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Power Series (power + series)
Selected AbstractsRitz finite elements for curvilinear particlesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2006Paul R. Heyliger Abstract A general finite element is presented for the representation of fields in curvilinear particles in two and three dimensions. The formulation of this element shares many similarities with usual finite element approximations, but differs in that nodal points are defined in part by contact points with other particles. Power series in the geometric coordinates are used as the starting basis functions, but are recast in terms of the field variables within the particle interior and the points of contact with other elements. There is no discretization error and the elements of the finite element matrices can all be evaluated in closed form. This approach is applicable to shapes in two and three dimensions, including discs, ellipses, spheres, spheroids, and potatoes. Examples are included for two-dimensional applications of steady-state heat transfer and elastostatics. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical method to solve chemical differential-algebraic equationsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2002Ercan Çelik Abstract In this article, the solution of a chemical differential-algebraic equation model of general type F(y, y,, x) = 0 has been done using MAPLE computer algebra systems. The MAPLE program is given in the Appendix. First we calculate the Power series of the given equations system, then we transform it into Padé series form, which gives an arbitrary order for solving chemical differential-algebraic equation numerically. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Field theory on nonanticommutative superspaceFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2008M. Dimitrijevi Abstract We discuss a deformation of the Hopf algebra of supersymmetry (SUSY) transformations based on a special choice of a twist. As usual, algebra itself remains unchanged, but the comultiplication changes. This leads to a deformed Leibniz rule for SUSY transformations. Superfields are multiplied by using a ,-product which is noncommutative, hermitian and finite when expanded in power series of the deformation parameter. One possible deformation of the Wess-Zumino action is proposed and analysed in detail. Differently from most of the literature concerning this subject, we work in Minkowski space-time. [source] Interpretation of the enhancement of field-scale effective matrix diffusion coefficient in a single fracture using a semi-analytical power series solutionHYDROLOGICAL PROCESSES, Issue 6 2009Tai-Sheng Liou Abstract A power series solution for convergent radial transport in a single fracture (PCRTSF) is developed. Transport processes considered in PCRTSF include advection and hydrodynamic dispersion in the fracture, molecular diffusion in the matrix, diffusive mass exchange across the fracture-matrix interface, and mixing effects in the injection and the extraction boreholes. An analytical solution in terms of a power series in Laplace domain is developed first, which is then numerically inverted by de-Hoog et al.'s algorithm. Four dimensionless parameters determine the behaviour of a breakthrough curve (BTC) calculated by PCRTSF, which are, in the order of decreasing sensitivity, the matrix diffusion factor, two mixing factors, and the Peclet number. The first parameter is lumped from matrix porosity, effective matrix diffusion coefficient, fracture aperture, and retardation factors. Its value increases as the matrix diffusion effect becomes significant. A non-zero matrix diffusion factor results in a , 3/2 slope of the tail of a log,log BTC, a common property for tracer diffusion into an infinite matrix. Both mixing factors have equal effects on BTC characteristics. However, the Peclet number has virtually no effect on BTC tail. PCRTSF is applied to re-analyse two published test results that were obtained from convergent radial tracer tests in a discrete, horizontal fracture in Silurian dolomite. PCRTSF is able to fit the field BTCs better than the original channel model does if a large matrix diffusion coefficient is used. Noticeably, the ratio of field-scale to lab-scale matrix diffusion coefficients can be as large as 378. This enhancement of the field-scale matrix diffusion coefficient may be ascribed to the presence of a degraded zone at the fracture-matrix interface because of karstic effects, or to flow channeling as a result of aperture heterogeneity. Copyright © 2009 John Wiley & Sons, Ltd. [source] On the solution of the nonlinear Korteweg,de Vries equation by the homotopy perturbation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009Ahmet Yildirim Abstract In this paper, the homotopy perturbation method is used to implement the nonlinear Korteweg,de Vries equation. The analytical solution of the equation is calculated in the form of a convergent power series with easily computable components. A suitable choice of an initial solution can lead to the needed exact solution by a few iterations. Copyright © 2008 John Wiley & Sons, Ltd. [source] On the inverse of generalized ,-matrices with singular leading termINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006N. A. Dumont Abstract An algorithm is introduced for the inverse of a ,-matrix given as the truncated series A0,i,A1,,2A2+i,3A3+,4A4+···+O(,n+1) with square coefficient matrices and singular leading term A0. Moreover, A1 may be conditionally singular and no restrictions are made for the remaining terms. The result is a ,-matrix given as a unique, truncated series of the same error order. Motivation for this problem is the evaluation of the frequency-dependent stiffness matrix of general boundary or macro-finite elements in the frame of a hybrid variational formulation that is based on a flexibility matrix F expressed as a truncated power series of the circular frequency ,. Copyright © 2005 John Wiley & Sons, Ltd. [source] On the differentiation of the Rodrigues formula and its significance for the vector-like parameterization of Reissner,Simo beam theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2002M. Ritto-Corrêa Abstract In this paper we present a systematic way of differentiating, up to the second directional derivative, (i) the Rodrigues formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner,Simo beam theory, enabling a straightforward derivation and leading to a clearer formulation. In particular, and in contrast with previous formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples. Copyright © 2002 John Wiley & Sons, Ltd. [source] Dynamic stiffness for piecewise non-uniform Timoshenko column by power series,part I: Conservative axial forceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2001A. Y. T. Leung Abstract The dynamic stiffness method uses the solutions of the governing equations as shape functions in a harmonic vibration analysis. One element can predict many modes exactly in the classical sense. The disadvantages lie in the transcendental nature and in the need to solve a non-linear eigenproblem for the natural modes, which can be solved by the Wittrick,William algorithm and the Leung theorem. Another practical problem is to solve the governing equations exactly for the shape functions, non-uniform members in particular. It is proposed to use power series for the purpose. Dynamic stiffness matrices for non-uniform Timoshenko column are taken as examples. The shape functions can be found easily by symbolic programming. Step beam structures can be treated without difficulty. The new contributions of the paper include a general formulation, an extended Leung's theorem and its application to parametric study. Copyright © 2001 John Wiley & Sons, Ltd. [source] Dynamic stiffness for piecewise non-uniform Timoshenko column by power series,part II: Follower forceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2001A. Y. T. Leung Abstract A follower force is an applied force whose direction changes according to the deformed shape during the course of deformation. The dynamic stiffness matrix of a non-uniform Timoshenko column under follower force is formed by the power-series method. The dynamic stiffness matrix is unsymmetrical due to the non-conservative nature of the follower force. The frequency-dependent mass matrix is still symmetrical and positive definite according to the extended Leung theorem. An arc length continuation method is introduced to find the influence of a concentrated follower force, distributed follower force, end mass and stiffness, slenderness, and taper ratio on the natural frequency and stability. It is found that the power-series method can handle a very wide class of dynamic stiffness problem. Copyright © 2001 John Wiley & Sons, Ltd. [source] Semilocalized approach to investigation of chemical reactivityINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003V. GineityteArticle first published online: 21 JUL 200 Abstract Application of the power series for the one-electron density matrix Gineityte, V., J Mol Struct Theochem 1995, 343, 183 to the case of two interacting molecules is shown to yield a semilocalized approach to investigate chemical reactivity, which is characterized by the following distinctive features: (1) Electron density (ED) redistributions embracing orbitals of the reaction centers of both molecules and of their neighboring fragments are studied instead of the total intermolecular interaction energy; (2) the ED redistributions are expressed directly in the basis of fragmental orbitals (FOs) without passing to the basis of delocalized molecular orbitals (MOs) of initial molecules; (3) terms describing the ED redistributions due to an intermolecular contact arise as additive corrections to the purely monomolecular terms and thereby may be analyzed independently; (4) local ED redistributions only between orbitals of the reaction centers of both molecules are described by lower-order ter s of the power series, whereas those embracing both the reaction centers and their neighborhoods are represented by higher-order terms. As opposed to the standard perturbative methods based on invoking the delocalized (canonical) MOs of isolated molecules, the results of the approach suggested are in-line with the well-known intuition-based concepts of the classic chemistry concerning reactivity, namely, with the assumption about different roles of the reaction center and of its neighborhood in a chemical process, with the expectation about extinction of the indirect influence of a certain fragment (substituent) when its distance from the reaction center grows, etc. Such a parallelism yields quantum chemical analogs for the classic concepts and thereby gives an additional insight into their nature. The scope of validity of these concepts also is discussed. Applicability of the approach suggested to specific chemical problems is illustrated by a brief consideration of the SN2 and AdE2 reactions. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 302,316, 2003 [source] New angle-dependent potential energy function for backbone,backbone hydrogen bond in protein,protein interactionsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 5 2010Hwanho Choi Abstract Backbone,backbone hydrogen bonds (BBHBs) are one of the most abundant interactions at the interface of protein,protein complex. Here, we propose an angle-dependent potential energy function for BBHB based on density functional theory (DFT) calculations and the operation of a genetic algorithm to find the optimal parameters in the potential energy function. The angular part of the energy funtion is assumed to be the product of the power series of sine and cosine functions with respect to the two angles associated with BBHB. Two radial functions are taken into account in this study: Morse and Leonard-Jones 12-10 potential functions. Of these two functions under consideration, the former is found to be more accurate than the latter in terms of predicting the binding energies obtained from DFT calculations. The new HB potential function also compares well with the knowledge-based potential derived by applying Boltzmann statistics for a variety of protein,protein complexes in protein data bank. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010 [source] On a generalized Appell system and monogenic power seriesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2010S. Bock Abstract Recently Appell systems of monogenic polynomials in ,3 were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion-valued functions. A new Taylor-type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one-dimensional case. These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space. Copyright © 2009 John Wiley & Sons, Ltd. [source] Eigen-frequencies in thin elastic 3-D domains and Reissner,Mindlin plate modelsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2002Monique Dauge Abstract The eigen-frequencies of elastic three-dimensional thin plates are addressed and compared to the eigen-frequencies of two-dimensional Reissner,Mindlin plate models obtained by dimension reduction. The qualitative mathematical analysis is supported by quantitative numerical data obtained by the p-version finite element method. The mathematical analysis establishes an asymptotic expansion for the eigen-frequencies in power series of the thickness parameter. Such results are new for orthotropic materials and for the Reissner,Mindlin model. The 3-D and R,M asymptotics have a common first term but differ in their second terms. Numerical experiments for clamped plates show that for isotropic materials and relatively thin plates the Reissner,Mindlin eigen-frequencies provide a good approximation to the three-dimensional eigen-frequencies. However, for some anisotropic materials this is no longer the case, and relative errors of the order of 30 per cent are obtained even for relatively thin plates. Moreover, we showed that no shear correction factor is known to be optimal in the sense that it provides the best approximation of the R,M eigen-frequencies to their 3-D counterparts uniformly (for all relevant thicknesses range). Copyright © 2002 John Wiley & Sons, Ltd. [source] On certain character sums over p -adic rings and their L -functionsMATHEMATISCHE NACHRICHTEN, Issue 15 2007Régis BlacheArticle first published online: 11 OCT 200 Abstract In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo pl, a power of a prime. We show that for sufficiently large l, these sums can be expressed in terms of Gauss sums. Moreover, we study the associated L -functions; we show that they are rational, then we determine their degrees and the weights as Weil numbers of their reciprocal roots and poles. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Symbolic analytical solutions for the abundances differential equations of the Helium burning phaseASTRONOMISCHE NACHRICHTEN, Issue 5 2003M.I. Nouh Abstract In this paper, a literal analytical solution is developed for the abundances differential equations of the helium burning phase in hot massive stars. The abundance for each of the basic elements 4He,12C,16O and 20Ne is obtained as a recurrent power series in time, which facilitates its symbolic and numerical evaluations. Numerical comparison between the present solution and the numerical integration of the differential equations for the abundances show good agreement. [source] | |||||||||||||||||||