summarized available records and knowledge for 17 species of bats in Wyoming, Records of the WSVL show that, between 1981 and 1992, 113 bats actually tested positive for rabies. We examined 45 of those rabies­ positive bats; E. fuscus had the highest incidence (60%) in the sample, followed by L. noctivagans (11 %) and L. cinereus (9%).

  4. Quantification of uncertainty in photon source spot size inference during laser-driven radiography experiments at TRIDENT

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tobias, Benjamin John; Palaniyappan, Sasikumar; Gautier, Donald Cort

    Images of the R2DTO resolution target were obtained during laser-driven-radiography experiments performed at the TRIDENT laser facility, and analysis of these images using the Bayesian Inference Engine (BIE) determines a most probable full-width half maximum (FWHM) spot size of 78 μm. However, significant uncertainty prevails due to variation in the measured detector blur. Propagating this uncertainty in detector blur through the forward model results in an interval of probabilistic ambiguity spanning approximately 35-195 μm when the laser energy impinges on a thick (1 mm) tantalum target. In other phases of the experiment, laser energy is deposited on a thin (~100more » nm) aluminum target placed 250 μm ahead of the tantalum converter. When the energetic electron beam is generated in this manner, upstream from the bremsstrahlung converter, the inferred spot size shifts to a range of much larger values, approximately 270-600 μm FWHM. This report discusses methods applied to obtain these intervals as well as concepts necessary for interpreting the result within a context of probabilistic quantitative inference.« less

  5. Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

    NASA Astrophysics Data System (ADS)

    Adib, Arash; Poorveis, Davood; Mehraban, Farid

    2018-03-01

    In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

  6. Prospection for Copper Mineralization with Contribution of Remote Sensing, Geochemical and Mineralographical Data in Abhar 1:100,000 Sheet, NW Iran / Poszukiwania ZASOBÓW Rud Miedzi Z Zastosowaniem Zdalnych Technik WYKORZYSTUJĄCYCH Dane Geochemiczne i Mineralogiczne W POKŁADZIE Geologicznym Abhar 1:100,000 W PÓŁNOCNO-ZACHODNIM Iranie

    NASA Astrophysics Data System (ADS)

    Nouri, Reza; Jafari, Mohammadreza; Arian, Mehran; Feizi, Faranak; Afzal, Peyman

    2013-12-01

    Abhar 1:100,000 sheet is located within the Cenozoic Tarom volcano-plutonic belt, NW Iran. The present study is based on the integration of remote sensing techniques on Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), geochemical data analysis consisting of stream sediment and lithogeochemical samples, within geological field observations and mineralographical studies to identify Cu prospect. On ASTER data; using a number of selected methods including band ratio, Least Square Fit (LS-Fit) and Minimum Noise Fraction (MNF) distinguished alternation zones. These methods revealed that three types of alterations: argillic, phyllic, and iron oxide zones occurring at the NE and SE of Abhar sheet, while the propylitic and silica zones are developed in NW and SW of the studied area. Lineaments were identified by aid of false color composite, high pass filters and hill-shade DEM techniques that two NW-SE and NE-SW major trends were determined. Geochemical anomalies were separated by number-size (N-S) method. Interpretation of N-S log-log plots of Cu in the area may be a result of the three steps of enrichment, i.e., mineralization and later dispersions. Field checks and Mineralgraphical studies also confirm the existence of suitable copper mineralization. Pokład geologiczny Abhar 1:100,100 zlokalizowany jest w obrębie kenozoicznego pasa skał magmowych pochodzenia wulkanicznego Tarom w północno-zachodnim Iranie. W pracy przedstawiono połączenie zastosowań metod zdalnych wykorzystujących technologię ASTER (Advanced Spaceborne Thermal Emission and Refelection Radiometer), analizę danych geochemicznych zebranych na podstawie osadów dennych ze strumieni oraz próbek skał w obrębie pola obserwacji a także danych mineralogicznych w celu rozpoznania skupisk rud miedzi. Na podstawie danych uzyskanych przy użyciu technologiiASTER i poddanych obróbce przy użyciu różnorodnych technik: badanie układu pasm, dopasowanie metodę najmniejszych kwadratów oraz minimalny współczynnik szumów, rozróżniono strefy przeobrażeń skał. Metody te pozwoliły na wykrycie trzech typów skał przeobrażonych: gliniaste, łupki ilasto-mikowe oraz strefy występowania tlenków żelaza występujące na północno-wschodnich (NE) i południowo- -zachodnich (NW) krańcach pasa Abhar. W części północno-zachodnie (NW) i południowo-zachodniej (SW) badanego obszaru stwierdzono występowanie stref propilitu i krzemianów. Lineacje wykryto przy pomocy metody badania zakresu barw, filtrów wysoko-przepustowych, techniki określania wysokości, na tej podstawie określono dwa główne trendy: NW-SE oraz NE-SW. Anomalie geologiczne wydzielono za pomocą metody N-S (liczba-wymiar). Interpretacja wykresów N-S wykonanych w skali logarytmicznej wykazała, że zaobserwowany układ może być wynikiem trzech etapów wzbogacania: mineralizacji i późniejszego rozproszenia. Badania terenowe oraz analizy mineralograficzne potwierdzają obecność odpowiednio zmineralizowanej miedzi.

  7. Comparison of Kernel Equating and Item Response Theory Equating Methods

    ERIC Educational Resources Information Center

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  8. A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

    ERIC Educational Resources Information Center

    Choi, Sae Il

    2009-01-01

    This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

  9. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

    PubMed

    Murase, Kenya

    2015-01-01

    In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

  10. [Herbal textual research on Chinese medicine "Huangjing" (Polygonati Rhizoma)and some enlightenments].

    PubMed

    Liu, Jing-Jing; Si, Jin-Ping

    2018-02-01

    To clarify the change and development of the original plants， medicinal organs， traditional functions， resource distribution of "Huangjing"(Polygonati Rhizome)， a traditional Chinese medicine， we investigated Polygonatum species on the ancient Chinese herbal texts. The name of "Nüwei" was first carried out in the book of Sheng Nong's Herbal Classic. Its effects included two aspects： one was similar to "Weirui"(Polygonati Odorati Rhizome， "Yuzhu")， that was tonifying， nourishing one's vitality， removing wind and dampness， settling five organs， making body lightness， keeping longevity and not being hungry; the second was alike to "Huangjing" recorded in the book of Ming Yi Bie Lu(Appendant Records of Famous Physicians). Specifically， "Weirui" possesses the therapeutic effect of "Nüwei"， while "Huangjing" possesses the tonic effect of " Nüwei". Thereafter， the following ancient Chinese herbal texts kept those two names and function records. Accordingly， we hold the point of view that "Huangjing" was first carried out in the book of Sheng Nong's Herbal Classic in the synonym of "Nüwei". "Yuzhu" included the "Huangjing" in ancient herbal text before Qing Dynasty， that was further confirmed by the research on change and development of the original plants. The identification between "Yuzhu" and "Huangjing" was based on the shape of rhizome and size before early Tang Dynasty. The shape was a key character and used up to now， but size was not reasonable. The opposite phyllotaxy was an important character of authentic "Huangjing" from Tang to Qing Dynasty. The seedling of Polygonatum sibiricum and P. kingianum， the adult plant of P. cyrtonema with alternate leaves were misused as "Yuzhu"("Nüwei" and "Weirui") at that time. Therefore， both "Yuzhu" and "Huangjing" should be used as key words during the search of ancient prescriptions and development of new drugs and health foods. The leaves， flowers， fruits and seedlings could be used as food or medicine other than the rhizomes in ancient China， but they haven't been developed in modern times. The culture of "Huangjing" had a long history starting with Tang Dynasty， which was recorded in Tang poetry. Then in Ming Dynasty， the culture method was described in Compendium of Materia Medica， that was cutting the rhizomes into 2 feet， planting sparsely(they would be grown densely in the next year)， or sowing the seeds. The harvesting and processing were first recorded in Ming Yi Bie Lu： "harvest the roots in February， dry in the shade". Then the processing method was changed to "steaming and drying in the sun， repeatedly for nine times" in Shi Liao Ben Cao(Dietetic Materia Medica) and "harvesting in August as well" in Ben Cao Tu Jing(Commentaries on the Illustrations). No breakthrough has been taken in the breeding of cultivars and key cultivation technologies yet. As to the geo-authentic habitats， Mount Songshan and Maoshan were firstly recorded as the best producing areas of "Huangjing" in Ben Cao Tu Jing. But Maoshan， Jiangsu province and Mount Songshan， Henan province， are not main producing areas in modern China. Consequently， the plantation plan of Polygonati Rhizome needs further study. Copyright© by the Chinese Pharmaceutical Association.

  11. Methods for Equating Mental Tests.

    DTIC Science & Technology

    1984-11-01

    1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

  12. A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

    PubMed Central

    Motsa, S. S.; Magagula, V. M.; Sibanda, P.

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

  13. A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

    PubMed

    Motsa, S S; Magagula, V M; Sibanda, P

    2014-01-01

    This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

  14. A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

    PubMed

    Sudao, Bilige; Wang, Xiaomin

    2015-01-01

    In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

  15. A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

    PubMed Central

    Sudao, Bilige; Wang, Xiaomin

    2015-01-01

    In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

  16. An Evaluation of Kernel Equating: Parallel Equating with Classical Methods in the SAT Subject Tests[TM] Program. Research Report. ETS RR-09-06

    ERIC Educational Resources Information Center

    Grant, Mary C.; Zhang, Lilly; Damiano, Michele

    2009-01-01

    This study investigated kernel equating methods by comparing these methods to operational equatings for two tests in the SAT Subject Tests[TM] program. GENASYS (ETS, 2007) was used for all equating methods and scaled score kernel equating results were compared to Tucker, Levine observed score, chained linear, and chained equipercentile equating…

  17. An efficient computational method for the approximate solution of nonlinear Lane-Emden type equations arising in astrophysics

    NASA Astrophysics Data System (ADS)

    Singh, Harendra

    2018-04-01

    The key purpose of this article is to introduce an efficient computational method for the approximate solution of the homogeneous as well as non-homogeneous nonlinear Lane-Emden type equations. Using proposed computational method given nonlinear equation is converted into a set of nonlinear algebraic equations whose solution gives the approximate solution to the Lane-Emden type equation. Various nonlinear cases of Lane-Emden type equations like standard Lane-Emden equation, the isothermal gas spheres equation and white-dwarf equation are discussed. Results are compared with some well-known numerical methods and it is observed that our results are more accurate.

  18. A hierarchical methodology for urban facade parsing from TLS point clouds

    NASA Astrophysics Data System (ADS)

    Li, Zhuqiang; Zhang, Liqiang; Mathiopoulos, P. Takis; Liu, Fangyu; Zhang, Liang; Li, Shuaipeng; Liu, Hao

    2017-01-01

    The effective and automated parsing of building facades from terrestrial laser scanning (TLS) point clouds of urban environments is an important research topic in the GIS and remote sensing fields. It is also challenging because of the complexity and great variety of the available 3D building facade layouts as well as the noise and data missing of the input TLS point clouds. In this paper, we introduce a novel methodology for the accurate and computationally efficient parsing of urban building facades from TLS point clouds. The main novelty of the proposed methodology is that it is a systematic and hierarchical approach that considers, in an adaptive way, the semantic and underlying structures of the urban facades for segmentation and subsequent accurate modeling. Firstly, the available input point cloud is decomposed into depth planes based on a data-driven method; such layer decomposition enables similarity detection in each depth plane layer. Secondly, the labeling of the facade elements is performed using the SVM classifier in combination with our proposed BieS-ScSPM algorithm. The labeling outcome is then augmented with weak architectural knowledge. Thirdly, least-squares fitted normalized gray accumulative curves are applied to detect regular structures, and a binarization dilation extraction algorithm is used to partition facade elements. A dynamic line-by-line division is further applied to extract the boundaries of the elements. The 3D geometrical façade models are then reconstructed by optimizing facade elements across depth plane layers. We have evaluated the performance of the proposed method using several TLS facade datasets. Qualitative and quantitative performance comparisons with several other state-of-the-art methods dealing with the same facade parsing problem have demonstrated its superiority in performance and its effectiveness in improving segmentation accuracy.

  19. The Examination of the Classification of Students into Performance Categories by Two Different Equating Methods

    ERIC Educational Resources Information Center

    Keller, Lisa A.; Keller, Robert R.; Parker, Pauline A.

    2011-01-01

    This study investigates the comparability of two item response theory based equating methods: true score equating (TSE), and estimated true equating (ETE). Additionally, six scaling methods were implemented within each equating method: mean-sigma, mean-mean, two versions of fixed common item parameter, Stocking and Lord, and Haebara. Empirical…

  20. Local Discontinuous Galerkin Methods for the Cahn-Hilliard Type Equations

    DTIC Science & Technology

    2007-01-01

    Kuramoto-Sivashinsky equations , the Ito-type coupled KdV equa- tions, the Kadomtsev - Petviashvili equation , and the Zakharov-Kuznetsov equation . A common...Local discontinuous Galerkin methods for the Cahn-Hilliard type equations Yinhua Xia∗, Yan Xu† and Chi-Wang Shu ‡ Abstract In this paper we develop...local discontinuous Galerkin (LDG) methods for the fourth-order nonlinear Cahn-Hilliard equation and system. The energy stability of the LDG methods is

  1. The Missing Data Assumptions of the Nonequivalent Groups with Anchor Test (NEAT) Design and Their Implications for Test Equating. Research Report. ETS RR-09-16

    ERIC Educational Resources Information Center

    Sinharay, Sandip; Holland, Paul W.

    2008-01-01

    The nonequivalent groups with anchor test (NEAT) design involves missing data that are missing by design. Three popular equating methods that can be used with a NEAT design are the poststratification equating method, the chain equipercentile equating method, and the item-response-theory observed-score-equating method. These three methods each…

  2. Finite elements and finite differences for transonic flow calculations

    NASA Technical Reports Server (NTRS)

    Hafez, M. M.; Murman, E. M.; Wellford, L. C.

    1978-01-01

    The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

  3. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (1)].

    PubMed

    Murase, Kenya

    2014-01-01

    Utilization of differential equations and methods for solving them in medical physics are presented. First, the basic concept and the kinds of differential equations were overviewed. Second, separable differential equations and well-known first-order and second-order differential equations were introduced, and the methods for solving them were described together with several examples. In the next issue, the symbolic and series expansion methods for solving differential equations will be mainly introduced.

  4. A Comparison of the Kernel Equating Method with Traditional Equating Methods Using SAT[R] Data

    ERIC Educational Resources Information Center

    Liu, Jinghua; Low, Albert C.

    2008-01-01

    This study applied kernel equating (KE) in two scenarios: equating to a very similar population and equating to a very different population, referred to as a distant population, using SAT[R] data. The KE results were compared to the results obtained from analogous traditional equating methods in both scenarios. The results indicate that KE results…

  5. Multigrid Methods for Fully Implicit Oil Reservoir Simulation

    NASA Technical Reports Server (NTRS)

    Molenaar, J.

    1996-01-01

    In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

  6. On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

    ERIC Educational Resources Information Center

    Savoye, Philippe

    2009-01-01

    In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

  7. [Textual research on Costus root (Aucklandia lappa Decne) in the Sheng nong ben cao jing (Shennong's Classic of Materia Medica)].

    PubMed

    Li, Guangyan; Wang, Dequn; Fang, Shiying; Xu, Maohong

    2014-05-01

    Aucklandia lappa Decne was first recorded in the Sheng nong ben cao jing (Shennong's Classic of Materia Medica). Through the textual research of herbal literature, it was found that the costus root in the Sheng nong ben cao jing perhaps was not the plant of Aucklandia lappa Decne of Compositae, but the eaglewood or Lignum Aquilasria Resinatum based on the comprehensive judgment of shape, taste, nature, and function etc. In the Sheng nong ben cao jing, it only includes costus root without the title of eaglewood, and Tao Hongjing recorded both herbs together in his Ming yi bie lu (Supplementary Records of Celebrated Physicians), which became a foreshadow of misunderstanding of the later generations. Beginning from the Tang ben cao (Materia Medica of the Tang Dynasty), the costus root was considered as the plant of Auckiandia lappa Decne from the Compostae with its profound influence until now.

  8. Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

    NASA Astrophysics Data System (ADS)

    Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

    2018-06-01

    In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

  9. Extension of Nikiforov-Uvarov method for the solution of Heun equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Karayer, H., E-mail: hale.karayer@gmail.com; Demirhan, D.; Büyükkılıç, F.

    2015-06-15

    We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere, and hyperbolic double-well potential are investigated by this method.

  10. An entropy correction method for unsteady full potential flows with strong shocks

    NASA Technical Reports Server (NTRS)

    Whitlow, W., Jr.; Hafez, M. M.; Osher, S. J.

    1986-01-01

    An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation.

  11. A new method of imposing boundary conditions for hyperbolic equations

    NASA Technical Reports Server (NTRS)

    Funaro, D.; ative.

    1987-01-01

    A new method to impose boundary conditions for pseudospectral approximations to hyperbolic equations is suggested. This method involves the collocation of the equation at the boundary nodes as well as satisfying boundary conditions. Stability and convergence results are proven for the Chebyshev approximation of linear scalar hyperbolic equations. The eigenvalues of this method applied to parabolic equations are shown to be real and negative.

  12. A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

    PubMed

    Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

    2014-10-01

    The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

  13. A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

    PubMed Central

    Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

    2014-01-01

    The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

  14. Generation and application of the equations of condition for high order Runge-Kutta methods

    NASA Technical Reports Server (NTRS)

    Haley, D. C.

    1972-01-01

    This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition are developed for Runge-Kutta methods of order four through order nine. Once developed, these equations are used in a comparison of the local truncation errors for several sets of Runge-Kutta coefficients for methods of order three up through methods of order eight.

  15. Method of mechanical quadratures for solving singular integral equations of various types

    NASA Astrophysics Data System (ADS)

    Sahakyan, A. V.; Amirjanyan, H. A.

    2018-04-01

    The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

  16. Solving the interval type-2 fuzzy polynomial equation using the ranking method

    NASA Astrophysics Data System (ADS)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim

    2014-07-01

    Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

  17. Local Linear Observed-Score Equating

    ERIC Educational Resources Information Center

    Wiberg, Marie; van der Linden, Wim J.

    2011-01-01

    Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980)…

  18. Assessing Equating Results on Different Equating Criteria

    ERIC Educational Resources Information Center

    Tong, Ye; Kolen, Michael

    2005-01-01

    The performance of three equating methods--the presmoothed equipercentile method, the item response theory (IRT) true score method, and the IRT observed score method--were examined based on three equating criteria: the same distributions property, the first-order equity property, and the second-order equity property. The magnitude of the…

  19. Condition Monitoring of Off-Highway Truck Tires at Sungun Copper Mine Using Neural Networks / Monitorowanie Stanu Technicznego Opon W CIĘŻKICH Pojazdach Terenowych Eksploatowanych W Kopalni Miedzi Sungun, Przy UŻYCIU Sieci Neuronowych

    NASA Astrophysics Data System (ADS)

    Morad, Amin Moniri; Sattarvand, Javad

    2013-12-01

    Maintenance cost of the equipment is one of the most important portions of the operating expenditures in mines; therefore, any change in the equipment productivity can lead to major changes in the unit cost of the production. This clearly shows the importance and necessity of using novel maintenance methods instead of traditional approaches, in order to reach the minimum sudden occurrence of the equipment failure. For instance, the tires are costly components in maintenance which should be regularly inspected and replaced among different axles. The paper investigates the current condition of equipment tires at Sungun Copper Mine and uses neural networks to estimate the wear of the tires. The Input parameters of the network composed of initial tread depth, time of inspection and consumed tread depth by the time of inspection. The output of the network is considered as the residual service time ratio of the tires. The network trained by the feed-forward back propagation learning algorithm. Results revealed a good coincidence between the real and estimated values as 96.6% of correlation coefficient. Hence, better decisions could be made about the tires to reduce the sudden failures and equipment breakdowns. Koszty użytkowania sprzętu stanowią jedną z najpoważniejszych pozycji w zestawieniu kosztów eksploatacyjnych kopalni, dlatego też każda poprawa wydajności sprzętu powoduje w efekcie zmianę jednostkowego kosztu produkcji. Wyraźnie pokazuje to wagę i konieczność stosowania nowoczesnych metod eksploatacji w miejsce podejścia tradycyjnego w celu minimalizacji ryzyka wystąpienia awarii sprzętu. Przykładowo, opony są elementami kosztownymi w eksploatacji, wymagają regularnego przeglądu i ponownego mocowania na osi. W artykule przebadano stan techniczny opon w maszynach i urządzeniach eksploatowanych w kopalni miedzi Sungun. Przy zastosowaniu metod wykorzystujących sieci neuronowe określano zużycie opon. Parametry wejściowe sieci to początkowa głębokość bieżnika, okres pomiędzy przeglądami, zużycie bieżnika do czasu przeglądu. Parametr wyjściowy to współczynnik określającyczas serwisowania opon. Sieć uczono przy użyciu algorytmu propagacji wstecznej z wyprzedzeniem (feedforward back-propagation algorithm). Uzyskane wyniki wskazują wysoką zbieżność pomiędzy wartościami rzeczywistymi a estymowanymi, współczynnik korelacji kształtuje się na poziomie 96.6%. Umożliwia to podejmowanie lepszych decyzji w odniesieniu do eksploatacji opon, tak by zapobiec nagłym uszkodzeniom i awariom sprzętu.

  20. A Comparative Analysis of Pre-Equating and Post-Equating in a Large-Scale Assessment, High Stakes Examination

    ERIC Educational Resources Information Center

    Ojerinde, Dibu; Popoola, Omokunmi; Onyeneho, Patrick; Egberongbe, Aminat

    2016-01-01

    Statistical procedure used in adjusting test score difficulties on test forms is known as "equating". Equating makes it possible for various test forms to be used interchangeably. In terms of where the equating method fits in the assessment cycle, there are pre-equating and post-equating methods. The major benefits of pre-equating, when…

  1. Modified harmonic balance method for the solution of nonlinear jerk equations

    NASA Astrophysics Data System (ADS)

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

    2018-03-01

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

  2. Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

    NASA Astrophysics Data System (ADS)

    Rasin, Alexander G.

    2010-06-01

    The application of the Gardner method for the generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely Bäcklund transformations and initial conservation laws, follows from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for the generation of symmetries is developed and applied to the discrete Korteweg-de Vries equation. It can also be applied to all the other ABS equations.

  3. The enigmatic Messinian-Pliocene section of Cuevas del Almanzora (Vera Basin, SE Spain) revisited—erosional features and strontium isotope ages

    NASA Astrophysics Data System (ADS)

    Fortuin, A. R.; Kelling, J. M. D.; Roep, Th. B.

    1995-07-01

    The Cuevas del Almanzora section was, in the late seventies, the focus of a discussion because of alleged continuous marine Messinian to Pliocene sedimentation. However, a discontinuity has been shown to exist in the shape of laminated strata including the late Messinian brackish/ lacustrine "Lago Mare" biofacies. More recently, Benson and Rakic-El Bied (1991) concluded that the section is still one of the best biostratigraphic successions for the western Mediterranean in which to document terminal Miocene events, but that it entirely has an early Messinian age (i.e. it antedates deposition of the main evaporites). This paper presents strontium isotope ages indicating that the "classic" threefold division in an earlier marine Messinian, a "Lago Mare", and a Pliocene interval (sensu Geerlings et al., 1980; Cita et al., 1980) should be maintained. Moreover, the Sr isotopic composition of the euryhaline Cyprideis ostracodes from the "Lago Mare" laminites is similar to those from central Mediterranean basins. This stresses the importance of late Messinian water exchange between the Vera Basin and the then enclosed Mediterranean. It thus refutes the opinion of Benson and Rakic-El Bied (1991) that this interval is a local facies, of no particular stratigraphic importance. A time gap of up to ˜0.8 Ma between the youngest marine strata of the Messinian and the overlying Pliocene provides a maximum timing for the duration of the Messinian salinity crisis during which very little net sedimentation occurred, compared to coeval deposits in, for example, the nearby Nijar and Sorbas basins. In the Cuevas section an inconspicuous, and hitherto overlooked, erosional gap has been observed. This separates the "Lago Mare" marls from the Pliocene marls. More field observations have been made and are discussed in the light of existing interpretations, in order to demonstrate the importance of more widespread erosion in the Vera Basin. Gypsum-containing mass-flow deposits, filling up a late Messinian palaeorelief in the Garrucha area, are shown to be derived from the basin. These probably continue offshore as feeder channels related to a late Messinian sea-level fall. A holistic approach of a key section, thereby not overlooking the regional geology, is a necessary step to be made before far-reaching claims can be made about its interregional significance.

  4. Diagnostic effectiveness of quantitative [18F]flutemetamol PET imaging for detection of fibrillar amyloid β using cortical biopsy histopathology as the standard of truth in subjects with idiopathic normal pressure hydrocephalus

    PubMed Central

    2014-01-01

    Introduction PET imaging of amyloid-β (Aβ) in vivo holds promise for aiding in earlier diagnosis and intervention in Alzheimer’s disease (AD) and mild cognitive impairment. AD-like Aβ pathology is a common comorbidity in patients with idiopathic normal pressure hydrocephalus (iNPH). Fifty patients with iNPH needing ventriculo-peritoneal shunting or intracranial pressure monitoring underwent [18F]flutemetamol PET before (N = 28) or after (N = 22) surgery. Cortical uptake of [18F]flutemetamol was assessed visually by blinded reviewers, and also quantitatively via standard uptake value ratio (SUVR) in specific neocortical regions in relation to either cerebellum or pons reference region: the cerebral cortex of (prospective studies) or surrounding (retrospective studies) the biopsy site, the contralateral homolog, and a calculated composite brain measure. Aβ pathology in the biopsy specimen (standard of truth [SoT]) was measured using Bielschowsky silver and thioflavin S plaque scores, percentage area of grey matter positive for monoclonal antibody to Aβ (4G8), and overall pathology impression. We set out to find (1) which pair(s) of PET SUVR and pathology SoT endpoints matched best, (2) whether quantitative measures of [18F]flutemetamol PET were better for predicting the pathology outcome than blinded image examination (BIE), and (3) whether there was a better match between PET image findings in retrospective vs. prospective studies. Results Of the 24 possible endpoint/SoT combinations, the one with composite-cerebellum SUVR and SoT based on overall pathology had the highest Youden index (1.000), receiver operating characteristic area under the curve (1.000), sensitivity (1.000), specificity (1.000), and sum of sensitivity and specificity for the pooled data as well as for the retrospective and prospective studies separately (2.00, for all 3). The BIE sum of sensitivity and specificity, comparable to that for quantitation, was highest using Bielschowsky silver as SoT for all SUVRs (ipsilateral, contralateral, and composite, for both reference regions). The composite SUVR had a 100% positive predictive value (both reference regions) for the overall pathology diagnosis. All SUVRs had a 100% negative predictive value for the Bielschowsky silver result. Conclusion Bielschowsky silver stain and overall pathology judgment showed the strongest associations with imaging results. PMID:24755237

  5. A three operator split-step method covering a larger set of non-linear partial differential equations

    NASA Astrophysics Data System (ADS)

    Zia, Haider

    2017-06-01

    This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

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

    NASA Astrophysics Data System (ADS)

    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.

  7. Integrability: mathematical methods for studying solitary waves theory

    NASA Astrophysics Data System (ADS)

    Wazwaz, Abdul-Majid

    2014-03-01

    In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the real features in a variety of vital areas in science, technology and engineering. In recognition of the importance of solitary waves theory and the underlying concept of integrable equations, a variety of powerful methods have been developed to carry out the required analysis. Examples of such methods which have been advanced are the inverse scattering method, the Hirota bilinear method, the simplified Hirota method, the Bäcklund transformation method, the Darboux transformation, the Pfaffian technique, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method, the mapping and deformation approach and many new other methods. The inverse scattering method, viewed as a nonlinear analogue of the Fourier transform method, is a powerful approach that demonstrates the existence of soliton solutions through intensive computations. At the center of the theory of integrable equations lies the bilinear forms and Hirota's direct method, which can be used to obtain soliton solutions by using exponentials. The Bäcklund transformation method is a useful invariant transformation that transforms one solution into another of a differential equation. The Darboux transformation method is a well known tool in the theory of integrable systems. It is believed that there is a connection between the Bäcklund transformation and the Darboux transformation, but it is as yet not known. Archetypes of integrable equations are the Korteweg-de Vries (KdV) equation, the modified KdV equation, the sine-Gordon equation, the Schrödinger equation, the Vakhnenko equation, the KdV6 equation, the Burgers equation, the fifth-order Lax equation and many others. These equations yield soliton solutions, multiple soliton solutions, breather solutions, quasi-periodic solutions, kink solutions, homo-clinic solutions and other solutions as well. The couplings of linear and nonlinear equations were recently discovered and subsequently received considerable attention. The concept of couplings forms a new direction for developing innovative construction methods. The recently obtained results in solitary waves theory highlight new approaches for additional creative ideas, promising further achievements and increased progress in this field. We are grateful to all of the authors who accepted our invitation to contribute to this comment section.

  8. Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Tay, Wei Choon; Tan, Eng Leong

    2014-07-01

    In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

  9. Application of the Green's function method for 2- and 3-dimensional steady transonic flows

    NASA Technical Reports Server (NTRS)

    Tseng, K.

    1984-01-01

    A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

  10. Numerical solution of distributed order fractional differential equations

    NASA Astrophysics Data System (ADS)

    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.

  11. Exact solutions for STO and (3+1)-dimensional KdV-ZK equations using (G‧/G2) -expansion method

    NASA Astrophysics Data System (ADS)

    Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Ullah, Rahmat; Ahmed, Naveed; Khan, Umar

    This article deals with finding some exact solutions of nonlinear fractional differential equations (NLFDEs) by applying a relatively new method known as (G‧/G2) -expansion method. Solutions of space-time fractional Sharma-Tasso-Olever (STO) equation of fractional order and (3+1)-dimensional KdV-Zakharov Kuznetsov (KdV-ZK) equation of fractional order are reckoned to demonstrate the validity of this method. The fractional derivative version of modified Riemann-Liouville, linked with Fractional complex transform is employed to transform fractional differential equations into the corresponding ordinary differential equations.

  12. Effect of picric acid and enzymatic creatinine on the efficiency of the glomerular filtration rate predicator formula.

    PubMed

    Qiu, Ling; Guo, Xiuzhi; Zhu, Yan; Shou, Weilin; Gong, Mengchun; Zhang, Lin; Han, Huijuan; Quan, Guoqiang; Xu, Tao; Li, Hang; Li, Xuewang

    2013-01-01

    To investigate the impact of serum creatinine measurement on the applicability of glomerular filtration rate (GFR) evaluation equations. 99mTc-DTPA plasma clearance rate was used as GFR reference (rGFR) in patients with chronic kidney disease (CKD). Serum creatinine was measureded using enzymatic or picric acid creatinine reagent. The GFR of the patients were estimated using the Cockcroft-Gault equation corrected for body surface area, simplified Modification of Diet in Renal Disease (MDRD) equation, simplified MDRD equation corrected to isotopes dilution mass spectrometry, the CKD epidemiology collaborative research equation, and two Chinese simplified MDRD equations. Significant differences in the eGFR results estimated through enzymatic and picric acid methods were observed for the same evaluation equation. The intraclass correlation coefficient (ICC) of eGFR when the creatinine was measured by the picric acid method was significantly lower than that of the enzymatic method. The assessment accuracy of every equation using the enzymatic method to measure creatinine was significantly higher than that measured by the picric acid method when rGFR was > or = 60 mL/min/1.73m2. A significant difference was demonstrated in the same GFR evaluation equation using the picric acid and enzymatic methods. The enzymatic creatinine method was better than the picric acid method.

  13. Prediction of unsteady transonic flow around missile configurations

    NASA Technical Reports Server (NTRS)

    Nixon, D.; Reisenthel, P. H.; Torres, T. O.; Klopfer, G. H.

    1990-01-01

    This paper describes the preliminary development of a method for predicting the unsteady transonic flow around missiles at transonic and supersonic speeds, with the final goal of developing a computer code for use in aeroelastic calculations or during maneuvers. The basic equations derived for this method are an extension of those derived by Klopfer and Nixon (1989) for steady flow and are a subset of the Euler equations. In this approach, the five Euler equations are reduced to an equation similar to the three-dimensional unsteady potential equation, and a two-dimensional Poisson equation. In addition, one of the equations in this method is almost identical to the potential equation for which there are well tested computer codes, allowing the development of a prediction method based in part on proved technology.

  14. An adaptive grid algorithm for one-dimensional nonlinear equations

    NASA Technical Reports Server (NTRS)

    Gutierrez, William E.; Hills, Richard G.

    1990-01-01

    Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

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

    PubMed

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

    2014-01-01

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

  16. A second order discontinuous Galerkin fast sweeping method for Eikonal equations

    NASA Astrophysics Data System (ADS)

    Li, Fengyan; Shu, Chi-Wang; Zhang, Yong-Tao; Zhao, Hongkai

    2008-09-01

    In this paper, we construct a second order fast sweeping method with a discontinuous Galerkin (DG) local solver for computing viscosity solutions of a class of static Hamilton-Jacobi equations, namely the Eikonal equations. Our piecewise linear DG local solver is built on a DG method developed recently [Y. Cheng, C.-W. Shu, A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations, Journal of Computational Physics 223 (2007) 398-415] for the time-dependent Hamilton-Jacobi equations. The causality property of Eikonal equations is incorporated into the design of this solver. The resulting local nonlinear system in the Gauss-Seidel iterations is a simple quadratic system and can be solved explicitly. The compactness of the DG method and the fast sweeping strategy lead to fast convergence of the new scheme for Eikonal equations. Extensive numerical examples verify efficiency, convergence and second order accuracy of the proposed method.

  17. Fokker-Planck Equations of Stochastic Acceleration: A Study of Numerical Methods

    NASA Astrophysics Data System (ADS)

    Park, Brian T.; Petrosian, Vahe

    1996-03-01

    Stochastic wave-particle acceleration may be responsible for producing suprathermal particles in many astrophysical situations. The process can be described as a diffusion process through the Fokker-Planck equation. If the acceleration region is homogeneous and the scattering mean free path is much smaller than both the energy change mean free path and the size of the acceleration region, then the Fokker-Planck equation reduces to a simple form involving only the time and energy variables. in an earlier paper (Park & Petrosian 1995, hereafter Paper 1), we studied the analytic properties of the Fokker-Planck equation and found analytic solutions for some simple cases. In this paper, we study the numerical methods which must be used to solve more general forms of the equation. Two classes of numerical methods are finite difference methods and Monte Carlo simulations. We examine six finite difference methods, three fully implicit and three semi-implicit, and a stochastic simulation method which uses the exact correspondence between the Fokker-Planck equation and the it5 stochastic differential equation. As discussed in Paper I, Fokker-Planck equations derived under the above approximations are singular, causing problems with boundary conditions and numerical overflow and underflow. We evaluate each method using three sample equations to test its stability, accuracy, efficiency, and robustness for both time-dependent and steady state solutions. We conclude that the most robust finite difference method is the fully implicit Chang-Cooper method, with minor extensions to account for the escape and injection terms. Other methods suffer from stability and accuracy problems when dealing with some Fokker-Planck equations. The stochastic simulation method, although simple to implement, is susceptible to Poisson noise when insufficient test particles are used and is computationally very expensive compared to the finite difference method.

  18. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

    PubMed

    Murase, Kenya

    2016-01-01

    In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

  19. An Evaluation of the Kernel Equating Method: A Special Study with Pseudotests Constructed from Real Test Data. Research Report. ETS RR-06-02

    ERIC Educational Resources Information Center

    von Davier, Alina A.; Holland, Paul W.; Livingston, Samuel A.; Casabianca, Jodi; Grant, Mary C.; Martin, Kathleen

    2006-01-01

    This study examines how closely the kernel equating (KE) method (von Davier, Holland, & Thayer, 2004a) approximates the results of other observed-score equating methods--equipercentile and linear equatings. The study used pseudotests constructed of item responses from a real test to simulate three equating designs: an equivalent groups (EG)…

  20. Chemical Equation Balancing.

    ERIC Educational Resources Information Center

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  1. Local Observed-Score Kernel Equating

    ERIC Educational Resources Information Center

    Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

    2014-01-01

    Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

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

    NASA Astrophysics Data System (ADS)

    S Saha, Ray

    2016-04-01

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

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

    NASA Astrophysics Data System (ADS)

    Ghanbari, Behzad; Inc, Mustafa

    2018-04-01

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

  4. Direct Discrete Method for Neutronic Calculations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

    The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for amore » cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)« less

  5. Standard Errors of Equating for the Percentile Rank-Based Equipercentile Equating with Log-Linear Presmoothing

    ERIC Educational Resources Information Center

    Wang, Tianyou

    2009-01-01

    Holland and colleagues derived a formula for analytical standard error of equating using the delta-method for the kernel equating method. Extending their derivation, this article derives an analytical standard error of equating procedure for the conventional percentile rank-based equipercentile equating with log-linear smoothing. This procedure is…

  6. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    NASA Astrophysics Data System (ADS)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  7. New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

    PubMed

    Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

    2014-01-01

    In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

  8. SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

    PubMed Central

    Wan, Xiaohai; Li, Zhilin

    2012-01-01

    Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

  9. SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

    PubMed

    Wan, Xiaohai; Li, Zhilin

    2012-06-01

    Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

  10. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    NASA Astrophysics Data System (ADS)

    Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

    2018-03-01

    We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  11. On method of solving third-order ordinary differential equations directly using Bernstein polynomials

    NASA Astrophysics Data System (ADS)

    Khataybeh, S. N.; Hashim, I.

    2018-04-01

    In this paper, we propose for the first time a method based on Bernstein polynomials for solving directly a class of third-order ordinary differential equations (ODEs). This method gives a numerical solution by converting the equation into a system of algebraic equations which is solved directly. Some numerical examples are given to show the applicability of the method.

  12. Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

    NASA Technical Reports Server (NTRS)

    Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

  13. Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

    Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

  14. Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

    DOE PAGES

    Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

    2018-04-23

    Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

  15. Equating Scores from Adaptive to Linear Tests

    ERIC Educational Resources Information Center

    van der Linden, Wim J.

    2006-01-01

    Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

  16. ESEA Title I Linking Project. Final Report.

    ERIC Educational Resources Information Center

    Holmes, Susan E.

    The Rasch model for test score equating was compared with three other equating procedures as methods for implementing the norm referenced method (RMC Model A) of evaluating ESEA Title I projects. The Rasch model and its theoretical limitations were described. The three other equating methods used were: linear observed score equating, linear true…

  17. Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

    NASA Technical Reports Server (NTRS)

    Abolhassani, J. S.; Tiwari, S. N.

    1983-01-01

    The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

  18. Investigations of Sayre's Equation.

    NASA Astrophysics Data System (ADS)

    Shiono, Masaaki

    Available from UMI in association with The British Library. Since the discovery of X-ray diffraction, various methods of using it to solve crystal structures have been developed. The major methods used can be divided into two categories: (1) Patterson function based methods; (2) Direct phase-determination methods. In the early days of structure determination from X-ray diffraction, Patterson methods played the leading role. Direct phase-determining methods ('direct methods' for short) were introduced by D. Harker and J. S. Kasper in the form of inequality relationships in 1948. A significant development of direct methods was produced by Sayre (1952). The equation he introduced, generally called Sayre's equation, gives exact relationships between structure factors for equal atoms. Later Cochran (1955) derived the so-called triple phase relationship, the main means by which it has become possible to find the structure factor phases automatically by computer. Although the background theory of direct methods is very mathematical, the user of direct-methods computer programs needs no detailed knowledge of these automatic processes in order to solve structures. Recently introduced direct methods are based on Sayre's equation, so it is important to investigate its properties thoroughly. One such new method involves the Sayre equation tangent formula (SETF) which attempts to minimise the least square residual for the Sayre's equations (Debaerdemaeker, Tate and Woolfson; 1985). In chapters I-III the principles and developments of direct methods will be described and in chapters IV -VI the properties of Sayre's equation and its modification will be discussed. Finally, in chapter VII, there will be described the investigation of the possible use of an equation, similar in type to Sayre's equation, derived from the characteristics of the Patterson function.

  19. The Effectiveness of Circular Equating as a Criterion for Evaluating Equating.

    ERIC Educational Resources Information Center

    Wang, Tianyou; Hanson, Bradley A.; Harris, Deborah J.

    Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

  20. Calculation of transonic flows using an extended integral equation method

    NASA Technical Reports Server (NTRS)

    Nixon, D.

    1976-01-01

    An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

  1. On the exact solutions of high order wave equations of KdV type (I)

    NASA Astrophysics Data System (ADS)

    Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

    2014-12-01

    In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

  2. Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

    PubMed

    Reck, Kasper; Thomsen, Erik V; Hansen, Ole

    2011-01-31

    The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.

  3. Analyzing Lie symmetry and constructing conservation laws for time-fractional Benny-Lin equation

    NASA Astrophysics Data System (ADS)

    Rashidi, Saeede; Hejazi, S. Reza

    This paper investigates the invariance properties of the time fractional Benny-Lin equation with Riemann-Liouville and Caputo derivatives. This equation can be reduced to the Kawahara equation, fifth-order Kdv equation, the Kuramoto-Sivashinsky equation and Navier-Stokes equation. By using the Lie group analysis method of fractional differential equations (FDEs), we derive Lie symmetries for the Benny-Lin equation. Conservation laws for this equation are obtained with the aid of the concept of nonlinear self-adjointness and the fractional generalization of the Noether’s operators. Furthermore, by means of the invariant subspace method, exact solutions of the equation are also constructed.

  4. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

    PubMed

    Murase, Kenya

    2016-01-01

    Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

  5. A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

    NASA Astrophysics Data System (ADS)

    Pei, Y.; Herbst, E.

    2011-05-01

    Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod 2008), which partially takes into account the stochastic effect for surface reactions, and (3) the master equation approach solved using a Monte Carlo technique. At 10 K and standard grain sizes, our model results agree well with the above three methods, while discrepancies appear at higher temperatures and smaller grain sizes.

  6. Managing Element Interactivity in Equation Solving

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Phan, Huy P.; Yeung, Alexander Seeshing; Chung, Siu Fung

    2018-01-01

    Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

  7. Historical Notes. A Madness in the Methods. Cubic and Quartic Equations: Are the General Solving Techniques Still Important?

    ERIC Educational Resources Information Center

    Francis, Richard L.

    1991-01-01

    Described is an outline for a school mathematics project dealing with the theory of equations, specifically solutions to polynomials of the third and of the fourth degree. Cardano's method for solution of cubic equations and Ferrari's method for solution of quartic equations are included with examples. (JJK)

  8. Numerical solution of nonlinear partial differential equations of mixed type. [finite difference approximation

    NASA Technical Reports Server (NTRS)

    Jameson, A.

    1976-01-01

    A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.

  9. Quadratically Convergent Method for Simultaneously Approaching the Roots of Polynomial Solutions of a Class of Differential Equations

    NASA Astrophysics Data System (ADS)

    Recchioni, Maria Cristina

    2001-12-01

    This paper investigates the application of the method introduced by L. Pasquini (1989) for simultaneously approaching the zeros of polynomial solutions to a class of second-order linear homogeneous ordinary differential equations with polynomial coefficients to a particular case in which these polynomial solutions have zeros symmetrically arranged with respect to the origin. The method is based on a family of nonlinear equations which is associated with a given class of differential equations. The roots of the nonlinear equations are related to the roots of the polynomial solutions of differential equations considered. Newton's method is applied to find the roots of these nonlinear equations. In (Pasquini, 1994) the nonsingularity of the roots of these nonlinear equations is studied. In this paper, following the lines in (Pasquini, 1994), the nonsingularity of the roots of these nonlinear equations is studied. More favourable results than the ones in (Pasquini, 1994) are proven in the particular case of polynomial solutions with symmetrical zeros. The method is applied to approximate the roots of Hermite-Sobolev type polynomials and Freud polynomials. A lower bound for the smallest positive root of Hermite-Sobolev type polynomials is given via the nonlinear equation. The quadratic convergence of the method is proven. A comparison with a classical method that uses the Jacobi matrices is carried out. We show that the algorithm derived by the proposed method is sometimes preferable to the classical QR type algorithms for computing the eigenvalues of the Jacobi matrices even if these matrices are real and symmetric.

  10. A fourth-order box method for solving the boundary layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1977-01-01

    A fourth order box method for calculating high accuracy numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations is presented. The method is the natural extension of the second order Keller Box scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary layer equations. Numerical results for high accuracy test cases show the method to be significantly faster than other higher order and second order methods.

  11. Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

    NASA Astrophysics Data System (ADS)

    Agarwal, P.; El-Sayed, A. A.

    2018-06-01

    In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

  12. Cognitive Load in Algebra: Element Interactivity in Solving Equations

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

    2015-01-01

    Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

  13. Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

    ERIC Educational Resources Information Center

    Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

    2012-01-01

    This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

  14. A fast marching algorithm for the factored eikonal equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Treister, Eran, E-mail: erantreister@gmail.com; Haber, Eldad, E-mail: haber@math.ubc.ca; Department of Mathematics, The University of British Columbia, Vancouver, BC

    The eikonal equation is instrumental in many applications in several fields ranging from computer vision to geoscience. This equation can be efficiently solved using the iterative Fast Sweeping (FS) methods and the direct Fast Marching (FM) methods. However, when used for a point source, the original eikonal equation is known to yield inaccurate numerical solutions, because of a singularity at the source. In this case, the factored eikonal equation is often preferred, and is known to yield a more accurate numerical solution. One application that requires the solution of the eikonal equation for point sources is travel time tomography. Thismore » inverse problem may be formulated using the eikonal equation as a forward problem. While this problem has been solved using FS in the past, the more recent choice for applying it involves FM methods because of the efficiency in which sensitivities can be obtained using them. However, while several FS methods are available for solving the factored equation, the FM method is available only for the original eikonal equation. In this paper we develop a Fast Marching algorithm for the factored eikonal equation, using both first and second order finite-difference schemes. Our algorithm follows the same lines as the original FM algorithm and requires the same computational effort. In addition, we show how to obtain sensitivities using this FM method and apply travel time tomography, formulated as an inverse factored eikonal equation. Numerical results in two and three dimensions show that our algorithm solves the factored eikonal equation efficiently, and demonstrate the achieved accuracy for computing the travel time. We also demonstrate a recovery of a 2D and 3D heterogeneous medium by travel time tomography using the eikonal equation for forward modeling and inversion by Gauss–Newton.« less

  15. Modified equations, rational solutions, and the Painleve property for the Kadomtsev--Petviashvili and Hirota--Satsuma equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Weiss, J.

    1985-09-01

    We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painleve property, a Baecklund transformation is defined in terms of an expansion about the singular manifold. This Baecklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Baecklund transformations of the modified equations provides a method for themore » iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev--Petviashvili equation and the Hirota--Satsuma equations.« less

  16. Discontinuous Finite Element Quasidiffusion Methods

    DOE PAGES

    Anistratov, Dmitriy Yurievich; Warsa, James S.

    2018-05-21

    Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

  17. Discontinuous Finite Element Quasidiffusion Methods

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Anistratov, Dmitriy Yurievich; Warsa, James S.

    Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and themore » LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.« less

  18. A procedure to construct exact solutions of nonlinear fractional differential equations.

    PubMed

    Güner, Özkan; Cevikel, Adem C

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

  19. Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis.

    PubMed

    Abbasi, Mahdi

    2014-01-01

    Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N (2)log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

  20. Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

    PubMed

    Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

    2015-07-01

    Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

  1. Nonlinear Conservation Laws and Finite Volume Methods

    NASA Astrophysics Data System (ADS)

    Leveque, Randall J.

    Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

  2. DustPedia: A Definitive Study of Cosmic Dust in the Local Universe

    NASA Astrophysics Data System (ADS)

    Davies, J. I.; Baes, M.; Bianchi, S.; Jones, A.; Madden, S.; Xilouris, M.; Bocchio, M.; Casasola, V.; Cassara, L.; Clark, C.; De Looze, I.; Evans, R.; Fritz, J.; Galametz, M.; Galliano, F.; Lianou, S.; Mosenkov, A. V.; Smith, M.; Verstocken, S.; Viaene, S.; Vika, M.; Wagle, G.; Ysard, N.

    2017-04-01

    The European Space Agency has invested heavily in two cornerstones missions: Herschel and Planck. The legacy data from these missions provides an unprecedented opportunity to study cosmic dust in galaxies so that we can, for example, answer fundamental questions about the origin of the chemical elements, physical processes in the interstellar medium (ISM), its effect on stellar radiation, its relation to star formation and how this relates to the cosmic far-infrared background. In this paper we describe the DustPedia project, which enables us to develop tools and computer models that will help us relate observed cosmic dust emission to its physical properties (chemical composition, size distribution, and temperature), its origins (evolved stars, supernovae, and growth in the ISM), and the processes that destroy it (high-energy collisions and shock heated gas). To carry out this research, we combine the Herschel/Planck data with that from other sources of data, and provide observations at numerous wavelengths (≤slant 41) across the spectral energy distribution, thus creating the DustPedia database. To maximize our spatial resolution and sensitivity to cosmic dust, we limit our analysis to 4231 local galaxies (v< 3000 km s-1) selected via their near-infrared luminosity (stellar mass). To help us interpret this data, we developed a new physical model for dust (THEMIS), a new Bayesian method of fitting and interpreting spectral energy distributions (HerBIE) and a state-of-the-art Monte Carlo photon-tracing radiative transfer model (SKIRT). In this, the first of the DustPedia papers, we describe the project objectives, data sets used, and provide an insight into the new scientific methods we plan to implement.

  3. The construction of partner potential from the general potential Rosen-Morse and Manning Rosen in 4 dimensional Schrodinger system

    NASA Astrophysics Data System (ADS)

    Nathalia Wea, Kristiana; Suparmi, A.; Cari, C.; Wahyulianti

    2017-11-01

    The solution of the Schrodinger equation with physical potential is the important part in quantum physics. Many methods have been developed to resolve the Schrodinger equation. The Nikiforov-Uvarov method and supersymmetric method are the most methods that interesting to be explored. The supersymmetric method not only used to solve the Schrodinger equation but also used to construct the partner potential from a general potential. In this study, the Nikiforov-Uvarov method was used to solve the Schrodinger equation while the supersymmetric method was used to construction partner potential. The study about the construction of the partner potential from general potential Rosen-Morse and Manning Rosen in D-dimensional Schrodinger system has been done. The partner potential was obtained are solvable. By using the Nikiforov-Uvarov method the eigenfunction of the Schrodinger equation in D-dimensional system with general potential Rosen-Morse and Manning Rosen and the Schrodinger equation in D-dimensional system with partner potential Rosen-Morse and Manning Rosen are determined. The eigenfunctions are different between the Schrodinger equation with general potential and the Schrodinger potential with the partner potential.

  4. Intermediate boundary conditions for LOD, ADI and approximate factorization methods

    NASA Technical Reports Server (NTRS)

    Leveque, R. J.

    1985-01-01

    A general approach to determining the correct intermediate boundary conditions for dimensional splitting methods is presented. The intermediate solution U is viewed as a second order accurate approximation to a modified equation. Deriving the modified equation and using the relationship between this equation and the original equation allows us to determine the correct boundary conditions for U*. This technique is illustrated by applying it to locally one dimensional (LOD) and alternating direction implicit (ADI) methods for the heat equation in two and three space dimensions. The approximate factorization method is considered in slightly more generality.

  5. On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations

    NASA Technical Reports Server (NTRS)

    Gunzburger, M. D.; Nicolaides, R. A.

    1986-01-01

    Substructuring methods are in common use in mechanics problems where typically the associated linear systems of algebraic equations are positive definite. Here these methods are extended to problems which lead to nonpositive definite, nonsymmetric matrices. The extension is based on an algorithm which carries out the block Gauss elimination procedure without the need for interchanges even when a pivot matrix is singular. Examples are provided wherein the method is used in connection with finite element solutions of the stationary Stokes equations and the Helmholtz equation, and dual methods for second-order elliptic equations.

  6. Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

    NASA Astrophysics Data System (ADS)

    Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

    2018-01-01

    In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

  7. The method of averages applied to the KS differential equations

    NASA Technical Reports Server (NTRS)

    Graf, O. F., Jr.; Mueller, A. C.; Starke, S. E.

    1977-01-01

    A new approach for the solution of artificial satellite trajectory problems is proposed. The basic idea is to apply an analytical solution method (the method of averages) to an appropriate formulation of the orbital mechanics equations of motion (the KS-element differential equations). The result is a set of transformed equations of motion that are more amenable to numerical solution.

  8. Comparing Alternative Kernels for the Kernel Method of Test Equating: Gaussian, Logistic, and Uniform Kernels. Research Report. ETS RR-08-12

    ERIC Educational Resources Information Center

    Lee, Yi-Hsuan; von Davier, Alina A.

    2008-01-01

    The kernel equating method (von Davier, Holland, & Thayer, 2004) is based on a flexible family of equipercentile-like equating functions that use a Gaussian kernel to continuize the discrete score distributions. While the classical equipercentile, or percentile-rank, equating method carries out the continuization step by linear interpolation,…

  9. Data-driven discovery of partial differential equations.

    PubMed

    Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

    2017-04-01

    We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

  10. Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

    NASA Astrophysics Data System (ADS)

    Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

    2018-05-01

    The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

  11. Exact traveling wave solutions for system of nonlinear evolution equations.

    PubMed

    Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

    2016-01-01

    In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

  12. Fast sweeping method for the factored eikonal equation

    NASA Astrophysics Data System (ADS)

    Fomel, Sergey; Luo, Songting; Zhao, Hongkai

    2009-09-01

    We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

  13. A Review of System Identification Methods Applied to Aircraft

    NASA Technical Reports Server (NTRS)

    Klein, V.

    1983-01-01

    Airplane identification, equation error method, maximum likelihood method, parameter estimation in frequency domain, extended Kalman filter, aircraft equations of motion, aerodynamic model equations, criteria for the selection of a parsimonious model, and online aircraft identification are addressed.

  14. A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

    PubMed Central

    Güner, Özkan; Cevikel, Adem C.

    2014-01-01

    We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

  15. Newton's method: A link between continuous and discrete solutions of nonlinear problems

    NASA Technical Reports Server (NTRS)

    Thurston, G. A.

    1980-01-01

    Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

  16. Preconditioned conjugate residual methods for the solution of spectral equations

    NASA Technical Reports Server (NTRS)

    Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

    1986-01-01

    Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

  17. An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

    NASA Technical Reports Server (NTRS)

    Roithmayr, Carlos M.; Hodges, Dewey H.

    2009-01-01

    Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.

  18. Solution of the Time-Dependent Schrödinger Equation by the Laplace Transform Method

    PubMed Central

    Lin, S. H.; Eyring, H.

    1971-01-01

    The time-dependent Schrödinger equation for two quite general types of perturbation has been solved by introducing the Laplace transforms to eliminate the time variable. The resulting time-independent differential equation can then be solved by the perturbation method, the variation method, the variation-perturbation method, and other methods. PMID:16591898

  19. Study of coupled nonlinear partial differential equations for finding exact analytical solutions

    PubMed Central

    Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

    2015-01-01

    Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

  20. Five-equation and robust three-equation methods for solution verification of large eddy simulation

    NASA Astrophysics Data System (ADS)

    Dutta, Rabijit; Xing, Tao

    2018-02-01

    This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

  1. Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

    NASA Technical Reports Server (NTRS)

    Ibrahim, A. H.; Hou, G. J.-W.; Tiwari, S. N. (Principal Investigator)

    1996-01-01

    Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

  2. A spectral boundary integral equation method for the 2-D Helmholtz equation

    NASA Technical Reports Server (NTRS)

    Hu, Fang Q.

    1994-01-01

    In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

  3. Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

    PubMed

    Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

    2017-06-01

    In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

  4. Exp-function method for solving fractional partial differential equations.

    PubMed

    Zheng, Bin

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

  5. The Impact of Test Dimensionality, Common-Item Set Format, and Scale Linking Methods on Mixed-Format Test Equating

    ERIC Educational Resources Information Center

    Öztürk-Gübes, Nese; Kelecioglu, Hülya

    2016-01-01

    The purpose of this study was to examine the impact of dimensionality, common-item set format, and different scale linking methods on preserving equity property with mixed-format test equating. Item response theory (IRT) true-score equating (TSE) and IRT observed-score equating (OSE) methods were used under common-item nonequivalent groups design.…

  6. Adjustment technique without explicit formation of normal equations /conjugate gradient method/

    NASA Technical Reports Server (NTRS)

    Saxena, N. K.

    1974-01-01

    For a simultaneous adjustment of a large geodetic triangulation system, a semiiterative technique is modified and used successfully. In this semiiterative technique, known as the conjugate gradient (CG) method, original observation equations are used, and thus the explicit formation of normal equations is avoided, 'huge' computer storage space being saved in the case of triangulation systems. This method is suitable even for very poorly conditioned systems where solution is obtained only after more iterations. A detailed study of the CG method for its application to large geodetic triangulation systems was done that also considered constraint equations with observation equations. It was programmed and tested on systems as small as two unknowns and three equations up to those as large as 804 unknowns and 1397 equations. When real data (573 unknowns, 965 equations) from a 1858-km-long triangulation system were used, a solution vector accurate to four decimal places was obtained in 2.96 min after 1171 iterations (i.e., 2.0 times the number of unknowns).

  7. Solution of Volterra and Fredholm Classes of Equations via Triangular Orthogonal Function (A Combination of Right Hand Triangular Function and Left Hand Triangular Function) and Hybrid Orthogonal Function (A Combination of Sample Hold Function and Right Hand Triangular Function)

    NASA Astrophysics Data System (ADS)

    Mukhopadhyay, Anirban; Ganguly, Anindita; Chatterjee, Saumya Deep

    2018-04-01

    In this paper the authors have dealt with seven kinds of non-linear Volterra and Fredholm classes of equations. The authors have formulated an algorithm for solving the aforementioned equation types via Hybrid Function (HF) and Triangular Function (TF) piecewise-linear orthogonal approach. In this approach the authors have reduced integral equation or integro-differential equation into equivalent system of simultaneous non-linear equation and have employed either Newton's method or Broyden's method to solve the simultaneous non-linear equations. The authors have calculated the L2-norm error and the max-norm error for both HF and TF method for each kind of equations. Through the illustrated examples, the authors have shown that the HF based algorithm produces stable result, on the contrary TF-computational method yields either stable, anomalous or unstable results.

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

    PubMed Central

    Rukhin, Andrew L.

    2011-01-01

    A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed. PMID:26989583

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

    PubMed

    Rukhin, Andrew L

    2011-01-01

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

  10. Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

    ERIC Educational Resources Information Center

    Ozdemir, Burhanettin

    2017-01-01

    The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

  11. Pseudo-time algorithms for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Swanson, R. C.; Turkel, E.

    1986-01-01

    A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

  12. Multicellularity arose several times in the evolution of eukaryotes (response to DOI 10.1002/bies.201100187).

    PubMed

    Parfrey, Laura Wegener; Lahr, Daniel J G

    2013-04-01

    The cellular slime mold Dictyostelium has cell-cell connections similar in structure, function, and underlying molecular mechanisms to animal epithelial cells. These similarities form the basis for the proposal that multicellularity is ancestral to the clade containing animals, fungi, and Amoebozoa (including Dictyostelium): Amorphea (formerly "unikonts"). This hypothesis is intriguing and if true could precipitate a paradigm shift. However, phylogenetic analyses of two key genes reveal patterns inconsistent with a single origin of multicellularity. A single origin in Amorphea would also require loss of multicellularity in each of the many unicellular lineages within this clade. Further, there are numerous other origins of multicellularity within eukaryotes, including three within Amorphea, that are not characterized by these structural and mechanistic similarities. Instead, convergent evolution resulting from similar selective pressures for forming multicellular structures with motile and differentiated cells is the most likely explanation for the observed similarities between animal and dictyostelid cell-cell connections. Copyright © 2013 WILEY Periodicals, Inc.

  13. [Herbological study on the botanical origin of the Chinese crude drug shan-zhu-yu].

    PubMed

    Mikage, Masayuki; Hutagi, Yukari

    2008-01-01

    The historical change in the botanical origin of the Chinese herbal drug Shan-zhu-yu, San-syu-yu in Japanese) was studied herbologically. The results obtained were as follows: The original plant, described in Shen-nong-ben-cao-jing written in the Hou-Han Dynasty (A.D. 25-220) and Wu-pu-ben-cao written in the Wei dynasty (A.D. 220-265), was Prunus pseudocerasus or an allied species such as P. tomentosa. However, the original plant described in Ming-yi-bie-lu, written in the same era, was thought to be Cornus officinalis; the fruit of which is used commonly today as Shan-zhu-yu. In addition to Prunus and Cornus, the plants of the genus Berberis, of the family Berberidaceae, and Zanthoxylum of Rutaceae were also used in China until the Ming Dynasty. The plants of Elaeagnus, of the family Elaeagnaceae, were possibly used in ancient Japan. Cornus officinalis was determined to be the origin of Shan-zhu-yu during the Qing Dynasty, China.

  14. How Should Equation Balancing Be Taught?

    ERIC Educational Resources Information Center

    Porter, Spencer K.

    1985-01-01

    Matrix methods and oxidation-number methods are currently advocated and used for balancing equations. This article shows how balancing equations can be introduced by a third method which is related to a fundamental principle, is easy to learn, and is powerful in its application. (JN)

  15. A Unified Approach to Teaching Quadratic and Cubic Equations.

    ERIC Educational Resources Information Center

    Ward, A. J. B.

    2003-01-01

    Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)

  16. An exact solution for the solidification of a liquid slab of binary mixture

    NASA Technical Reports Server (NTRS)

    Antar, B. N.; Collins, F. G.; Aumalia, A. E.

    1986-01-01

    The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations.

  17. Exact solutions to the time-fractional differential equations via local fractional derivatives

    NASA Astrophysics Data System (ADS)

    Guner, Ozkan; Bekir, Ahmet

    2018-01-01

    This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

  18. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    NASA Astrophysics Data System (ADS)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  20. Exact solution of some linear matrix equations using algebraic methods

    NASA Technical Reports Server (NTRS)

    Djaferis, T. E.; Mitter, S. K.

    1977-01-01

    A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.

  1. Critical study of higher order numerical methods for solving the boundary-layer equations

    NASA Technical Reports Server (NTRS)

    Wornom, S. F.

    1978-01-01

    A fourth order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method, which is the natural extension of the second order box scheme to fourth order, was demonstrated with application to the incompressible, laminar and turbulent, boundary layer equations. The efficiency of the present method is compared with two point and three point higher order methods, namely, the Keller box scheme with Richardson extrapolation, the method of deferred corrections, a three point spline method, and a modified finite element method. For equivalent accuracy, numerical results show the present method to be more efficient than higher order methods for both laminar and turbulent flows.

  2. Mathematical Methods for Physics and Engineering Third Edition Paperback Set

    NASA Astrophysics Data System (ADS)

    Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

    2006-06-01

    Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

  3. A Method for the Construction of Hereditary Constitutive Equations of Laminates Bases on a Hereditary Constitutive Equation for a Layer

    NASA Astrophysics Data System (ADS)

    Dumansky, Alexander M.; Tairova, Lyudmila P.

    2008-09-01

    A method for the construction of hereditary constitutive equation is proposed for the laminate on the basis of hereditary constitutive equations of a layer. The method is developed from the assumption that in the directions of axes of orthotropy the layer follows elastic behavior, and obeys hereditary constitutive equations under shear. The constitutive equations of the laminate are constructed on the basis of classical laminate theory and algebra of resolvent operators. Effective matrix algorithm and relationships of operator algebra are used to derive visco-elastic stiffness and compliance of the laminate. The example of construction of hereditary constitutive equations of cross-ply carbon fiber-reinforced plastic is presented.

  4. The Continuized Log-Linear Method: An Alternative to the Kernel Method of Continuization in Test Equating

    ERIC Educational Resources Information Center

    Wang, Tianyou

    2008-01-01

    Von Davier, Holland, and Thayer (2004) laid out a five-step framework of test equating that can be applied to various data collection designs and equating methods. In the continuization step, they presented an adjusted Gaussian kernel method that preserves the first two moments. This article proposes an alternative continuization method that…

  5. Novel asymmetric representation method for solving the higher-order Ginzburg-Landau equation

    PubMed Central

    Wong, Pring; Pang, Lihui; Wu, Ye; Lei, Ming; Liu, Wenjun

    2016-01-01

    In ultrafast optics, optical pulses are generated to be of shorter pulse duration, which has enormous significance to industrial applications and scientific research. The ultrashort pulse evolution in fiber lasers can be described by the higher-order Ginzburg-Landau (GL) equation. However, analytic soliton solutions for this equation have not been obtained by use of existing methods. In this paper, a novel method is proposed to deal with this equation. The analytic soliton solution is obtained for the first time, and is proved to be stable against amplitude perturbations. Through the split-step Fourier method, the bright soliton solution is studied numerically. The analytic results here may extend the integrable methods, and could be used to study soliton dynamics for some equations in other disciplines. It may also provide the other way to obtain two-soliton solutions for higher-order GL equations. PMID:27086841

  6. Numerical solution of the nonlinear Schrodinger equation by feedforward neural networks

    NASA Astrophysics Data System (ADS)

    Shirvany, Yazdan; Hayati, Mohsen; Moradian, Rostam

    2008-12-01

    We present a method to solve boundary value problems using artificial neural networks (ANN). A trial solution of the differential equation is written as a feed-forward neural network containing adjustable parameters (the weights and biases). From the differential equation and its boundary conditions we prepare the energy function which is used in the back-propagation method with momentum term to update the network parameters. We improved energy function of ANN which is derived from Schrodinger equation and the boundary conditions. With this improvement of energy function we can use unsupervised training method in the ANN for solving the equation. Unsupervised training aims to minimize a non-negative energy function. We used the ANN method to solve Schrodinger equation for few quantum systems. Eigenfunctions and energy eigenvalues are calculated. Our numerical results are in agreement with their corresponding analytical solution and show the efficiency of ANN method for solving eigenvalue problems.

  7. Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

    NASA Astrophysics Data System (ADS)

    Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

    2018-01-01

    In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

  8. The discrete adjoint method for parameter identification in multibody system dynamics.

    PubMed

    Lauß, Thomas; Oberpeilsteiner, Stefan; Steiner, Wolfgang; Nachbagauer, Karin

    2018-01-01

    The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method , where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.

  9. Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

    PubMed

    Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

    2014-01-01

    We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

  10. Group foliation of finite difference equations

    NASA Astrophysics Data System (ADS)

    Thompson, Robert; Valiquette, Francis

    2018-06-01

    Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

  11. Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

    NASA Technical Reports Server (NTRS)

    Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

    1992-01-01

    A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

  12. Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

    2014-03-14

    The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

  13. Symmetry methods for option pricing

    NASA Astrophysics Data System (ADS)

    Davison, A. H.; Mamba, S.

    2017-06-01

    We obtain a solution of the Black-Scholes equation with a non-smooth boundary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are first transformed into the one dimensional heat equation and an initial condition respectively. We then find an appropriate general symmetry generator of the heat equation using symmetries and the fundamental solution of the heat equation. The symmetry generator is chosen such that the boundary condition is left invariant; the symmetry can be used to solve the heat equation and hence the Black-Scholes equation.

  14. Data-driven discovery of partial differential equations

    PubMed Central

    Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

    2017-01-01

    We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

  15. Solving Nonlinear Coupled Differential Equations

    NASA Technical Reports Server (NTRS)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  16. Principles of the radiosity method versus radiative transfer for canopy reflectance modeling

    NASA Technical Reports Server (NTRS)

    Gerstl, Siegfried A. W.; Borel, Christoph C.

    1992-01-01

    The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.

  17. Discovery and Optimization of Low-Storage Runge-Kutta Methods

    DTIC Science & Technology

    2015-06-01

    NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential...algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a

  18. On the singular perturbations for fractional differential equation.

    PubMed

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  19. Un-collided-flux preconditioning for the first order transport equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rigley, M.; Koebbe, J.; Drumm, C.

    2013-07-01

    Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

  20. An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

    NASA Technical Reports Server (NTRS)

    Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

    1986-01-01

    A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

  1. OpenMP performance for benchmark 2D shallow water equations using LBM

    NASA Astrophysics Data System (ADS)

    Sabri, Khairul; Rabbani, Hasbi; Gunawan, Putu Harry

    2018-03-01

    Shallow water equations or commonly referred as Saint-Venant equations are used to model fluid phenomena. These equations can be solved numerically using several methods, like Lattice Boltzmann method (LBM), SIMPLE-like Method, Finite Difference Method, Godunov-type Method, and Finite Volume Method. In this paper, the shallow water equation will be approximated using LBM or known as LABSWE and will be simulated in performance of parallel programming using OpenMP. To evaluate the performance between 2 and 4 threads parallel algorithm, ten various number of grids Lx and Ly are elaborated. The results show that using OpenMP platform, the computational time for solving LABSWE can be decreased. For instance using grid sizes 1000 × 500, the speedup of 2 and 4 threads is observed 93.54 s and 333.243 s respectively.

  2. A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Wu, Zedong; Alkhalifah, Tariq

    2018-07-01

    Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

  3. New conditions for obtaining the exact solutions of the general Riccati equation.

    PubMed

    Bougoffa, Lazhar

    2014-01-01

    We propose a direct method for solving the general Riccati equation y' = f(x) + g(x)y + h(x)y(2). We first reduce it into an equivalent equation, and then we formulate the relations between the coefficients functions f(x), g(x), and h(x) of the equation to obtain an equivalent separable equation from which the previous equation can be solved in closed form. Several examples are presented to demonstrate the efficiency of this method.

  4. On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

    NASA Astrophysics Data System (ADS)

    Akbulut, Arzu; Taşcan, Filiz

    2018-04-01

    In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

  5. Analytic solution for the space-time fractional Klein-Gordon and coupled conformable Boussinesq equations

    NASA Astrophysics Data System (ADS)

    Shallal, Muhannad A.; Jabbar, Hawraz N.; Ali, Khalid K.

    2018-03-01

    In this paper, we constructed a travelling wave solution for space-time fractional nonlinear partial differential equations by using the modified extended Tanh method with Riccati equation. The method is used to obtain analytic solutions for the space-time fractional Klein-Gordon and coupled conformable space-time fractional Boussinesq equations. The fractional complex transforms and the properties of modified Riemann-Liouville derivative have been used to convert these equations into nonlinear ordinary differential equations.

  6. Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

    NASA Astrophysics Data System (ADS)

    Riley, K. F.; Hobson, M. P.

    2006-03-01

    Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

  7. Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

    NASA Astrophysics Data System (ADS)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

  8. Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

    2013-10-01

    In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

  9. Determination of lateral-stability derivatives and transfer-function coefficients from frequency-response data for lateral motions

    NASA Technical Reports Server (NTRS)

    Donegan, James J; Robinson, Samuel W , Jr; Gates, Ordway, B , jr

    1955-01-01

    A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.

  10. Time-dependent spectral renormalization method

    NASA Astrophysics Data System (ADS)

    Cole, Justin T.; Musslimani, Ziad H.

    2017-11-01

    The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

  11. Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

    NASA Astrophysics Data System (ADS)

    Vitanov, Nikolay K.

    2011-03-01

    We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

  12. Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

    PubMed

    Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

    2018-01-01

    A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

  13. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

    We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

  14. Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

    NASA Astrophysics Data System (ADS)

    Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

    2018-06-01

    Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

  15. The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

    PubMed

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

    2013-01-01

    Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.

  16. An implicit time-marching method for the three-dimensional Navier-Stokes equations of contravariant velocity components

    NASA Astrophysics Data System (ADS)

    Daiguji, Hisaaki; Yamamoto, Satoru

    1988-12-01

    The implicit time-marching finite-difference method for solving the three-dimensional compressible Euler equations developed by the authors is extended to the Navier-Stokes equations. The distinctive features of this method are to make use of momentum equations of contravariant velocities instead of physical boundaries, and to be able to treat the periodic boundary condition for the three-dimensional impeller flow easily. These equations can be solved by using the same techniques as the Euler equations, such as the delta-form approximate factorization, diagonalization and upstreaming. In addition to them, a simplified total variation diminishing scheme by the authors is applied to the present method in order to capture strong shock waves clearly. Finally, the computed results of the three-dimensional flow through a transonic compressor rotor with tip clearance are shown.

  17. Long-Term Dynamics of Autonomous Fractional Differential Equations

    NASA Astrophysics Data System (ADS)

    Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun

    This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.

  18. Insights: A New Method to Balance Chemical Equations.

    ERIC Educational Resources Information Center

    Garcia, Arcesio

    1987-01-01

    Describes a method designed to balance oxidation-reduction chemical equations. Outlines a method which is based on changes in the oxidation number that can be applied to both molecular reactions and ionic reactions. Provides examples and delineates the steps to follow for each type of equation balancing. (TW)

  19. Variable-mesh method of solving differential equations

    NASA Technical Reports Server (NTRS)

    Van Wyk, R.

    1969-01-01

    Multistep predictor-corrector method for numerical solution of ordinary differential equations retains high local accuracy and convergence properties. In addition, the method was developed in a form conducive to the generation of effective criteria for the selection of subsequent step sizes in step-by-step solution of differential equations.

  20. Analytical studies on the Benney-Luke equation in mathematical physics

    NASA Astrophysics Data System (ADS)

    Islam, S. M. Rayhanul; Khan, Kamruzzaman; Woadud, K. M. Abdul Al

    2018-04-01

    The enhanced (G‧/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney-Luke equation by using the enhanced (G‧/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.

  1. Analysis of stability for stochastic delay integro-differential equations.

    PubMed

    Zhang, Yu; Li, Longsuo

    2018-01-01

    In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.

  2. A General Linear Method for Equating with Small Samples

    ERIC Educational Resources Information Center

    Albano, Anthony D.

    2015-01-01

    Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

  3. The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

    NASA Astrophysics Data System (ADS)

    Kudryashov, Nikolay A.; Volkov, Alexandr K.

    2017-01-01

    We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

  4. Enhancing the Equating of Item Difficulty Metrics: Estimation of Reference Distribution. Research Report. ETS RR-14-07

    ERIC Educational Resources Information Center

    Ali, Usama S.; Walker, Michael E.

    2014-01-01

    Two methods are currently in use at Educational Testing Service (ETS) for equating observed item difficulty statistics. The first method involves the linear equating of item statistics in an observed sample to reference statistics on the same items. The second method, or the item response curve (IRC) method, involves the summation of conditional…

  5. Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

    NASA Astrophysics Data System (ADS)

    Finster, Felix; Smoller, Joel

    2010-09-01

    A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.

  6. Direct Coupling Method for Time-Accurate Solution of Incompressible Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Soh, Woo Y.

    1992-01-01

    A noniterative finite difference numerical method is presented for the solution of the incompressible Navier-Stokes equations with second order accuracy in time and space. Explicit treatment of convection and diffusion terms and implicit treatment of the pressure gradient give a single pressure Poisson equation when the discretized momentum and continuity equations are combined. A pressure boundary condition is not needed on solid boundaries in the staggered mesh system. The solution of the pressure Poisson equation is obtained directly by Gaussian elimination. This method is tested on flow problems in a driven cavity and a curved duct.

  7. Numerical solutions to the time-dependent Bloch equations revisited.

    PubMed

    Murase, Kenya; Tanki, Nobuyoshi

    2011-01-01

    The purpose of this study was to demonstrate a simple and fast method for solving the time-dependent Bloch equations. First, the time-dependent Bloch equations were reduced to a homogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. The validity of this method was investigated by comparing with the analytical solutions in the case of constant radiofrequency irradiation. There was a good agreement between them, indicating the validity of this method. As a further example, this method was applied to the time-dependent Bloch equations in the two-pool exchange model for chemical exchange saturation transfer (CEST) or amide proton transfer (APT) magnetic resonance imaging (MRI), and the Z-spectra and asymmetry spectra were calculated from their solutions. They were also calculated using the fourth/fifth-order Runge-Kutta-Fehlberg (RKF) method for comparison. There was also a good agreement between them, and this method was much faster than the RKF method. In conclusion, this method will be useful for analyzing the complex CEST or APT contrast mechanism and/or investigating the optimal conditions for CEST or APT MRI. Copyright © 2011 Elsevier Inc. All rights reserved.

  8. Pseudo-time methods for constrained optimization problems governed by PDE

    NASA Technical Reports Server (NTRS)

    Taasan, Shlomo

    1995-01-01

    In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

  9. Algebraic methods for the solution of some linear matrix equations

    NASA Technical Reports Server (NTRS)

    Djaferis, T. E.; Mitter, S. K.

    1979-01-01

    The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

  10. Geometrical and Graphical Solutions of Quadratic Equations.

    ERIC Educational Resources Information Center

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  11. Exercise tolerance and selected motor skills in young females with idiopathic scoliosis treated with different physiotherapeutic methods.

    PubMed

    Fabian, Krzysztof Marek; Rożek-Piechura, Krystyna

    2014-01-01

    Scoliosis is a disorder that leads to dysfunction of a number of systems in the body, especially in young females. Physical capacity is one of the most important elements of good health as well as ofbiological development. Adolescence is a time when physical capacity develops intensively, and the condition of the respiratory system is one of many factors that have an impact on the level of physical capacity. This paper aims to evaluate a short-term application of two methods of physiotherapy and their influence on the level of exercise tolerance in young females suffering from idiopathic scoliosis. The study involved a group of 49 young females aged 14-15 years diagnosed with (2040°) thoracic and lumbar scoliosis who were in-patients at the rehabilitation ward of the Regional Paediatric Rehabilitation Hospital in Jastrzębie Zdrój. The group was divided into two subgroups depending on the method of rehabilitation employed: the first subgroup received asymmetric breathing exercise therapy by Dobosiewicz and the second subgroup practised symmetric remedial exercises. Cobb's angle, the degree of skeletal maturity, i.e. the Risser sign and the degree trunk rotation of the apex of the curvature by means of Raimondi's coefficient were determined once in an x-ray image. Basic somatic features, maximal voluntary ventilation (MVV parameter), selected motor skills and exercise tolerance were assessed on two occasions (before beginning and after completion of the rehabilitation treatment). 1. Young females suffering from (20-40°) thoracic and lumbar scoliosis demonstrate respiratory dysfunction, as shown by decreased maximal voluntary ventilation (MVV) in the two subgroups in the present study. Exercises according to Dobosiewicz's method brought about a significantly higher degree of improvement in this parameter. 2. The physiotherapeutic regimen administered to the young girls with scoliosis significantly improved their strength motor skills and exercise tolerance. A significantly higher improvement was observed in the subgroup treated using Dobosiewicz's method, in particular, in the strength of abdominal muscles, which play an important role in both respiratory function and body posture maintenance.

  12. Conservation properties of numerical integration methods for systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Rosenbaum, J. S.

    1976-01-01

    If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

  13. Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

    NASA Technical Reports Server (NTRS)

    Lyusternik, L. A.

    1980-01-01

    The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

  14. Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

    NASA Technical Reports Server (NTRS)

    Chuang, Ching H.; Hou, Gene J. W.

    1991-01-01

    Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

  15. Fourth-order numerical solutions of diffusion equation by using SOR method with Crank-Nicolson approach

    NASA Astrophysics Data System (ADS)

    Muhiddin, F. A.; Sulaiman, J.

    2017-09-01

    The aim of this paper is to investigate the effectiveness of the Successive Over-Relaxation (SOR) iterative method by using the fourth-order Crank-Nicolson (CN) discretization scheme to derive a five-point Crank-Nicolson approximation equation in order to solve diffusion equation. From this approximation equation, clearly, it can be shown that corresponding system of five-point approximation equations can be generated and then solved iteratively. In order to access the performance results of the proposed iterative method with the fourth-order CN scheme, another point iterative method which is Gauss-Seidel (GS), also presented as a reference method. Finally the numerical results obtained from the use of the fourth-order CN discretization scheme, it can be pointed out that the SOR iterative method is superior in terms of number of iterations, execution time, and maximum absolute error.

  16. A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hong Luo; Luqing Luo; Robert Nourgaliev

    2010-09-01

    A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi–Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier–Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier–Stokes equations.« less

  17. A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hong Luo; Luqing Luo; Robert Nourgaliev

    2010-01-01

    A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.« less

  18. Flood-frequency prediction methods for unregulated streams of Tennessee, 2000

    USGS Publications Warehouse

    Law, George S.; Tasker, Gary D.

    2003-01-01

    Up-to-date flood-frequency prediction methods for unregulated, ungaged rivers and streams of Tennessee have been developed. Prediction methods include the regional-regression method and the newer region-of-influence method. The prediction methods were developed using stream-gage records from unregulated streams draining basins having from 1 percent to about 30 percent total impervious area. These methods, however, should not be used in heavily developed or storm-sewered basins with impervious areas greater than 10 percent. The methods can be used to estimate 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence-interval floods of most unregulated rural streams in Tennessee. A computer application was developed that automates the calculation of flood frequency for unregulated, ungaged rivers and streams of Tennessee. Regional-regression equations were derived by using both single-variable and multivariable regional-regression analysis. Contributing drainage area is the explanatory variable used in the single-variable equations. Contributing drainage area, main-channel slope, and a climate factor are the explanatory variables used in the multivariable equations. Deleted-residual standard error for the single-variable equations ranged from 32 to 65 percent. Deleted-residual standard error for the multivariable equations ranged from 31 to 63 percent. These equations are included in the computer application to allow easy comparison of results produced by the different methods. The region-of-influence method calculates multivariable regression equations for each ungaged site and recurrence interval using basin characteristics from 60 similar sites selected from the study area. Explanatory variables that may be used in regression equations computed by the region-of-influence method include contributing drainage area, main-channel slope, a climate factor, and a physiographic-region factor. Deleted-residual standard error for the region-of-influence method tended to be only slightly smaller than those for the regional-regression method and ranged from 27 to 62 percent.

  19. On linearization and preconditioning for radiation diffusion coupled to material thermal conduction equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Feng, Tao, E-mail: fengtao2@mail.ustc.edu.cn; Graduate School of China Academy Engineering Physics, Beijing 100083; An, Hengbin, E-mail: an_hengbin@iapcm.ac.cn

    2013-03-01

    Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods canmore » improve the convergence behavior and efficiency of JFNK method.« less

  20. A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

    PubMed Central

    Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

    2013-01-01

    We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

  1. Generalized Lagrangian Jacobi Gauss collocation method for solving unsteady isothermal gas through a micro-nano porous medium

    NASA Astrophysics Data System (ADS)

    Parand, Kourosh; Latifi, Sobhan; Delkhosh, Mehdi; Moayeri, Mohammad M.

    2018-01-01

    In the present paper, a new method based on the Generalized Lagrangian Jacobi Gauss (GLJG) collocation method is proposed. The nonlinear Kidder equation, which explains unsteady isothermal gas through a micro-nano porous medium, is a second-order two-point boundary value ordinary differential equation on the unbounded interval [0, ∞). Firstly, using the quasilinearization method, the equation is converted to a sequence of linear ordinary differential equations. Then, by using the GLJG collocation method, the problem is reduced to solving a system of algebraic equations. It must be mentioned that this equation is solved without domain truncation and variable changing. A comparison with some numerical solutions made and the obtained results indicate that the presented solution is highly accurate. The important value of the initial slope, y'(0), is obtained as -1.191790649719421734122828603800159364 for η = 0.5. Comparing to the best result obtained so far, it is accurate up to 36 decimal places.

  2. A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

    PubMed

    Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

    2013-01-01

    We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

  3. F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

    PubMed Central

    Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

    2014-01-01

    F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics. PMID:24672327

  4. F-expansion method and new exact solutions of the Schrödinger-KdV equation.

    PubMed

    Filiz, Ali; Ekici, Mehmet; Sonmezoglu, Abdullah

    2014-01-01

    F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

  5. On the Singular Perturbations for Fractional Differential Equation

    PubMed Central

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

  6. Application of the Discrete Regularization Method to the Inverse of the Chord Vibration Equation

    NASA Astrophysics Data System (ADS)

    Wang, Linjun; Han, Xu; Wei, Zhouchao

    The inverse problem of the initial condition about the boundary value of the chord vibration equation is ill-posed. First, we transform it into a Fredholm integral equation. Second, we discretize it by the trapezoidal formula method, and then obtain a severely ill-conditioned linear equation, which is sensitive to the disturbance of the data. In addition, the tiny error of right data causes the huge concussion of the solution. We cannot obtain good results by the traditional method. In this paper, we solve this problem by the Tikhonov regularization method, and the numerical simulations demonstrate that this method is feasible and effective.

  7. Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Poleshkin, Sergey O.; Malkov, Ewgenij A.; Kudryavtsev, Alexey N.; Shershnev, Anton A.; Bondar, Yevgeniy A.; Kohanchik, A. A.

    2017-10-01

    There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

  8. A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

    NASA Astrophysics Data System (ADS)

    Parand, K.; Nikarya, M.

    2017-11-01

    In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

  9. The origin of spurious solutions in computational electromagnetics

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Wu, Jie; Povinelli, L. A.

    1995-01-01

    The origin of spurious solutions in computational electromagnetics, which violate the divergence equations, is deeply rooted in a misconception about the first-order Maxwell's equations and in an incorrect derivation and use of the curl-curl equations. The divergence equations must be always included in the first-order Maxwell's equations to maintain the ellipticity of the system in the space domain and to guarantee the uniqueness of the solution and/or the accuracy of the numerical solutions. The div-curl method and the least-squares method provide rigorous derivation of the equivalent second-order Maxwell's equations and their boundary conditions. The node-based least-squares finite element method (LSFEM) is recommended for solving the first-order full Maxwell equations directly. Examples of the numerical solutions by LSFEM for time-harmonic problems are given to demonstrate that the LSFEM is free of spurious solutions.

  10. A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

    PubMed

    Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

    2009-02-01

    Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

  11. On the solution of the complex eikonal equation in acoustic VTI media: A perturbation plus optimization scheme

    NASA Astrophysics Data System (ADS)

    Huang, Xingguo; Sun, Jianguo; Greenhalgh, Stewart

    2018-04-01

    We present methods for obtaining numerical and analytic solutions of the complex eikonal equation in inhomogeneous acoustic VTI media (transversely isotropic media with a vertical symmetry axis). The key and novel point of the method for obtaining numerical solutions is to transform the problem of solving the highly nonlinear acoustic VTI eikonal equation into one of solving the relatively simple eikonal equation for the background (isotropic) medium and a system of linear partial differential equations. Specifically, to obtain the real and imaginary parts of the complex traveltime in inhomogeneous acoustic VTI media, we generalize a perturbation theory, which was developed earlier for solving the conventional real eikonal equation in inhomogeneous anisotropic media, to the complex eikonal equation in such media. After the perturbation analysis, we obtain two types of equations. One is the complex eikonal equation for the background medium and the other is a system of linearized partial differential equations for the coefficients of the corresponding complex traveltime formulas. To solve the complex eikonal equation for the background medium, we employ an optimization scheme that we developed for solving the complex eikonal equation in isotropic media. Then, to solve the system of linearized partial differential equations for the coefficients of the complex traveltime formulas, we use the finite difference method based on the fast marching strategy. Furthermore, by applying the complex source point method and the paraxial approximation, we develop the analytic solutions of the complex eikonal equation in acoustic VTI media, both for the isotropic and elliptical anisotropic background medium. Our numerical results demonstrate the effectiveness of our derivations and illustrate the influence of the beam widths and the anisotropic parameters on the complex traveltimes.

  12. An enriched finite element method to fractional advection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

    2017-08-01

    In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

  13. An Equation-Free Reduced-Order Modeling Approach to Tropical Pacific Simulation

    NASA Astrophysics Data System (ADS)

    Wang, Ruiwen; Zhu, Jiang; Luo, Zhendong; Navon, I. M.

    2009-03-01

    The “equation-free” (EF) method is often used in complex, multi-scale problems. In such cases it is necessary to know the closed form of the required evolution equations about oscopic variables within some applied fields. Conceptually such equations exist, however, they are not available in closed form. The EF method can bypass this difficulty. This method can obtain oscopic information by implementing models at a microscopic level. Given an initial oscopic variable, through lifting we can obtain the associated microscopic variable, which may be evolved using Direct Numerical Simulations (DNS) and by restriction, we can obtain the necessary oscopic information and the projective integration to obtain the desired quantities. In this paper we apply the EF POD-assisted method to the reduced modeling of a large-scale upper ocean circulation in the tropical Pacific domain. The computation cost is reduced dramatically. Compared with the POD method, the method provided more accurate results and it did not require the availability of any explicit equations or the right-hand side (RHS) of the evolution equation.

  14. Using a Linear Regression Method to Detect Outliers in IRT Common Item Equating

    ERIC Educational Resources Information Center

    He, Yong; Cui, Zhongmin; Fang, Yu; Chen, Hanwei

    2013-01-01

    Common test items play an important role in equating alternate test forms under the common item nonequivalent groups design. When the item response theory (IRT) method is applied in equating, inconsistent item parameter estimates among common items can lead to large bias in equated scores. It is prudent to evaluate inconsistency in parameter…

  15. Robust Scale Transformation Methods in IRT True Score Equating under Common-Item Nonequivalent Groups Design

    ERIC Educational Resources Information Center

    He, Yong

    2013-01-01

    Common test items play an important role in equating multiple test forms under the common-item nonequivalent groups design. Inconsistent item parameter estimates among common items can lead to large bias in equated scores for IRT true score equating. Current methods extensively focus on detection and elimination of outlying common items, which…

  16. Kernel and Traditional Equipercentile Equating with Degrees of Presmoothing. Research Report. ETS RR-07-15

    ERIC Educational Resources Information Center

    Moses, Tim; Holland, Paul

    2007-01-01

    The purpose of this study was to empirically evaluate the impact of loglinear presmoothing accuracy on equating bias and variability across chained and post-stratification equating methods, kernel and percentile-rank continuization methods, and sample sizes. The results of evaluating presmoothing on equating accuracy generally agreed with those of…

  17. A New Factorisation of a General Second Order Differential Equation

    ERIC Educational Resources Information Center

    Clegg, Janet

    2006-01-01

    A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

  18. The Parker-Sochacki Method--A Powerful New Method for Solving Systems of Differential Equations

    NASA Astrophysics Data System (ADS)

    Rudmin, Joseph W.

    2001-04-01

    The Parker-Sochacki Method--A Powerful New Method for Solving Systems of Differential Equations Joseph W. Rudmin (Physics Dept, James Madison University) A new system of solving systems of differential equations will be presented, which has been developed by J. Edgar Parker and James Sochacki, of the James Madison University Mathematics Department. The method produces MacClaurin Series solutions to systems of differential equations, with the coefficients in either algebraic or numerical form. The method yields high-degree solutions: 20th degree is easily obtainable. It is conceptually simple, fast, and extremely general. It has been applied to over a hundred systems of differential equations, some of which were previously unsolved, and has yet to fail to solve any system for which the MacClaurin series converges. The method is non-recursive: each coefficient in the series is calculated just once, in closed form, and its accuracy is limited only by the digital accuracy of the computer. Although the original differential equations may include any mathematical functions, the computational method includes ONLY the operations of addition, subtraction, and multiplication. Furthermore, it is perfectly suited to parallel -processing computer languages. Those who learn this system will never use Runge-Kutta or predictor-corrector methods again. Examples will be presented, including the classical many-body problem.

  19. Evaluation of Maryland abutment scour equation through selected threshold velocity methods

    USGS Publications Warehouse

    Benedict, S.T.

    2010-01-01

    The U.S. Geological Survey, in cooperation with the Maryland State Highway Administration, used field measurements of scour to evaluate the sensitivity of the Maryland abutment scour equation to the critical (or threshold) velocity variable. Four selected methods for estimating threshold velocity were applied to the Maryland abutment scour equation, and the predicted scour to the field measurements were compared. Results indicated that performance of the Maryland abutment scour equation was sensitive to the threshold velocity with some threshold velocity methods producing better estimates of predicted scour than did others. In addition, results indicated that regional stream characteristics can affect the performance of the Maryland abutment scour equation with moderate-gradient streams performing differently from low-gradient streams. On the basis of the findings of the investigation, guidance for selecting threshold velocity methods for application to the Maryland abutment scour equation are provided, and limitations are noted.

  20. Mechanical modeling for magnetorheological elastomer isolators based on constitutive equations and electromagnetic analysis

    NASA Astrophysics Data System (ADS)

    Wang, Qi; Dong, Xufeng; Li, Luyu; Ou, Jinping

    2018-06-01

    As constitutive models are too complicated and existing mechanical models lack universality, these models are beyond satisfaction for magnetorheological elastomer (MRE) devices. In this article, a novel universal method is proposed to build concise mechanical models. Constitutive model and electromagnetic analysis were applied in this method to ensure universality, while a series of derivations and simplifications were carried out to obtain a concise formulation. To illustrate the proposed modeling method, a conical MRE isolator was introduced. Its basic mechanical equations were built based on equilibrium, deformation compatibility, constitutive equations and electromagnetic analysis. An iteration model and a highly efficient differential equation editor based model were then derived to solve the basic mechanical equations. The final simplified mechanical equations were obtained by re-fitting the simulations with a novel optimal algorithm. In the end, verification test of the isolator has proved the accuracy of the derived mechanical model and the modeling method.

  1. The method of Ritz applied to the equation of Hamilton. [for pendulum systems

    NASA Technical Reports Server (NTRS)

    Bailey, C. D.

    1976-01-01

    Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.

  2. Comparing Balance and Inverse Methods on Learning Conceptual and Procedural Knowledge in Equation Solving: A Cognitive Load Perspective

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Phan, Huy Phuong

    2016-01-01

    We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for…

  3. Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

    NASA Astrophysics Data System (ADS)

    Wang, Yi-Hong; Wu, Guo-Cheng; Baleanu, Dumitru

    2013-10-01

    The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.

  4. Systems of fuzzy equations in structural mechanics

    NASA Astrophysics Data System (ADS)

    Skalna, Iwona; Rama Rao, M. V.; Pownuk, Andrzej

    2008-08-01

    Systems of linear and nonlinear equations with fuzzy parameters are relevant to many practical problems arising in structure mechanics, electrical engineering, finance, economics and physics. In this paper three methods for solving such equations are discussed: method for outer interval solution of systems of linear equations depending linearly on interval parameters, fuzzy finite element method proposed by Rama Rao and sensitivity analysis method. The performance and advantages of presented methods are described with illustrative examples. Extended version of the present paper can be downloaded from the web page of the UTEP [I. Skalna, M.V. Rama Rao, A. Pownuk, Systems of fuzzy equations in structural mechanics, The University of Texas at El Paso, Department of Mathematical Sciences Research Reports Series, , Texas Research Report No. 2007-01, 2007].

  5. On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1980-01-01

    New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

  6. A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Emami, F.; Hatami, M.; Keshavarz, A. R.

    2009-08-13

    Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

  7. Numerical methods for stochastic differential equations

    NASA Astrophysics Data System (ADS)

    Kloeden, Peter; Platen, Eckhard

    1991-06-01

    The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.

  8. Local Analysis of Shock Capturing Using Discontinuous Galerkin Methodology

    NASA Technical Reports Server (NTRS)

    Atkins, H. L.

    1997-01-01

    The compact form of the discontinuous Galerkin method allows for a detailed local analysis of the method in the neighborhood of the shock for a non-linear model problem. Insight gained from the analysis leads to new flux formulas that are stable and that preserve the compactness of the method. Although developed for a model equation, the flux formulas are applicable to systems such as the Euler equations. This article presents the analysis for methods with a degree up to 5. The analysis is accompanied by supporting numerical experiments using Burgers' equation and the Euler equations.

  9. Exponential Methods for the Time Integration of Schroedinger Equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Cano, B.; Gonzalez-Pachon, A.

    2010-09-30

    We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

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

    PubMed

    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.

  11. Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

    PubMed Central

    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. PMID:25811858

  12. The Boundary Integral Equation Method for Porous Media Flow

    NASA Astrophysics Data System (ADS)

    Anderson, Mary P.

    Just as groundwater hydrologists are breathing sighs of relief after the exertions of learning the finite element method, a new technique has reared its nodes—the boundary integral equation method (BIEM) or the boundary equation method (BEM), as it is sometimes called. As Liggett and Liu put it in the preface to The Boundary Integral Equation Method for Porous Media Flow, “Lately, the Boundary Integral Equation Method (BIEM) has emerged as a contender in the computation Derby.” In fact, in July 1984, the 6th International Conference on Boundary Element Methods in Engineering will be held aboard the Queen Elizabeth II, en route from Southampton to New York. These conferences are sponsored by the Department of Civil Engineering at Southampton College (UK), whose members are proponents of BIEM. The conferences have featured papers on applications of BIEM to all aspects of engineering, including flow through porous media. Published proceedings are available, as are textbooks on application of BIEM to engineering problems. There is even a 10-minute film on the subject.

  13. Numerical method for the solution of large systems of differential equations of the boundary layer type

    NASA Technical Reports Server (NTRS)

    Green, M. J.; Nachtsheim, P. R.

    1972-01-01

    A numerical method for the solution of large systems of nonlinear differential equations of the boundary-layer type is described. The method is a modification of the technique for satisfying asymptotic boundary conditions. The present method employs inverse interpolation instead of the Newton method to adjust the initial conditions of the related initial-value problem. This eliminates the so-called perturbation equations. The elimination of the perturbation equations not only reduces the user's preliminary work in the application of the method, but also reduces the number of time-consuming initial-value problems to be numerically solved at each iteration. For further ease of application, the solution of the overdetermined system for the unknown initial conditions is obtained automatically by applying Golub's linear least-squares algorithm. The relative ease of application of the proposed numerical method increases directly as the order of the differential-equation system increases. Hence, the method is especially attractive for the solution of large-order systems. After the method is described, it is applied to a fifth-order problem from boundary-layer theory.

  14. [Comparison of three stand-level biomass estimation methods].

    PubMed

    Dong, Li Hu; Li, Feng Ri

    2016-12-01

    At present, the forest biomass methods of regional scale attract most of attention of the researchers, and developing the stand-level biomass model is popular. Based on the forestry inventory data of larch plantation (Larix olgensis) in Jilin Province, we used non-linear seemly unrelated regression (NSUR) to estimate the parameters in two additive system of stand-level biomass equations, i.e., stand-level biomass equations including the stand variables and stand biomass equations including the biomass expansion factor (i.e., Model system 1 and Model system 2), listed the constant biomass expansion factor for larch plantation and compared the prediction accuracy of three stand-level biomass estimation methods. The results indicated that for two additive system of biomass equations, the adjusted coefficient of determination (R a 2 ) of the total and stem equations was more than 0.95, the root mean squared error (RMSE), the mean prediction error (MPE) and the mean absolute error (MAE) were smaller. The branch and foliage biomass equations were worse than total and stem biomass equations, and the adjusted coefficient of determination (R a 2 ) was less than 0.95. The prediction accuracy of a constant biomass expansion factor was relatively lower than the prediction accuracy of Model system 1 and Model system 2. Overall, although stand-level biomass equation including the biomass expansion factor belonged to the volume-derived biomass estimation method, and was different from the stand biomass equations including stand variables in essence, but the obtained prediction accuracy of the two methods was similar. The constant biomass expansion factor had the lower prediction accuracy, and was inappropriate. In addition, in order to make the model parameter estimation more effective, the established stand-level biomass equations should consider the additivity in a system of all tree component biomass and total biomass equations.

  15. Methods for estimating flood frequency in Montana based on data through water year 1998

    USGS Publications Warehouse

    Parrett, Charles; Johnson, Dave R.

    2004-01-01

    Annual peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (T-year floods) were determined for 660 gaged sites in Montana and in adjacent areas of Idaho, Wyoming, and Canada, based on data through water year 1998. The updated flood-frequency information was subsequently used in regression analyses, either ordinary or generalized least squares, to develop equations relating T-year floods to various basin and climatic characteristics, equations relating T-year floods to active-channel width, and equations relating T-year floods to bankfull width. The equations can be used to estimate flood frequency at ungaged sites. Montana was divided into eight regions, within which flood characteristics were considered to be reasonably homogeneous, and the three sets of regression equations were developed for each region. A measure of the overall reliability of the regression equations is the average standard error of prediction. The average standard errors of prediction for the equations based on basin and climatic characteristics ranged from 37.4 percent to 134.1 percent. Average standard errors of prediction for the equations based on active-channel width ranged from 57.2 percent to 141.3 percent. Average standard errors of prediction for the equations based on bankfull width ranged from 63.1 percent to 155.5 percent. In most regions, the equations based on basin and climatic characteristics generally had smaller average standard errors of prediction than equations based on active-channel or bankfull width. An exception was the Southeast Plains Region, where all equations based on active-channel width had smaller average standard errors of prediction than equations based on basin and climatic characteristics or bankfull width. Methods for weighting estimates derived from the basin- and climatic-characteristic equations and the channel-width equations also were developed. The weights were based on the cross correlation of residuals from the different methods and the average standard errors of prediction. When all three methods were combined, the average standard errors of prediction ranged from 37.4 percent to 120.2 percent. Weighting of estimates reduced the standard errors of prediction for all T-year flood estimates in four regions, reduced the standard errors of prediction for some T-year flood estimates in two regions, and provided no reduction in average standard error of prediction in two regions. A computer program for solving the regression equations, weighting estimates, and determining reliability of individual estimates was developed and placed on the USGS Montana District World Wide Web page. A new regression method, termed Region of Influence regression, also was tested. Test results indicated that the Region of Influence method was not as reliable as the regional equations based on generalized least squares regression. Two additional methods for estimating flood frequency at ungaged sites located on the same streams as gaged sites also are described. The first method, based on a drainage-area-ratio adjustment, is intended for use on streams where the ungaged site of interest is located near a gaged site. The second method, based on interpolation between gaged sites, is intended for use on streams that have two or more streamflow-gaging stations.

  16. Fast wavelet based algorithms for linear evolution equations

    NASA Technical Reports Server (NTRS)

    Engquist, Bjorn; Osher, Stanley; Zhong, Sifen

    1992-01-01

    A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.

  17. An extension of the Derrida-Lebowitz-Speer-Spohn equation

    NASA Astrophysics Data System (ADS)

    Bordenave, Charles; Germain, Pierre; Trogdon, Thomas

    2015-12-01

    We show how the derivation of the Derrida-Lebowitz-Speer-Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the paper by these authors. We then investigate its properties from both an analytical and numerical perspective. Specifically, a numerical method is presented to approximate solutions of the prolonged equation. Using this method, we investigate the relationship between the solutions of the prolonged equation and the Tracy-Widom GOE distribution.

  18. Method of controlling chaos in laser equations

    NASA Astrophysics Data System (ADS)

    Duong-van, Minh

    1993-01-01

    A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

  19. Soliton evolution and radiation loss for the sine-Gordon equation.

    PubMed

    Smyth, N F; Worthy, A L

    1999-08-01

    An approximate method for describing the evolution of solitonlike initial conditions to solitons for the sine-Gordon equation is developed. This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian is then used to determine ordinary differential equations governing the evolution of the pulse parameters. The pulse evolves to a steady soliton by shedding dispersive radiation. The effect of this radiation is determined by examining the linearized sine-Gordon equation and loss terms are added to the variational equations derived from the averaged Lagrangian by using the momentum and energy conservation equations for the sine-Gordon equation. Solutions of the resulting approximate equations, which include loss, are found to be in good agreement with full numerical solutions of the sine-Gordon equation.

  20. Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Loh, Ching Y.; Povinelli, Louis A.

    1994-01-01

    Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

  1. Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

    NASA Astrophysics Data System (ADS)

    Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

    2018-03-01

    In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

  2. Quantum trajectories for time-dependent adiabatic master equations

    NASA Astrophysics Data System (ADS)

    Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.

    2018-02-01

    We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

  3. Governing equations for electro-conjugate fluid flow

    NASA Astrophysics Data System (ADS)

    Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

    2013-12-01

    An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

  4. Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

    NASA Technical Reports Server (NTRS)

    Majumdar, Alok; Schallhorn, Paul

    1998-01-01

    This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

  5. An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

    NASA Technical Reports Server (NTRS)

    Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

    1974-01-01

    The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

  6. Multigrid method for the equilibrium equations of elasticity using a compact scheme

    NASA Technical Reports Server (NTRS)

    Taasan, S.

    1986-01-01

    A compact difference scheme is derived for treating the equilibrium equations of elasticity. The scheme is inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just two multigrid cycles.

  7. Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

    NASA Astrophysics Data System (ADS)

    Berkeley, George; Igonin, Sergei

    2016-07-01

    Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

  8. A deterministic particle method for one-dimensional reaction-diffusion equations

    NASA Technical Reports Server (NTRS)

    Mascagni, Michael

    1995-01-01

    We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

  9. Adomian decomposition method used to solve the one-dimensional acoustic equations

    NASA Astrophysics Data System (ADS)

    Dispini, Meta; Mungkasi, Sudi

    2017-05-01

    In this paper we propose the use of Adomian decomposition method to solve one-dimensional acoustic equations. This recursive method can be calculated easily and the result is an approximation of the exact solution. We use the Maple software to compute the series in the Adomian decomposition. We obtain that the Adomian decomposition method is able to solve the acoustic equations with the physically correct behavior.

  10. A New Family of Schroder's Method and Its Variants Based on Power Means for Multiple Roots of Nonlinear Equations

    ERIC Educational Resources Information Center

    Kanwar, V.; Sharma, Kapil K.; Behl, Ramandeep

    2010-01-01

    In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…

  11. A review of spectral methods

    NASA Technical Reports Server (NTRS)

    Lustman, L.

    1984-01-01

    An outline for spectral methods for partial differential equations is presented. The basic spectral algorithm is defined, collocation are emphasized and the main advantage of the method, the infinite order of accuracy in problems with smooth solutions are discussed. Examples of theoretical numerical analysis of spectral calculations are presented. An application of spectral methods to transonic flow is presented. The full potential transonic equation is among the best understood among nonlinear equations.

  12. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

    PubMed

    Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n ) ( n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

  13. A multilevel correction adaptive finite element method for Kohn-Sham equation

    NASA Astrophysics Data System (ADS)

    Hu, Guanghui; Xie, Hehu; Xu, Fei

    2018-02-01

    In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

  14. An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

    NASA Technical Reports Server (NTRS)

    Rybicki, G. B.; Hummer, D. G.

    1991-01-01

    A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

  15. Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

    NASA Astrophysics Data System (ADS)

    Ali, Asghar; Seadawy, Aly R.; Lu, Dianchen

    2018-05-01

    The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.

  16. A method for the selection of a functional form for a thermodynamic equation of state using weighted linear least squares stepwise regression

    NASA Technical Reports Server (NTRS)

    Jacobsen, R. T.; Stewart, R. B.; Crain, R. W., Jr.; Rose, G. L.; Myers, A. F.

    1976-01-01

    A method was developed for establishing a rational choice of the terms to be included in an equation of state with a large number of adjustable coefficients. The methods presented were developed for use in the determination of an equation of state for oxygen and nitrogen. However, a general application of the methods is possible in studies involving the determination of an optimum polynomial equation for fitting a large number of data points. The data considered in the least squares problem are experimental thermodynamic pressure-density-temperature data. Attention is given to a description of stepwise multiple regression and the use of stepwise regression in the determination of an equation of state for oxygen and nitrogen.

  17. Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

    NASA Astrophysics Data System (ADS)

    El-Kalla, I. L.; Al-Bugami, A. M.

    2010-11-01

    In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

  18. Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Rzasnicki, W.

    1973-01-01

    A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

  19. Finite difference methods for transient signal propagation in stratified dispersive media

    NASA Technical Reports Server (NTRS)

    Lam, D. H.

    1975-01-01

    Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

  20. Variational Methods in Design Optimization and Sensitivity Analysis for Two-Dimensional Euler Equations

    NASA Technical Reports Server (NTRS)

    Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.

    1997-01-01

    Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

  1. A least-squares finite element method for 3D incompressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Jiang, Bo-Nan; Lin, T. L.; Hou, Lin-Jun; Povinelli, Louis A.

    1993-01-01

    The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

  2. Validity of Bioelectrical Impedance Analysis to Estimation Fat-Free Mass in the Army Cadets.

    PubMed

    Langer, Raquel D; Borges, Juliano H; Pascoa, Mauro A; Cirolini, Vagner X; Guerra-Júnior, Gil; Gonçalves, Ezequiel M

    2016-03-11

    Bioelectrical Impedance Analysis (BIA) is a fast, practical, non-invasive, and frequently used method for fat-free mass (FFM) estimation. The aims of this study were to validate predictive equations of BIA to FFM estimation in Army cadets and to develop and validate a specific BIA equation for this population. A total of 396 males, Brazilian Army cadets, aged 17-24 years were included. The study used eight published predictive BIA equations, a specific equation in FFM estimation, and dual-energy X-ray absorptiometry (DXA) as a reference method. Student's t-test (for paired sample), linear regression analysis, and Bland-Altman method were used to test the validity of the BIA equations. Predictive BIA equations showed significant differences in FFM compared to DXA (p < 0.05) and large limits of agreement by Bland-Altman. Predictive BIA equations explained 68% to 88% of FFM variance. Specific BIA equations showed no significant differences in FFM, compared to DXA values. Published BIA predictive equations showed poor accuracy in this sample. The specific BIA equations, developed in this study, demonstrated validity for this sample, although should be used with caution in samples with a large range of FFM.

  3. A parallel algorithm for nonlinear convection-diffusion equations

    NASA Technical Reports Server (NTRS)

    Scroggs, Jeffrey S.

    1990-01-01

    A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

  4. The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

    NASA Technical Reports Server (NTRS)

    Balasubramanian, R.; Norrie, D. H.; De Vries, G.

    1979-01-01

    Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

  5. Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model

    NASA Astrophysics Data System (ADS)

    Wang, Huimin

    2017-01-01

    In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.

  6. Automatic computation and solution of generalized harmonic balance equations

    NASA Astrophysics Data System (ADS)

    Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.

    2018-02-01

    Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.

  7. Parallel iterative solution for h and p approximations of the shallow water equations

    USGS Publications Warehouse

    Barragy, E.J.; Walters, R.A.

    1998-01-01

    A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used. ?? 1998 Elsevier Science Ltd. All rights reserved.

  8. The Modelling of Axially Translating Flexible Beams

    NASA Astrophysics Data System (ADS)

    Theodore, R. J.; Arakeri, J. H.; Ghosal, A.

    1996-04-01

    The axially translating flexible beam with a prismatic joint can be modelled by using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, a non-dimensional form of the Euler Bernoulli beam equation is presented, obtained by using the concept of group velocity, and also the conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions leads to a time-dependent frequency equation for the translating flexible beam. A novel method is presented for solving this time dependent frequency equation by using a differential form of the frequency equation. The assume mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. It is shown by using Lyapunov's first method that the dynamic responses of flexural modal variables become unstable during retraction of the flexible beam, which the dynamic response during extension of the beam is stable. Numerical simulation results are presented for the uniform axial motion induced transverse vibration for a typical flexible beam.

  9. Identification of unmeasured variables in the set of model constraints of the data reconciliation in a power unit

    NASA Astrophysics Data System (ADS)

    Szega, Marcin; Nowak, Grzegorz Tadeusz

    2013-12-01

    In generalized method of data reconciliation as equations of conditions beside substance and energy balances can be used equations which don't have precisely the status of conservation lows. Empirical coefficients in these equations are traded as unknowns' values. To this kind of equations, in application of the generalized method of data reconciliation in supercritical power unit, can be classified: steam flow capacity of a turbine for a group of stages, adiabatic internal efficiency of group of stages, equations for pressure drop in pipelines and equations for heat transfer in regeneration heat exchangers. Mathematical model of a power unit was developed in the code Thermoflex. Using this model the off-design calculation has been made in several points of loads for the power unit. Using these calculations identification of unknown values and empirical coefficients for generalized method of data reconciliation used in power unit has been made. Additional equations of conditions will be used in the generalized method of data reconciliation which will be used in optimization of measurement placement in redundant measurement system in power unit for new control systems

  10. Lie Symmetry Analysis and Explicit Solutions of the Time Fractional Fifth-Order KdV Equation

    PubMed Central

    Wang, Gang wei; Xu, Tian zhou; Feng, Tao

    2014-01-01

    In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional fifth-order KdV equation. A systematic research to derive Lie point symmetries to time fractional fifth-order KdV equation is performed. In the sense of point symmetry, all of the vector fields and the symmetry reductions of the fractional fifth-order KdV equation are obtained. At last, by virtue of the sub-equation method, some exact solutions to the fractional fifth-order KdV equation are provided. PMID:24523885

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

    NASA Astrophysics Data System (ADS)

    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.

  12. Stability analysis of a liquid fuel annular combustion chamber. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Mcdonald, G. H.

    1978-01-01

    High frequency combustion instability problems in a liquid fuel annular combustion chamber are examined. A modified Galerkin method was used to produce a set of modal amplitude equations from the general nonlinear partial differential acoustic wave equation in order to analyze the problem of instability. From these modal amplitude equations, the two variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitive combustion instabilities by evaluating the effects of certain parameters in the given set of equations.

  13. New solitary wave and multiple soliton solutions for fifth order nonlinear evolution equation with time variable coefficients

    NASA Astrophysics Data System (ADS)

    Jaradat, H. M.; Syam, Muhammed; Jaradat, M. M. M.; Mustafa, Zead; Moman, S.

    2018-03-01

    In this paper, we investigate the multiple soliton solutions and multiple singular soliton solutions of a class of the fifth order nonlinear evolution equation with variable coefficients of t using the simplified bilinear method based on a transformation method combined with the Hirota's bilinear sense. In addition, we present analysis for some parameters such as the soliton amplitude and the characteristic line. Several equation in the literature are special cases of the class which we discuss such as Caudrey-Dodd-Gibbon equation and Sawada-Kotera. Comparison with several methods in the literature, such as Helmholtz solution of the inverse variational problem, rational exponential function method, tanh method, homotopy perturbation method, exp-function method, and coth method, are made. From these comparisons, we conclude that the proposed method is efficient and our solutions are correct. It is worth mention that the proposed solution can solve many physical problems.

  14. Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K.

    2016-12-15

    Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

  15. Methods for estimating the optical constants of atmospheric hazes based on complex optical measurements

    NASA Technical Reports Server (NTRS)

    Zuev, V. E.; Kostin, B. S.; Naats, I. E.

    1986-01-01

    The methods of multifrequency laser sounding (MLS) are the most effective remote methods for investigating the atmospheric aerosols, since it is possible to obtain complete information on aerosol microstructure and the effective methods for estimating the aerosol optical constants can be developed. The MLS data interpretation consists in the solution of the set of equations containing those of laser sounding and equations for polydispersed optical characteristics. As a rule, the laser sounding equation is written in the approximation of single scattering and the equations for optical characteristics are written assuming that the atmospheric aerosol is formed by spherical and homogeneous particles. To remove the indeterminacy of equations, the method of optical sounding of atmospheric aerosol, consisting in a joint use of a mutifrequency lidar and a spectral photometer in common geometrical scheme of the optical experiment was suggested. The method is used for investigating aerosols in the cases when absorption by particles is small and indicates the minimum necessary for interpretation of a series of measurements.

  16. Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

    DOE PAGES

    Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

    2016-09-01

    We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

  17. Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

    PubMed

    Li, Q; He, Y L; Wang, Y; Tao, W Q

    2007-11-01

    A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

  18. A moving mesh finite difference method for equilibrium radiation diffusion equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

    2015-10-01

    An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

  19. Development of monitoring system of helium leakage from canister

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Toriu, D.; Ushijima, S.; Takeda, H.

    2013-07-01

    This paper presents a computational method for the helium leakage from a canister. The governing equations for compressible fluids consist of mass conservation equation in Eulerian description, momentum equations and energy equation. The numerical procedures are divided into three phases, advection, diffusion and acoustic phases, and the equations of compressible fluids are discretized with a finite volume method. Thus, the mass conservation law is sufficiently satisfied in the calculation region. In particular, our computational method enables us to predict the change of the temperature distributions around the canister boundaries by calculating the governing equations for the compressible gas flows, whichmore » are leaked out from a slight crack on the canister boundary. In order to confirm the validity of our method, it was applied to the basic problem, 2-dimensional natural convection flows in a rectangular cavity. As a result, it was shown that the naturally convected flows can be reasonably simulated by our method. Furthermore, numerical experiments were conducted for the helium leakage from canister and we derived a close relationship between the inner pressure and the boundary temperature distributions.« less

  20. Operator Approach to the Master Equation for the One-Step Process

    NASA Astrophysics Data System (ADS)

    Hnatič, M.; Eferina, E. G.; Korolkova, A. V.; Kulyabov, D. S.; Sevastyanov, L. A.

    2016-02-01

    Background. Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. The expansion of the equation in a formal Taylor series (the so called Kramers-Moyal's expansion) is used in the procedure of stochastization of one-step processes. Purpose. However, this does not eliminate the need for the study of the master equation. Method. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). Results: This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. Conclusions: We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation.

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

    NASA Astrophysics Data System (ADS)

    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.

  2. Solving Ordinary Differential Equations

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  3. FAST TRACK COMMUNICATION: On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

    NASA Astrophysics Data System (ADS)

    Man, Yiu-Kwong

    2010-10-01

    In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.

  4. Study of analytical method to seek for exact solutions of variant Boussinesq equations.

    PubMed

    Khan, Kamruzzaman; Akbar, M Ali

    2014-01-01

    In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G'/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function solutions of this equation. 35 K99; 35P05; 35P99.

  5. Variation of Parameters in Differential Equations (A Variation in Making Sense of Variation of Parameters)

    ERIC Educational Resources Information Center

    Quinn, Terry; Rai, Sanjay

    2012-01-01

    The method of variation of parameters can be found in most undergraduate textbooks on differential equations. The method leads to solutions of the non-homogeneous equation of the form y = u[subscript 1]y[subscript 1] + u[subscript 2]y[subscript 2], a sum of function products using solutions to the homogeneous equation y[subscript 1] and…

  6. A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

    NASA Astrophysics Data System (ADS)

    Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

    2015-11-01

    This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture the steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier-Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.

  7. A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kawai, Soshi, E-mail: kawai@cfd.mech.tohoku.ac.jp; Terashima, Hiroshi; Negishi, Hideyo

    2015-11-01

    This paper addresses issues in high-fidelity numerical simulations of transcritical turbulent flows at supercritical pressure. The proposed strategy builds on a tabulated look-up table method based on REFPROP database for an accurate estimation of non-linear behaviors of thermodynamic and fluid transport properties at the transcritical conditions. Based on the look-up table method we propose a numerical method that satisfies high-order spatial accuracy, spurious-oscillation-free property, and capability of capturing the abrupt variation in thermodynamic properties across the transcritical contact surface. The method introduces artificial mass diffusivity to the continuity and momentum equations in a physically-consistent manner in order to capture themore » steep transcritical thermodynamic variations robustly while maintaining spurious-oscillation-free property in the velocity field. The pressure evolution equation is derived from the full compressible Navier–Stokes equations and solved instead of solving the total energy equation to achieve the spurious pressure oscillation free property with an arbitrary equation of state including the present look-up table method. Flow problems with and without physical diffusion are employed for the numerical tests to validate the robustness, accuracy, and consistency of the proposed approach.« less

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

    PubMed

    Căruntu, Bogdan; Bota, Constantin

    2014-01-01

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

  9. Finite element methods and Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Cuvelier, C.; Segal, A.; van Steenhoven, A. A.

    This book is devoted to two and three-dimensional FEM analysis of the Navier-Stokes (NS) equations describing one flow of a viscous incompressible fluid. Three different approaches to the NS equations are described: a direct method, a penalty method, and a method that constructs discrete solenoidal vector fields. Subjects of current research which are important from the industrial/technological viewpoint are considered, including capillary-free boundaries, nonisothermal flows, turbulence, and non-Newtonian fluids.

  10. Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation.

    PubMed

    Ferenczy, György G

    2013-04-05

    The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. Copyright © 2013 Wiley Periodicals, Inc.

  11. Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

    NASA Astrophysics Data System (ADS)

    Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

    2018-04-01

    Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

  12. Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

    NASA Astrophysics Data System (ADS)

    Simbanefayi, Innocent; Khalique, Chaudry Masood

    2018-03-01

    In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

  13. A method of solving simple harmonic oscillator Schroedinger equation

    NASA Technical Reports Server (NTRS)

    Maury, Juan Carlos F.

    1995-01-01

    A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.

  14. Transport Equations Resolution By N-BEE Anti-Dissipative Scheme In 2D Model Of Low Pressure Glow Discharge

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kraloua, B.; Hennad, A.

    The aim of this paper is to determine electric and physical properties by 2D modelling of glow discharge low pressure in continuous regime maintained by term constant source. This electric discharge is confined in reactor plan-parallel geometry. This reactor is filled by Argon monatomic gas. Our continuum model the order two is composed the first three moments the Boltzmann's equations coupled with Poisson's equation by self consistent method. These transport equations are discretized by the finite volumes method. The equations system is resolved by a new technique, it is about the N-BEE explicit scheme using the time splitting method.

  15. Navier-Stokes Dynamics by a Discrete Boltzmann Model

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robet

    2010-01-01

    This work investigates the possibility of particle-based algorithms for the Navier-Stokes equations and higher order continuum approximations of the Boltzmann equation; such algorithms would generalize the well-known Pullin scheme for the Euler equations. One such method is proposed in the context of a discrete velocity model of the Boltzmann equation. Preliminary results on shock structure are consistent with the expectation that the shock should be much broader than the near discontinuity predicted by the Pullin scheme, yet narrower than the prediction of the Boltzmann equation. We discuss the extension of this essentially deterministic method to a stochastic particle method that, like DSMC, samples the distribution function rather than resolving it completely.

  16. Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

    NASA Astrophysics Data System (ADS)

    Tsalamengas, John L.

    2018-07-01

    We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

  17. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    NASA Astrophysics Data System (ADS)

    Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

    2017-11-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

  18. A robust, finite element model for hydrostatic surface water flows

    USGS Publications Warehouse

    Walters, R.A.; Casulli, V.

    1998-01-01

    A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

  19. A diagonal algorithm for the method of pseudocompressibility. [for steady-state solution to incompressible Navier-Stokes equation

    NASA Technical Reports Server (NTRS)

    Rogers, S. E.; Kwak, D.; Chang, J. L. C.

    1986-01-01

    The method of pseudocompressibility has been shown to be an efficient method for obtaining a steady-state solution to the incompressible Navier-Stokes equations. Recent improvements to this method include the use of a diagonal scheme for the inversion of the equations at each iteration. The necessary transformations have been derived for the pseudocompressibility equations in generalized coordinates. The diagonal algorithm reduces the computing time necessary to obtain a steady-state solution by a factor of nearly three. Implicit viscous terms are maintained in the equations, and it has become possible to use fourth-order implicit dissipation. The steady-state solution is unchanged by the approximations resulting from the diagonalization of the equations. Computed results for flow over a two-dimensional backward-facing step and a three-dimensional cylinder mounted normal to a flat plate are presented for both the old and new algorithms. The accuracy and computing efficiency of these algorithms are compared.

  20. A parameter study of the two-fluid solar wind

    NASA Technical Reports Server (NTRS)

    Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

    1992-01-01

    A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

  1. A general method to determine the stability of compressible flows

    NASA Technical Reports Server (NTRS)

    Guenther, R. A.; Chang, I. D.

    1982-01-01

    Several problems were studied using two completely different approaches. The initial method was to use the standard linearized perturbation theory by finding the value of the individual small disturbance quantities based on the equations of motion. These were serially eliminated from the equations of motion to derive a single equation that governs the stability of fluid dynamic system. These equations could not be reduced unless the steady state variable depends only on one coordinate. The stability equation based on one dependent variable was found and was examined to determine the stability of a compressible swirling jet. The second method applied a Lagrangian approach to the problem. Since the equations developed were based on different assumptions, the condition of stability was compared only for the Rayleigh problem of a swirling flow, both examples reduce to the Rayleigh criterion. This technique allows including the viscous shear terms which is not possible in the first method. The same problem was then examined to see what effect shear has on stability.

  2. Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile

    NASA Astrophysics Data System (ADS)

    Pozderac, Preston; Leary, Cody

    We investigated the solutions to the Helmholtz equation in the case of a spherically symmetric refractive index using three different methods. The first method involves solving the Helmholtz equation for a step index profile and applying further constraints contained in Maxwell's equations. Utilizing these equations, we can simultaneously solve for the electric and magnetic fields as well as the allowed energies of photons propagating in this system. The second method applies a perturbative correction to these energies, which surfaces when deriving a Helmholtz type equation in a medium with an inhomogeneous refractive index. Applying first order perturbation theory, we examine how the correction term affects the energy of the photon. In the third method, we investigate the effects of the above perturbation upon solutions to the scalar Helmholtz equation, which are separable with respect to its polarization and spatial degrees of freedom. This work provides insights into the vector field structure of a photon guided by a glass microsphere.

  3. On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.

    PubMed

    Ross, David S; Thurston, George M; Lutzer, Carl V

    2008-08-14

    In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

  4. Tensor-GMRES method for large sparse systems of nonlinear equations

    NASA Technical Reports Server (NTRS)

    Feng, Dan; Pulliam, Thomas H.

    1994-01-01

    This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

  5. Solution of the Burnett equations for hypersonic flows near the continuum limit

    NASA Technical Reports Server (NTRS)

    Imlay, Scott T.

    1992-01-01

    The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

  6. Simulations of Fluvial Landscapes

    NASA Astrophysics Data System (ADS)

    Cattan, D.; Birnir, B.

    2013-12-01

    The Smith-Bretherton-Birnir (SBB) model for fluvial landsurfaces consists of a pair of partial differential equations, one governing water flow and one governing the sediment flow. Numerical solutions of these equations have been shown to provide realistic models in the evolution of fluvial landscapes. Further analysis of these equations shows that they possess scaling laws (Hack's Law) that are known to exist in nature. However, the simulations are highly dependent on the numerical methods used; with implicit methods exhibiting the correct scaling laws, but the explicit methods fail to do so. These equations, and the resulting models, help to bridge the gap between the deterministic and the stochastic theories of landscape evolution. Slight modifications of the SBB equations make the results of the model more realistic. By modifying the sediment flow equation, the model obtains more pronounced meandering rivers. Typical landsurface with rivers.

  7. Study of travelling wave solutions for some special-type nonlinear evolution equations

    NASA Astrophysics Data System (ADS)

    Song, Junquan; Hu, Lan; Shen, Shoufeng; Ma, Wen-Xiu

    2018-07-01

    The tanh-function expansion method has been improved and used to construct travelling wave solutions of the form U={\\sum }j=0n{a}j{\\tanh }jξ for some special-type nonlinear evolution equations, which have a variety of physical applications. The positive integer n can be determined by balancing the highest order linear term with the nonlinear term in the evolution equations. We improve the tanh-function expansion method with n = 0 by introducing a new transform U=-W\\prime (ξ )/{W}2. A nonlinear wave equation with source terms, and mKdV-type equations, are considered in order to show the effectiveness of the improved scheme. We also propose the tanh-function expansion method of implicit function form, and apply it to a Harry Dym-type equation as an example.

  8. Krylov subspace methods - Theory, algorithms, and applications

    NASA Technical Reports Server (NTRS)

    Sad, Youcef

    1990-01-01

    Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

  9. A diffuse-interface method for two-phase flows with soluble surfactants

    PubMed Central

    Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

    2010-01-01

    A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

  10. A particle-particle hybrid method for kinetic and continuum equations

    NASA Astrophysics Data System (ADS)

    Tiwari, Sudarshan; Klar, Axel; Hardt, Steffen

    2009-10-01

    We present a coupling procedure for two different types of particle methods for the Boltzmann and the Navier-Stokes equations. A variant of the DSMC method is applied to simulate the Boltzmann equation, whereas a meshfree Lagrangian particle method, similar to the SPH method, is used for simulations of the Navier-Stokes equations. An automatic domain decomposition approach is used with the help of a continuum breakdown criterion. We apply adaptive spatial and time meshes. The classical Sod's 1D shock tube problem is solved for a large range of Knudsen numbers. Results from Boltzmann, Navier-Stokes and hybrid solvers are compared. The CPU time for the hybrid solver is 3-4 times faster than for the Boltzmann solver.

  11. Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

    PubMed

    Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

    2014-01-01

    We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

  12. Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

    NASA Astrophysics Data System (ADS)

    Doha, E. H.; Abd-Elhameed, W. M.

    2005-09-01

    We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

  13. A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

    ERIC Educational Resources Information Center

    Chen, Haiwen

    2012-01-01

    In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

  14. Discussion summary: Fictitious domain methods

    NASA Technical Reports Server (NTRS)

    Glowinski, Rowland; Rodrigue, Garry

    1991-01-01

    Fictitious Domain methods are constructed in the following manner: Suppose a partial differential equation is to be solved on an open bounded set, Omega, in 2-D or 3-D. Let R be a rectangle domain containing the closure of Omega. The partial differential equation is first solved on R. Using the solution on R, the solution of the equation on Omega is then recovered by some procedure. The advantage of the fictitious domain method is that in many cases the solution of a partial differential equation on a rectangular region is easier to compute than on a nonrectangular region. Fictitious domain methods for solving elliptic PDEs on general regions are also very efficient when used on a parallel computer. The reason is that one can use the many domain decomposition methods that are available for solving the PDE on the fictitious rectangular region. The discussion on fictitious domain methods began with a talk by R. Glowinski in which he gave some examples of a variational approach to ficititious domain methods for solving the Helmholtz and Navier-Stokes equations.

  15. A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chen, Luoping; Zheng, Bin; Lin, Guang

    In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

  16. Validation of Field Methods to Assess Body Fat Percentage in Elite Youth Soccer Players.

    PubMed

    Munguia-Izquierdo, Diego; Suarez-Arrones, Luis; Di Salvo, Valter; Paredes-Hernandez, Victor; Alcazar, Julian; Ara, Ignacio; Kreider, Richard; Mendez-Villanueva, Alberto

    2018-05-01

    This study determined the most effective field method for quantifying body fat percentage in male elite youth soccer players and developed prediction equations based on anthropometric variables. Forty-four male elite-standard youth soccer players aged 16.3-18.0 years underwent body fat percentage assessments, including bioelectrical impedance analysis and the calculation of various skinfold-based prediction equations. Dual X-ray absorptiometry provided a criterion measure of body fat percentage. Correlation coefficients, bias, limits of agreement, and differences were used as validity measures, and regression analyses were used to develop soccer-specific prediction equations. The equations from Sarria et al. (1998) and Durnin & Rahaman (1967) reached very large correlations and the lowest biases, and they reached neither the practically worthwhile difference nor the substantial difference between methods. The new youth soccer-specific skinfold equation included a combination of triceps and supraspinale skinfolds. None of the practical methods compared in this study are adequate for estimating body fat percentage in male elite youth soccer players, except for the equations from Sarria et al. (1998) and Durnin & Rahaman (1967). The new youth soccer-specific equation calculated in this investigation is the only field method specifically developed and validated in elite male players, and it shows potentially good predictive power. © Georg Thieme Verlag KG Stuttgart · New York.

  17. Receptor binding kinetics equations: Derivation using the Laplace transform method.

    PubMed

    Hoare, Sam R J

    Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time-dependent pharmacological activities. Copyright © 2017 Elsevier Inc. All rights reserved.

  18. Maine StreamStats: a water-resources web application

    USGS Publications Warehouse

    Lombard, Pamela J.

    2015-01-01

    Reports referenced in this fact sheet present the regression equations used to estimate the flow statistics, describe the errors associated with the estimates, and describe the methods used to develop the equations and to measure the basin characteristics used in the equations. Limitations of the methods are also described in the reports; for example, all of the equations are appropriate only for ungaged, unregulated, rural streams in Maine.

  19. A method for the automated construction of the joint system of equations to solve the problem of the flow distribution in hydraulic networks

    NASA Astrophysics Data System (ADS)

    Novikov, A. E.

    1993-10-01

    There are several methods of solving the problem of the flow distribution in hydraulic networks. But all these methods have no mathematical tools for forming joint systems of equations to solve this problem. This paper suggests a method of constructing joint systems of equations to calculate hydraulic circuits of the arbitrary form. The graph concept, according to Kirchhoff, has been introduced.

  20. Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

    NASA Astrophysics Data System (ADS)

    Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

  1. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Liemert, André, E-mail: andre.liemert@ilm.uni-ulm.de; Kienle, Alwin

    Purpose: Explicit solutions of the monoenergetic radiative transport equation in the P{sub 3} approximation have been derived which can be evaluated with nearly the same computational effort as needed for solving the standard diffusion equation (DE). In detail, the authors considered the important case of a semi-infinite medium which is illuminated by a collimated beam of light. Methods: A combination of the classic spherical harmonics method and the recently developed method of rotated reference frames is used for solving the P{sub 3} equations in closed form. Results: The derived solutions are illustrated and compared to exact solutions of the radiativemore » transport equation obtained via the Monte Carlo (MC) method as well as with other approximated analytical solutions. It is shown that for the considered cases which are relevant for biomedical optics applications, the P{sub 3} approximation is close to the exact solution of the radiative transport equation. Conclusions: The authors derived exact analytical solutions of the P{sub 3} equations under consideration of boundary conditions for defining a semi-infinite medium. The good agreement to Monte Carlo simulations in the investigated domains, for example, in the steady-state and time domains, as well as the short evaluation time needed suggests that the derived equations can replace the often applied solutions of the diffusion equation for the homogeneous semi-infinite medium.« less

  2. A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling

    NASA Astrophysics Data System (ADS)

    Pain, C. C.; Saunders, J. H.; Worthington, M. H.; Singer, J. M.; Stuart-Bruges, W.; Mason, G.; Goddard, A.

    2005-02-01

    In this paper, a numerical method for solving the Biot poroelastic equations is developed. These equations comprise acoustic (typically water) and elastic (porous medium frame) equations, which are coupled mainly through fluid/solid drag terms. This wave solution is coupled to a simplified form of Maxwell's equations, which is solved for the streaming potential resulting from electrokinesis. The ultimate aim is to use the generated electrical signals to provide porosity, permeability and other information about the formation surrounding a borehole. The electrical signals are generated through electrokinesis by seismic waves causing movement of the fluid through pores or fractures of a porous medium. The focus of this paper is the numerical solution of the Biot equations in displacement form, which is achieved using a mixed finite-element formulation with a different finite-element representation for displacements and stresses. The mixed formulation is used in order to reduce spurious displacement modes and fluid shear waves in the numerical solutions. These equations are solved in the time domain using an implicit unconditionally stable time-stepping method using iterative solution methods amenable to solving large systems of equations. The resulting model is embodied in the MODELLING OF ACOUSTICS, POROELASTICS AND ELECTROKINETICS (MAPEK) computer model for electroseismic analysis.

  3. Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

    NASA Astrophysics Data System (ADS)

    Resita Arum, Sari; A, Suparmi; C, Cari

    2016-01-01

    The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation, then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function. Project supported by the Higher Education Project (Grant No. 698/UN27.11/PN/2015).

  4. A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

    PubMed Central

    Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

    2012-01-01

    An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

  5. Solution of the Orr-Sommerfeld equation for the Blausius boundary-layer documentation of program ORRBL and a test case

    NASA Technical Reports Server (NTRS)

    Biringen, S.; Danabasoglu, G.

    1988-01-01

    A Chebyshev matrix collocation method is outlined for the solution of the Orr-Sommerfeld equation for the Blausius boundary layer. User information is provided for FORTRAN program ORRBL which solves the equation by the QR method.

  6. Reverse and direct methods for solving the characteristic equation

    NASA Astrophysics Data System (ADS)

    Lozhkin, Alexander; Bozek, Pavol; Lyalin, Vadim; Tarasov, Vladimir; Tothova, Maria; Sultanov, Ravil

    2016-06-01

    Fundamentals of information-linguistic interpretation of the geometry presented shortly. The method of solving the characteristic equation based on Euler's formula is described. The separation of the characteristic equation for several disassembled for Jordan curves. Applications of the theory for problems of mechatronics outlined briefly.

  7. Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods

    ERIC Educational Resources Information Center

    Zhang, Ying

    2011-01-01

    Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…

  8. Numerical solutions for Helmholtz equations using Bernoulli polynomials

    NASA Astrophysics Data System (ADS)

    Bicer, Kubra Erdem; Yalcinbas, Salih

    2017-07-01

    This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

  9. Agreement between different methods and predictive equations for resting energy expenditure in overweight and obese Brazilian men.

    PubMed

    de Oliveira, Fernanda Cristina Esteves; Alves, Raquel Duarte Moreira; Zuconi, Carolina Pereira; Ribeiro, Andréia Queiroz; Bressan, Josefina

    2012-09-01

    Predictive equations and methods tend to overestimate or underestimate resting energy expenditure (REE) compared with indirect calorimetry (IC). This cross-sectional study aimed to evaluate the agreement between methods and equations for REE estimation of overweight and obese Brazilian men. Data from 48 healthy volunteers, ages 20 to 43 years and with body mass index ranging from 26.4 to 35.2, were collected between October 2008 and October 2009. REE was measured by IC, using Deltatrac (IC1) and KORR-MetaCheck (IC2) devices. It was estimated by bioelectrical impedance analysis (BIA) using tetrapolar (BIA1) and bipolar (BIA2) devices, and by the equations of Mifflin, World Health Organization/Food and Agriculture Organization/United Nations University, Fleisch, Horie-Waitzberg and Gonzalez, and Ireton-Jones. The association and agreement among the methods and equations were assessed by the interclass correlation coefficient, Bland-Altman analysis, and by the percentage of the difference between values obtained from the standard method and alternative methods and equations. Most methods showed high agreement with IC1. The highest agreements were found for Mifflin (-2.14%), Fleisch (-3.05%), Horie-Waitzberg and Gonzalez (4.41%), and BIA2 (5.25%). Similar results were shown by the Bland-Altman analyses. BIA2, followed by BIA1, Ireton-Jones, Mifflin, and Fleisch, showed the highest association with IC1. Thus, the Mifflin, Fleisch, Horie-Waitzberg and Gonzalez equations, and BIA2, were the most accurate methods for REE estimation in this study. However, because those equations have shown considerable variability, they should be used cautiously. In addition, the IC2 was not found to be an accurate method for REE estimation in overweight and obese men included in this study. Copyright © 2012 Academy of Nutrition and Dietetics. Published by Elsevier Inc. All rights reserved.

  10. Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

    NASA Technical Reports Server (NTRS)

    Mickens, R. E.

    1985-01-01

    The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

  11. Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics

    DTIC Science & Technology

    2015-09-14

    discontinuous Galerkin method for the numerical solution of the Helmholtz equation , J. Comp. Phys., 290, 318–335, 2015. [14] N.C. NGUYEN, J. PERAIRE...approximations of the Helmholtz equation for a very wide range of wave frequencies. Our approach combines the hybridizable discontinuous Galerkin methodology...local approximation spaces of the hybridizable discontinuous Galerkin methods with precomputed phases which are solutions of the eikonal equation in

  12. Estimated tetrachloroethylene (C2Cl4) emissions for 1992 2014 in China and a high resolution gridded emission in 2010

    NASA Astrophysics Data System (ADS)

    Bie, P.; Li, Z.; Hu, J.

    2016-12-01

    Estimated tetrachloroethylene (C2Cl4) emissions for 1992 2014 in China and a high resolution gridded emission in 2010 Pengju Bie1, Zhifang Li1, Jianxin Hu1,*1Collaborative Innovation Center for Regional Environmental Quality, College of Environmental Sciences and Engineering, Peking University, Beijing 100871, China *Corresponding author E-mail: jianxin@pku.edu.cnTel: 86-10-62756593 Fax: 86-10-62760755 Evaluating the contribution from tetrachloroethylene (C2Cl4, PCE) to stratospheric halogen loading requires the knowledge of the spatial and temporal variability of emissions, and thus the tropospheric degradation and removal. And the short atmospheric lifetime (90 days) leads to a large regional variability. This study estimated the emissions of China from 1992 to 2014, based on emission functions and aggregated information given reasonable uncertainties. Results show that the emissions increased from 5.3(3.8 7.0) Gg to 176.9(131.2 232.1) Gg with a moderate growth rate of 17.3%/yr during 1992 2014. More than 97.3% of emissions stemmed from solvents sector. Considering the GDP data availability and the comparable estimate to that of top-down method in 2010, we developed a gridded emission inventory on a 0.5°×0.5° latitude-longitude grid of this year. Due to the more advanced social-economic conditions and more intensive industrial establishment, greater PCE emissions were observed to originate from East China, especially for Jiangsu and Zhejiang provinces, and Beijing-Tianjin-Hebei region and Pearl River Delta (PRD) region.

  13. Studying relaxation phenomena via effective master equations

    NASA Astrophysics Data System (ADS)

    Chan, David; Wan, Jones T. K.; Chu, L. L.; Yu, K. W.

    2000-04-01

    The real-time dynamics of various relaxation phenomena can be conveniently formulated by a master equation with the enumeration of transition rates between given classes of conformations. To study the relaxation time towards equilibrium, it suffices to solve for the second largest eigenvalue of the resulting eigenvalue equation. Generally speaking, there is no analytic solution for the dynamic equation. Mean-field approaches generally yield misleading results while the presumably exact Monte-Carlo methods require prohibitive time steps in most real systems. In this work, we propose an exact decimation procedure for reducing the number of conformations significantly, while there is no loss of information, i.e., the reduced (or effective) equation is an exact transformed version of the original one. However, we have to pay the price: the initial Markovianity of the evolution equation is lost and the reduced equation contains memory terms in the transition rates. Since the transformed equation has significantly reduced number of degrees of freedom, the systems can readily be diagonalized by iterative means, to obtain the exact second largest eigenvalue and hence the relaxation time. The decimation method has been applied to various relaxation equations with generally desirable results. The advantages and limitations of the method will be discussed.

  14. Legendre-tau approximations for functional differential equations

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1986-01-01

    The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

  15. Legendre-Tau approximations for functional differential equations

    NASA Technical Reports Server (NTRS)

    Ito, K.; Teglas, R.

    1983-01-01

    The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

  16. Protein electrostatics: a review of the equations and methods used to model electrostatic equations in biomolecules--applications in biotechnology.

    PubMed

    Neves-Petersen, Maria Teresa; Petersen, Steffen B

    2003-01-01

    The molecular understanding of the initial interaction between a protein and, e.g., its substrate, a surface or an inhibitor is essentially an understanding of the role of electrostatics in intermolecular interactions. When studying biomolecules it is becoming increasingly evident that electrostatic interactions play a role in folding, conformational stability, enzyme activity and binding energies as well as in protein-protein interactions. In this chapter we present the key basic equations of electrostatics necessary to derive the equations used to model electrostatic interactions in biomolecules. We will also address how to solve such equations. This chapter is divided into two major sections. In the first part we will review the basic Maxwell equations of electrostatics equations called the Laws of Electrostatics that combined will result in the Poisson equation. This equation is the starting point of the Poisson-Boltzmann (PB) equation used to model electrostatic interactions in biomolecules. Concepts as electric field lines, equipotential surfaces, electrostatic energy and when can electrostatics be applied to study interactions between charges will be addressed. In the second part we will arrive at the electrostatic equations for dielectric media such as a protein. We will address the theory of dielectrics and arrive at the Poisson equation for dielectric media and at the PB equation, the main equation used to model electrostatic interactions in biomolecules (e.g., proteins, DNA). It will be shown how to compute forces and potentials in a dielectric medium. In order to solve the PB equation we will present the continuum electrostatic models, namely the Tanford-Kirkwood and the modified Tandord-Kirkwood methods. Priority will be given to finding the protonation state of proteins prior to solving the PB equation. We also present some methods that can be used to map and study the electrostatic potential distribution on the molecular surface of proteins. The combination of graphical visualisation of the electrostatic fields combined with knowledge about the location of key residues on the protein surface allows us to envision atomic models for enzyme function. Finally, we exemplify the use of some of these methods on the enzymes of the lipase family.

  17. New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

    NASA Astrophysics Data System (ADS)

    Seadawy, Aly R.; Manafian, Jalil

    2018-03-01

    This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

  18. On the validity of the modified equation approach to the stability analysis of finite-difference methods

    NASA Technical Reports Server (NTRS)

    Chang, Sin-Chung

    1987-01-01

    The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

  19. Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

    NASA Astrophysics Data System (ADS)

    Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

    2018-01-01

    In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

  20. Overview of Krylov subspace methods with applications to control problems

    NASA Technical Reports Server (NTRS)

    Saad, Youcef

    1989-01-01

    An overview of projection methods based on Krylov subspaces are given with emphasis on their application to solving matrix equations that arise in control problems. The main idea of Krylov subspace methods is to generate a basis of the Krylov subspace Span and seek an approximate solution the the original problem from this subspace. Thus, the original matrix problem of size N is approximated by one of dimension m typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now just becoming popular for solving nonlinear equations. It is shown how they can be used to solve partial pole placement problems, Sylvester's equation, and Lyapunov's equation.

  1. Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method

    ERIC Educational Resources Information Center

    Cui, Zhongmin; Kolen, Michael J.

    2009-01-01

    This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

  2. Equating in Small-Scale Language Testing Programs

    ERIC Educational Resources Information Center

    LaFlair, Geoffrey T.; Isbell, Daniel; May, L. D. Nicolas; Gutierrez Arvizu, Maria Nelly; Jamieson, Joan

    2017-01-01

    Language programs need multiple test forms for secure administrations and effective placement decisions, but can they have confidence that scores on alternate test forms have the same meaning? In large-scale testing programs, various equating methods are available to ensure the comparability of forms. The choice of equating method is informed by…

  3. Solving ay'' + by' + cy = 0 with a Simple Product Rule Approach

    ERIC Educational Resources Information Center

    Tolle, John

    2011-01-01

    When elementary ordinary differential equations (ODEs) of first and second order are included in the calculus curriculum, second-order linear constant coefficient ODEs are typically solved by a method more appropriate to differential equations courses. This method involves the characteristic equation and its roots, complex-valued solutions, and…

  4. Improving the Bandwidth Selection in Kernel Equating

    ERIC Educational Resources Information Center

    Andersson, Björn; von Davier, Alina A.

    2014-01-01

    We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…

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

    NASA Technical Reports Server (NTRS)

    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.

  6. A new stream function formulation for the Euler equations

    NASA Technical Reports Server (NTRS)

    Atkins, H. L.; Hassan, H. A.

    1983-01-01

    A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

  7. Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field

    NASA Astrophysics Data System (ADS)

    Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

    2017-10-01

    In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

  8. Fokker-Planck equation for the non-Markovian Brownian motion in the presence of a magnetic field.

    PubMed

    Das, Joydip; Mondal, Shrabani; Bag, Bidhan Chandra

    2017-10-28

    In the present study, we have proposed the Fokker-Planck equation in a simple way for a Langevin equation of motion having ordinary derivative (OD), the Gaussian random force and a generalized frictional memory kernel. The equation may be associated with or without conservative force field from harmonic potential. We extend this method for a charged Brownian particle in the presence of a magnetic field. Thus, the present method is applicable for a Langevin equation of motion with OD, the Gaussian colored thermal noise and any kind of linear force field that may be conservative or not. It is also simple to apply this method for the colored Gaussian noise that is not related to the damping strength.

  9. Singularity Preserving Numerical Methods for Boundary Integral Equations

    NASA Technical Reports Server (NTRS)

    Kaneko, Hideaki (Principal Investigator)

    1996-01-01

    In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

  10. The F(N) method for the one-angle radiative transfer equation applied to plant canopies

    NASA Technical Reports Server (NTRS)

    Ganapol, B. D.; Myneni, R. B.

    1992-01-01

    The paper presents a semianalytical solution method, called the F(N) method, for the one-angle radiative transfer equation in slab geometry. The F(N) method is based on two integral equations specifying the intensities exiting the boundaries of the vegetation canopy; the solution is obtained through an expansion in a set of basis functions with expansion coefficients to be determined. The advantage of this method is that it avoids spatial truncation error entirely because it requires discretization only in the angular variable.

  11. Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

    NASA Astrophysics Data System (ADS)

    DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.

    2008-06-01

    For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).

  12. Accuracy of least-squares methods for the Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Bochev, Pavel B.; Gunzburger, Max D.

    1993-01-01

    Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

  13. Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

    NASA Astrophysics Data System (ADS)

    Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

    In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

  14. Method of Conjugate Radii for Solving Linear and Nonlinear Systems

    NASA Technical Reports Server (NTRS)

    Nachtsheim, Philip R.

    1999-01-01

    This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

  15. Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

    NASA Astrophysics Data System (ADS)

    Lai, Wencong; Khan, Abdul A.

    2018-04-01

    A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

  16. The numerical solution of ordinary differential equations by the Taylor series method

    NASA Technical Reports Server (NTRS)

    Silver, A. H.; Sullivan, E.

    1973-01-01

    A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

  17. An asymptotic induced numerical method for the convection-diffusion-reaction equation

    NASA Technical Reports Server (NTRS)

    Scroggs, Jeffrey S.; Sorensen, Danny C.

    1988-01-01

    A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

  18. The method of projected characteristics for the evolution of magnetic arches

    NASA Technical Reports Server (NTRS)

    Nakagawa, Y.; Hu, Y. Q.; Wu, S. T.

    1987-01-01

    A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

  19. Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

    NASA Astrophysics Data System (ADS)

    Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

    2018-06-01

    In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

  20. Linear ordinary differential equations with constant coefficients. Revisiting the impulsive response method using factorization

    NASA Astrophysics Data System (ADS)

    Camporesi, Roberto

    2011-06-01

    We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations based on the factorization of the differential operator. The approach is elementary, we only assume a basic knowledge of calculus and linear algebra. In particular, we avoid the use of distribution theory, as well as of the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and the variation of constants method. The approach presented here can be used in a first course on differential equations for science and engineering majors.

  1. A new multigroup method for cross-sections that vary rapidly in energy

    DOE PAGES

    Haut, Terry Scot; Ahrens, Cory D.; Jonko, Alexandra; ...

    2016-11-04

    Here, we present a numerical method for solving the time-independent thermal radiative transfer (TRT) equation or the neutron transport (NT) equation when the opacity (cross-section) varies rapidly in frequency (energy) on the microscale ε; ε corresponds to the characteristic spacing between absorption lines or resonances, and is much smaller than the macroscopic frequency (energy) variation of interest. The approach is based on a rigorous homogenization of the TRT/NT equation in the frequency (energy) variable. Discretization of the homogenized TRT/NT equation results in a multigroup-type system, and can therefore be solved by standard methods.

  2. Topics in spectral methods

    NASA Technical Reports Server (NTRS)

    Gottlieb, D.; Turkel, E.

    1985-01-01

    After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

  3. Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

    NASA Technical Reports Server (NTRS)

    Sidi, A.; Israeli, M.

    1986-01-01

    High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

  4. The use of spectral methods in bidomain studies.

    PubMed

    Trayanova, N; Pilkington, T

    1992-01-01

    A Fourier transform method is developed for solving the bidomain coupled differential equations governing the intracellular and extracellular potentials on a finite sheet of cardiac cells undergoing stimulation. The spectral formulation converts the system of differential equations into a "diagonal" system of algebraic equations. Solving the algebraic equations directly and taking the inverse transform of the potentials proved numerically less expensive than solving the coupled differential equations by means of traditional numerical techniques, such as finite differences; the comparison between the computer execution times showed that the Fourier transform method was about 40 times faster than the finite difference method. By application of the Fourier transform method, transmembrane potential distributions in the two-dimensional myocardial slice were calculated. For a tissue characterized by a ratio of the intra- to extracellular conductivities that is different in all principal directions, the transmembrane potential distribution exhibits a rather complicated geometrical pattern. The influence of the different anisotropy ratios, the finite tissue size, and the stimuli configuration on the pattern of membrane polarization is investigated.

  5. Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

    PubMed

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

  6. Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

    PubMed Central

    Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

    2015-01-01

    In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

  7. A homotopy analysis method for the nonlinear partial differential equations arising in engineering

    NASA Astrophysics Data System (ADS)

    Hariharan, G.

    2017-05-01

    In this article, we have established the homotopy analysis method (HAM) for solving a few partial differential equations arising in engineering. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of nonlinear terms appearing in the governing differential equations. The convergence analysis of the proposed method is also discussed. Finally, we have given some illustrative examples to demonstrate the validity and applicability of the proposed method.

  8. A new Newton-like method for solving nonlinear equations.

    PubMed

    Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

    2016-01-01

    This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

  9. The convergence study of the homotopy analysis method for solving nonlinear Volterra-Fredholm integrodifferential equations.

    PubMed

    Ghanbari, Behzad

    2014-01-01

    We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

  10. GHM method for obtaining rationalsolutions of nonlinear differential equations.

    PubMed

    Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

    2015-01-01

    In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

  11. Evolution of nonlinear waves in a blood-filled artery with an aneurysm

    NASA Astrophysics Data System (ADS)

    Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

    2017-10-01

    We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

  12. Symplectic partitioned Runge-Kutta scheme for Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Huang, Zhi-Xiang; Wu, Xian-Liang

    Using the symplectic partitioned Runge-Kutta (PRK) method, we construct a new scheme for approximating the solution to infinite dimensional nonseparable Hamiltonian systems of Maxwell's equations for the first time. The scheme is obtained by discretizing the Maxwell's equations in the time direction based on symplectic PRK method, and then evaluating the equation in the spatial direction with a suitable finite difference approximation. Several numerical examples are presented to verify the efficiency of the scheme.

  13. Heat Transfer Effects on a Fully Premixed Methane Impinging Flame

    DTIC Science & Technology

    2014-10-30

    Houzeaux et al., 2009). The GM- RES solver is also employed to solve for the enthalpy and species mass fractions. The Gauss - Seidel iterative method is...the system is therefore split to solve the mo- mentum and continuity equations independently. This is achieved by applying an iterative strategy...the momentum equation twice and the continuity equation once. The momentum equation is solved using the GMRES or BICGSTAB method (diagonal and Gauss

  14. Baecklund transformation for the Ernst equation of general relativity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Harrison, B.K.

    A Baecklund transformation for the Ernst equation arising in general relativity in connection with several physical problems is derived, using the pseudopotential method of Wahlquist and Estabrook. A prolongation structure is also constructed, using a method of writing the equations in terms of differential forms, and an equation in the spirit of Lax is constructed, somewhat different from that given by Maison. Possible uses of the Baecklund transformation to generate new solutions are mentioned.

  15. Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

    NASA Astrophysics Data System (ADS)

    Seadawy, Aly R.

    2017-09-01

    Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

  16. Incompressible spectral-element method: Derivation of equations

    NASA Technical Reports Server (NTRS)

    Deanna, Russell G.

    1993-01-01

    A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

  17. A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

    NASA Astrophysics Data System (ADS)

    Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

    2016-10-01

    Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

  18. Effective quadrature formula in solving linear integro-differential equations of order two

    NASA Astrophysics Data System (ADS)

    Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

    2017-08-01

    In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

  19. A new treatment of nonlocality in scattering process

    NASA Astrophysics Data System (ADS)

    Upadhyay, N. J.; Bhagwat, A.; Jain, B. K.

    2018-01-01

    Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,{r}{\\prime }-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.

  20. Probabilistic density function method for nonlinear dynamical systems driven by colored noise

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Barajas-Solano, David A.; Tartakovsky, Alexandre M.

    2016-05-01

    We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integro-differential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified Large-Eddy-Diffusivity-type closure. Additionally, we introduce the generalized local linearization (LL) approximation for deriving a computable PDF equation in the form of the second-order partial differential equation (PDE). We demonstrate the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary auto-correlation time.more » We apply the proposed PDF method to the analysis of a set of Kramers equations driven by exponentially auto-correlated Gaussian colored noise to study the dynamics and stability of a power grid.« less

  1. Numerical solution of the electron transport equation

    NASA Astrophysics Data System (ADS)

    Woods, Mark

    The electron transport equation has been solved many times for a variety of reasons. The main difficulty in its numerical solution is that it is a very stiff boundary value problem. The most common numerical methods for solving boundary value problems are symmetric collocation methods and shooting methods. Both of these types of methods can only be applied to the electron transport equation if the boundary conditions are altered with unrealistic assumptions because they require too many points to be practical. Further, they result in oscillating and negative solutions, which are physically meaningless for the problem at hand. For these reasons, all numerical methods for this problem to date are a bit unusual because they were designed to try and avoid the problem of extreme stiffness. This dissertation shows that there is no need to introduce spurious boundary conditions or invent other numerical methods for the electron transport equation. Rather, there already exists methods for very stiff boundary value problems within the numerical analysis literature. We demonstrate one such method in which the fast and slow modes of the boundary value problem are essentially decoupled. This allows for an upwind finite difference method to be applied to each mode as is appropriate. This greatly reduces the number of points needed in the mesh, and we demonstrate how this eliminates the need to define new boundary conditions. This method is verified by showing that under certain restrictive assumptions, the electron transport equation has an exact solution that can be written as an integral. We show that the solution from the upwind method agrees with the quadrature evaluation of the exact solution. This serves to verify that the upwind method is properly solving the electron transport equation. Further, it is demonstrated that the output of the upwind method can be used to compute auroral light emissions.

  2. Comment on ``Alternative approach to the solution of the dispersion relation for a generalized lattice Boltzmann equation''

    NASA Astrophysics Data System (ADS)

    Lallemand, Pierre; Luo, Li-Shi

    2008-12-01

    Recently Reis and Phillips [Phys. Rev. E 77, 026702 (2008)] proposed a perturbative method to solve the dispersion equation derived from the linearized lattice Boltzmann equation. We will demonstrate that the method proposed by Reis and Phillips is a reinvention of an existing method. We would also like to refute a number of claims made by Reis and Phillips.

  3. Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

    DTIC Science & Technology

    1983-12-01

    numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

  4. Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes

    ERIC Educational Resources Information Center

    Gauthier, N.

    2004-01-01

    An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…

  5. Fluctuations of thermodynamic quantities calculated from the fundamental equation of thermodynamics

    NASA Astrophysics Data System (ADS)

    Yan, Zijun; Chen, Jincan

    1992-02-01

    On the basis of the probability distribution of the various values of the fluctuation and the fundamental equation of thermodynamics of any given system, a simple and useful method of calculating the fluctuations is presented. By using the method, the fluctuations of thermodynamic quantities can be directly determined from the fundamental equation of thermodynamics. Finally, some examples are given to illustrate the use of the method.

  6. Numerical solution of boundary-integral equations for molecular electrostatics.

    PubMed

    Bardhan, Jaydeep P

    2009-03-07

    Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

  7. Probabilistic density function method for nonlinear dynamical systems driven by colored noise.

    PubMed

    Barajas-Solano, David A; Tartakovsky, Alexandre M

    2016-05-01

    We present a probability density function (PDF) method for a system of nonlinear stochastic ordinary differential equations driven by colored noise. The method provides an integrodifferential equation for the temporal evolution of the joint PDF of the system's state, which we close by means of a modified large-eddy-diffusivity (LED) closure. In contrast to the classical LED closure, the proposed closure accounts for advective transport of the PDF in the approximate temporal deconvolution of the integrodifferential equation. In addition, we introduce the generalized local linearization approximation for deriving a computable PDF equation in the form of a second-order partial differential equation. We demonstrate that the proposed closure and localization accurately describe the dynamics of the PDF in phase space for systems driven by noise with arbitrary autocorrelation time. We apply the proposed PDF method to analyze a set of Kramers equations driven by exponentially autocorrelated Gaussian colored noise to study nonlinear oscillators and the dynamics and stability of a power grid. Numerical experiments show the PDF method is accurate when the noise autocorrelation time is either much shorter or longer than the system's relaxation time, while the accuracy decreases as the ratio of the two timescales approaches unity. Similarly, the PDF method accuracy decreases with increasing standard deviation of the noise.

  8. A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

    2018-01-01

    In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

  9. A Spectral Multi-Domain Penalty Method for Elliptic Problems Arising From a Time-Splitting Algorithm For the Incompressible Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Diamantopoulos, Theodore; Rowe, Kristopher; Diamessis, Peter

    2017-11-01

    The Collocation Penalty Method (CPM) solves a PDE on the interior of a domain, while weakly enforcing boundary conditions at domain edges via penalty terms, and naturally lends itself to high-order and multi-domain discretization. Such spectral multi-domain penalty methods (SMPM) have been used to solve the Navier-Stokes equations. Bounds for penalty coefficients are typically derived using the energy method to guarantee stability for time-dependent problems. The choice of collocation points and penalty parameter can greatly affect the conditioning and accuracy of a solution. Effort has been made in recent years to relate various high-order methods on multiple elements or domains under the umbrella of the Correction Procedure via Reconstruction (CPR). Most applications of CPR have focused on solving the compressible Navier-Stokes equations using explicit time-stepping procedures. A particularly important aspect which is still missing in the context of the SMPM is a study of the Helmholtz equation arising in many popular time-splitting schemes for the incompressible Navier-Stokes equations. Stability and convergence results for the SMPM for the Helmholtz equation will be presented. Emphasis will be placed on the efficiency and accuracy of high-order methods.

  10. The staircase method: integrals for periodic reductions of integrable lattice equations

    NASA Astrophysics Data System (ADS)

    van der Kamp, Peter H.; Quispel, G. R. W.

    2010-11-01

    We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

  11. Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

    NASA Astrophysics Data System (ADS)

    Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

    2018-05-01

    The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

  12. Integrated force method versus displacement method for finite element analysis

    NASA Technical Reports Server (NTRS)

    Patnaik, S. N.; Berke, L.; Gallagher, R. H.

    1991-01-01

    A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

  13. Integrated force method versus displacement method for finite element analysis

    NASA Technical Reports Server (NTRS)

    Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.

    1990-01-01

    A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

  14. Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

    2014-02-15

    Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to variousmore » forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.« less

  15. A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

    1989-01-01

    A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

  16. Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

    NASA Astrophysics Data System (ADS)

    Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

    2018-05-01

    In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

  17. The study of the plasmon modes of square atomic clusters based on the eigen-oscillation equation of charge under the free-electron gas model

    NASA Astrophysics Data System (ADS)

    Xue, Hong-Jie; Wu, Reng-Lai; Hu, Cheng-Xi; Zhang, Ming

    2018-04-01

    In atomic clusters, plasmon modes are generally gained by the resonant responses for external fields. However, these resonant methods still carry some defects: some plasmon modes may not have been found as that may not have been excited by the external fields. Recently, by employing the extended Hubbard model to describe electron systems of atomic clusters, we have presented the eigen-oscillation equation of charge to study plasmon modes. In this work, based on the free-electron gas model, we further explore the eigen-equation method. Under different external electric fields, some of the plasmon mode spectrums with obvious differences are found, which display the defects of the resonant methods. All the plasmon modes obtained by the resonant methods are predicted by the eigen-equation method. This effectively shows that the eigen-equation method is feasible and reliable in the process of finding plasmon. In addition, various kinds of plasmons are displayed by charge distributions, and the evolution features of plasmon with system parameters are gained by the energy absorption spectrum.

  18. Low-Storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Kennedy, Chistopher A.; Carpenter, Mark H.; Lewis, R. Michael

    1999-01-01

    The derivation of storage explicit Runge-Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier-Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, 16 ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third- to fifth-order. Methods have been assessed using the differential equation testing code DETEST, and with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methane-air and hydrogen-air flames. Derived 3(2) and 4(3) pairs are competitive with existing full-storage methods. Although a substantial efficiency penalty accompanies use of two- and three-register, fifth-order methods, the best contemporary full-storage methods can be pearl), matched while still saving two to three registers of memory.

  19. A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

    NASA Astrophysics Data System (ADS)

    Zhao, J. M.; Tan, J. Y.; Liu, L. H.

    2013-01-01

    A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

  20. Investigation of viscous/inviscid interaction in transonic flow over airfoils with suction

    NASA Technical Reports Server (NTRS)

    Vemuru, C. S.; Tiwari, S. N.

    1988-01-01

    The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region, the Euler equations are solved using the method of integral relations. For this, the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solution for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundry-layer equations. The Euler equations are solved for the inviscid flow using the finite volume technique and the coupling is achieved by a surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The results are found to be in good agreement with available experimental data and with the results of other computational methods.

  1. AIEgens-Functionalized Inorganic-Organic Hybrid Materials: Fabrications and Applications.

    PubMed

    Li, Dongdong; Yu, Jihong

    2016-12-01

    Inorganic materials functionalized with organic fluorescent molecules combine advantages of them both, showing potential applications in biomedicine, chemosensors, light-emitting, and so on. However, when more traditional organic dyes are doped into the inorganic materials, the emission of resulting hybrid materials may be quenched, which is not conducive to the efficiency and sensitivity of detection. In contrast to the aggregation-caused quenching (ACQ) system, the aggregation-induced emission luminogens (AIEgens) with high solid quantum efficiency, offer new potential for developing highly efficient inorganic-organic hybrid luminescent materials. So far, many AIEgens have been incorporated into inorganic materials through either physical doping caused by aggregation induced emission (AIE) or chemical bonding (e.g., covalent bonding, ionic bonding, and coordination bonding) caused by bonding induced emission (BIE) strategy. The hybrid materials exhibit excellent photoactive properties due to the intramolecular motion of AIEgens is restricted by inorganic matrix. Recent advances in the fabrication of AIEgens-functionalized inorganic-organic hybrid materials and their applications in biomedicine, chemical sensing, and solid-state light emitting are presented. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  2. Stratigraphic correlations in mid- to late-Proterozoic carbonates of the Democratic Republic of Congo using magnetic susceptibility

    NASA Astrophysics Data System (ADS)

    Delpomdor, Franck R. A.; Devleeschouwer, Xavier; Spassov, Simo; Préat, Alain R.

    2017-04-01

    In this paper, we have tested the application of magnetic susceptibility measurements in Cu-Ag-Zn-Pb-(Fe)-mineralized carbonates of the BIe subgroup (Democratic Republic of Congo) as an efficient tool for regional and global high-resolution stratigraphic correlations in the Neoproterozoic marine carbonates. To achieve this goal, we integrate the low-field magnetic susceptibility (XLF) data with facies analyses, geochemistry and isotope stratigraphy. The microfacies analyses of two cores, Tshinyama#S70 and Kafuku#15, drilled in the early Neoproterozoic carbonates of the Mbuji-Mayi Supergroup reveal a deep carbonate ramp setting associated with a microbial/stromatolitic mid-ramp environment. High-resolution stratigraphic correlations using magnetic susceptibility and C-isotope curves established for both cores, 190 km apart, suggest a sedimentary hiatus at the base of the Tshinyama#S70 succession. C-O and Sr isotopes and Sr/Ca and Fe abundances show that a diagenetic meteoric overprint affected the series of the Tshinyama#S70 core and a thermal effect related to mineralizing fluids affected the Kafuku#15 core carbonates.

  3. Enzymatic Transition States, Transition-State Analogs, Dynamics, Thermodynamics, and Lifetimes

    PubMed Central

    Schramm, Vern L.

    2017-01-01

    Experimental analysis of enzymatic transition-state structures uses kinetic isotope effects (KIEs) to report on bonding and geometry differences between reactants and the transition state. Computational correlation of experimental values with chemical models permits three-dimensional geometric and electrostatic assignment of transition states formed at enzymatic catalytic sites. The combination of experimental and computational access to transition-state information permits (a) the design of transition-state analogs as powerful enzymatic inhibitors, (b) exploration of protein features linked to transition-state structure, (c) analysis of ensemble atomic motions involved in achieving the transition state, (d) transition-state lifetimes, and (e) separation of ground-state (Michaelis complexes) from transition-state effects. Transition-state analogs with picomolar dissociation constants have been achieved for several enzymatic targets. Transition states of closely related isozymes indicate that the protein’s dynamic architecture is linked to transition-state structure. Fast dynamic motions in catalytic sites are linked to transition-state generation. Enzymatic transition states have lifetimes of femtoseconds, the lifetime of bond vibrations. Binding isotope effects (BIEs) reveal relative reactant and transition-state analog binding distortion for comparison with actual transition states. PMID:21675920

  4. Differential reactivities of four homogeneous assays for LDL-cholesterol in serum to intermediate-density lipoproteins and small dense LDL: comparisons with the Friedewald equation.

    PubMed

    Yamashita, Shizuya; Kawase, Ryota; Nakaoka, Hajime; Nakatani, Kazuhiro; Inagaki, Miwako; Yuasa-Kawase, Miyako; Tsubakio-Yamamoto, Kazumi; Sandoval, Jose C; Masuda, Daisaku; Ohama, Tohru; Nakagawa-Toyama, Yumiko; Matsuyama, Akifumi; Nishida, Makoto; Ishigami, Masato

    2009-12-01

    In routine clinical laboratory testing and numerous epidemiological studies, LDL-cholesterol (LDL-C) has been estimated commonly using the Friedewald equation. We investigated the relationship between the Friedewald equation and 4 homogeneous assays for LDL-C. LDL-C was determined by 4 homogeneous assays [liquid selective detergent method: LDL-C (L), selective solubilization method: LDL-C (S), elimination method: LDL-C (E), and enzyme selective protecting method: LDL-C (P)]. Samples with discrepancies between the Friedewald equation and the 4 homogeneous assays for LDL-C were subjected to polyacrylamide gel electrophoresis and the beta-quantification method. The correlations between the Friedewald equation and the 4 homogeneous LDL-C assays were as follows: LDL-C (L) (r=0.962), LDL-C (S) (r=0.986), LDL-C (E) (r=0.946) and LDL-C (P) (r=0.963). Discrepancies were observed in sera from type III hyperlipoproteinemia patients and in sera containing large amounts of midband and small dense LDL on polyacrylamide gel electrophoresis. LDL-C (S) was most strongly correlated with the beta-quantification method even in sera from patients with type III hyperlipoproteinemia. Of the 4 homogeneous assays for LDL-C, LDL-C (S) exhibited the closest correlation with the Friedewald equation and the beta-quantification method, thus reflecting the current clinical databases for coronary heart disease.

  5. Iterative discrete ordinates solution of the equation for surface-reflected radiance

    NASA Astrophysics Data System (ADS)

    Radkevich, Alexander

    2017-11-01

    This paper presents a new method of numerical solution of the integral equation for the radiance reflected from an anisotropic surface. The equation relates the radiance at the surface level with BRDF and solutions of the standard radiative transfer problems for a slab with no reflection on its surfaces. It is also shown that the kernel of the equation satisfies the condition of the existence of a unique solution and the convergence of the successive approximations to that solution. The developed method features two basic steps: discretization on a 2D quadrature, and solving the resulting system of algebraic equations with successive over-relaxation method based on the Gauss-Seidel iterative process. Presented numerical examples show good coincidence between the surface-reflected radiance obtained with DISORT and the proposed method. Analysis of contributions of the direct and diffuse (but not yet reflected) parts of the downward radiance to the total solution is performed. Together, they represent a very good initial guess for the iterative process. This fact ensures fast convergence. The numerical evidence is given that the fastest convergence occurs with the relaxation parameter of 1 (no relaxation). An integral equation for BRDF is derived as inversion of the original equation. The potential of this new equation for BRDF retrievals is analyzed. The approach is found not viable as the BRDF equation appears to be an ill-posed problem, and it requires knowledge the surface-reflected radiance on the entire domain of both Sun and viewing zenith angles.

  6. Application of Stochastic and Deterministic Approaches to Modeling Interstellar Chemistry

    NASA Astrophysics Data System (ADS)

    Pei, Yezhe

    This work is about simulations of interstellar chemistry using the deterministic rate equation (RE) method and the stochastic moment equation (ME) method. Primordial metal-poor interstellar medium (ISM) is of our interest and the socalled “Population-II” stars could have been formed in this environment during the “Epoch of Reionization” in the baby universe. We build a gas phase model using the RE scheme to describe the ionization-powered interstellar chemistry. We demonstrate that OH replaces CO as the most abundant metal-bearing molecule in such interstellar clouds of the early universe. Grain surface reactions play an important role in the studies of astrochemistry. But the lack of an accurate yet effective simulation method still presents a challenge, especially for large, practical gas-grain system. We develop a hybrid scheme of moment equations and rate equations (HMR) for large gas-grain network to model astrochemical reactions in the interstellar clouds. Specifically, we have used a large chemical gas-grain model, with stochastic moment equations to treat the surface chemistry and deterministic rate equations to treat the gas phase chemistry, to simulate astrochemical systems as of the ISM in the Milky Way, the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). We compare the results to those of pure rate equations and modified rate equations and present a discussion about how moment equations improve our theoretical modeling and how the abundances of the assorted species are changed by varied metallicity. We also model the observed composition of H2O, CO and CO2 ices toward Young Stellar Objects in the LMC and show that the HMR method gives a better match to the observation than the pure RE method.

  7. Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

    ERIC Educational Resources Information Center

    Kull, Trent C.

    2011-01-01

    A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

  8. True amplitude wave equation migration arising from true amplitude one-way wave equations

    NASA Astrophysics Data System (ADS)

    Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

    2003-10-01

    One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition to these newly defined wavefields in heterogeneous media leads to the Kirchhoff inversion formula for common-shot data when the one-way wavefields are replaced by their ray theoretic approximations. This extension enhances the original WEM method. The objective of that technique was a reflector map, only. The underlying theory did not address amplitude issues. Computer output obtained using numerically generated data confirms the accuracy of this inversion method. However, there are practical limitations. The observed data must be a solution of the wave equation. Therefore, the data over the entire survey area must be collected from a single common-shot experiment. Multi-experiment data, such as common-offset data, cannot be used with this method as currently formulated. Research on extending the method is ongoing at this time.

  9. A Graphical Approach to Evaluating Equating Using Test Characteristic Curves

    ERIC Educational Resources Information Center

    Wyse, Adam E.; Reckase, Mark D.

    2011-01-01

    An essential concern in the application of any equating procedure is determining whether tests can be considered equated after the tests have been placed onto a common scale. This article clarifies one equating criterion, the first-order equity property of equating, and develops a new method for evaluating equating that is linked to this…

  10. Optimization of one-way wave equations.

    USGS Publications Warehouse

    Lee, M.W.; Suh, S.Y.

    1985-01-01

    The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors

  11. Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

    NASA Astrophysics Data System (ADS)

    Muruganandam, P.; Adhikari, S. K.

    2009-10-01

    Here we develop simple numerical algorithms for both stationary and non-stationary solutions of the time-dependent Gross-Pitaevskii (GP) equation describing the properties of Bose-Einstein condensates at ultra low temperatures. In particular, we consider algorithms involving real- and imaginary-time propagation based on a split-step Crank-Nicolson method. In a one-space-variable form of the GP equation we consider the one-dimensional, two-dimensional circularly-symmetric, and the three-dimensional spherically-symmetric harmonic-oscillator traps. In the two-space-variable form we consider the GP equation in two-dimensional anisotropic and three-dimensional axially-symmetric traps. The fully-anisotropic three-dimensional GP equation is also considered. Numerical results for the chemical potential and root-mean-square size of stationary states are reported using imaginary-time propagation programs for all the cases and compared with previously obtained results. Also presented are numerical results of non-stationary oscillation for different trap symmetries using real-time propagation programs. A set of convenient working codes developed in Fortran 77 are also provided for all these cases (twelve programs in all). In the case of two or three space variables, Fortran 90/95 versions provide some simplification over the Fortran 77 programs, and these programs are also included (six programs in all). Program summaryProgram title: (i) imagetime1d, (ii) imagetime2d, (iii) imagetime3d, (iv) imagetimecir, (v) imagetimesph, (vi) imagetimeaxial, (vii) realtime1d, (viii) realtime2d, (ix) realtime3d, (x) realtimecir, (xi) realtimesph, (xii) realtimeaxial Catalogue identifier: AEDU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 122 907 No. of bytes in distributed program, including test data, etc.: 609 662 Distribution format: tar.gz Programming language: FORTRAN 77 and Fortran 90/95 Computer: PC Operating system: Linux, Unix RAM: 1 GByte (i, iv, v), 2 GByte (ii, vi, vii, x, xi), 4 GByte (iii, viii, xii), 8 GByte (ix) Classification: 2.9, 4.3, 4.12 Nature of problem: These programs are designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-, two- or three-space dimensions with a harmonic, circularly-symmetric, spherically-symmetric, axially-symmetric or anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Solution method: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation, in either imaginary or real time, over small time steps. The method yields the solution of stationary and/or non-stationary problems. Additional comments: This package consists of 12 programs, see "Program title", above. FORTRAN77 versions are provided for each of the 12 and, in addition, Fortran 90/95 versions are included for ii, iii, vi, viii, ix, xii. For the particular purpose of each program please see the below. Running time: Minutes on a medium PC (i, iv, v, vii, x, xi), a few hours on a medium PC (ii, vi, viii, xii), days on a medium PC (iii, ix). Program summary (1)Title of program: imagtime1d.F Title of electronic file: imagtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (2)Title of program: imagtimecir.F Title of electronic file: imagtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (3)Title of program: imagtimesph.F Title of electronic file: imagtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 1 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (4)Title of program: realtime1d.F Title of electronic file: realtime1d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in one-space dimension with a harmonic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (5)Title of program: realtimecir.F Title of electronic file: realtimecir.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with a circularly-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (6)Title of program: realtimesph.F Title of electronic file: realtimesph.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 Typical running time: Minutes on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with a spherically-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (7)Title of programs: imagtimeaxial.F and imagtimeaxial.f90 Title of electronic file: imagtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (8)Title of program: imagtime2d.F and imagtime2d.f90 Title of electronic file: imagtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 2 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (9)Title of program: realtimeaxial.F and realtimeaxial.f90 Title of electronic file: realtimeaxial.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an axially-symmetric trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (10)Title of program: realtime2d.F and realtime2d.f90 Title of electronic file: realtime2d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Hours on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in two-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems. Program summary (11)Title of program: imagtime3d.F and imagtime3d.f90 Title of electronic file: imagtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum RAM memory: 4 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Few days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in imaginary time over small time steps. The method yields the solution of stationary problems. Program summary (12)Title of program: realtime3d.F and realtime3d.f90 Title of electronic file: realtime3d.tar.gz Catalogue identifier: Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Distribution format: tar.gz Computers: PC/Linux, workstation/UNIX Maximum Ram Memory: 8 GByte Programming language used: Fortran 77 and Fortran 90 Typical running time: Days on a medium PC Unusual features: None Nature of physical problem: This program is designed to solve the time-dependent Gross-Pitaevskii nonlinear partial differential equation in three-space dimensions with an anisotropic trap. The Gross-Pitaevskii equation describes the properties of a dilute trapped Bose-Einstein condensate. Method of solution: The time-dependent Gross-Pitaevskii equation is solved by the split-step Crank-Nicolson method by discretizing in space and time. The discretized equation is then solved by propagation in real time over small time steps. The method yields the solution of stationary and non-stationary problems.

  12. A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

    2014-08-01

    We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

  13. [Equating scores using bridging stations on the clinical performance examination].

    PubMed

    Yoo, Dong-Mi; Han, Jae-Jin

    2013-06-01

    This study examined the use of the Tucker linear equating method in producing an individual student's score in 3 groups with bridging stations over 3 consecutive days of the clinical performance examination (CPX) and compared the differences in scoring patterns by bridging number. Data were drawn from 88 examinees from 3 different CPX groups-DAY1, DAY2, and DAY3-each of which comprised of 6 stations. Each group had 3 common stations, and each group had 2 or 3 stations that differed from other groups. DAY1 and DAY3 were equated to DAY2. Equated mean scores and standard deviations were compared with the originals. DAY1 and DAY3 were equated again, and the differences in scores (equated score-raw score) were compared between the 3 sets of equated scores. By equating to DAY2, DAY1 decreased in mean score from 58.188 to 56.549 and in standard deviation from 4.991 to 5.046, and DAY3 fell in mean score from 58.351 to 58.057 and in standard deviation from 5.546 to 5.856, which demonstrates that the scores of examinees in DAY1 and DAY2 were accentuated after use of the equation. The patterns in score differences between the equated sets to DAY1, DAY2, and DAY3 yielded information on the soundness of the equating results from individual and overall comparisons. To generate equated scores between 3 groups on 3 consecutive days of the CPX, we applied the Tucker linear equating method. We also present a method of equating reciprocal days to the anchoring day as much as bridging stations.

  14. Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

    PubMed

    Vlad, Marcel Ovidiu; Ross, John

    2002-12-01

    We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

  15. Item Response Theory Equating Using Bayesian Informative Priors.

    ERIC Educational Resources Information Center

    de la Torre, Jimmy; Patz, Richard J.

    This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from…

  16. Quasi-generalized variables

    NASA Technical Reports Server (NTRS)

    Baumgarten, J.; Ostermeyer, G. P.

    1986-01-01

    The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics.

  17. Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method

    NASA Astrophysics Data System (ADS)

    Choudhury, A. Ghose; Guha, Partha; Khanra, Barun

    2009-10-01

    The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, which has appeared in string inspired modern cosmology.

  18. Estimating and Interpreting Latent Variable Interactions: A Tutorial for Applying the Latent Moderated Structural Equations Method

    ERIC Educational Resources Information Center

    Maslowsky, Julie; Jager, Justin; Hemken, Douglas

    2015-01-01

    Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS)…

  19. The Use of Kruskal-Newton Diagrams for Differential Equations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    T. Fishaleck and R.B. White

    2008-02-19

    The method of Kruskal-Newton diagrams for the solution of differential equations with boundary layers is shown to provide rapid intuitive understanding of layer scaling and can result in the conceptual simplification of some problems. The method is illustrated using equations arising in the theory of pattern formation and in plasma physics.

  20. Method of sections in analytical calculations of pneumatic tires

    NASA Astrophysics Data System (ADS)

    Tarasov, V. N.; Boyarkina, I. V.

    2018-01-01

    Analytical calculations in the pneumatic tire theory are more preferable in comparison with experimental methods. The method of section of a pneumatic tire shell allows to obtain equations of intensities of internal forces in carcass elements and bead rings. Analytical dependencies of intensity of distributed forces have been obtained in tire equator points, on side walls (poles) and pneumatic tire bead rings. Along with planes in the capacity of secant surfaces cylindrical surfaces are used for the first time together with secant planes. The tire capacity equation has been obtained using the method of section, by means of which a contact body is cut off from the tire carcass along the contact perimeter by the surface which is normal to the bearing surface. It has been established that the Laplace equation for the solution of tasks of this class of pneumatic tires contains two unknown values that requires the generation of additional equations. The developed computational schemes of pneumatic tire sections and new equations allow to accelerate the pneumatic tire structure improvement process during engineering.

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