bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Huber Polygonal Method for the One‐Phase Stefan Problem with the Specification of Energy
Authors: Sartori C. , Spigler R. 
Published: May 2007

AbstractA scheme based on time‐discretization (with step‐size ϑ) and piecewise linear approximation of the interface is proposed for solving a Stefan‐like free‐boundary problem for the heat equation in one dimension. In such a problem, an integral condition prescribing the internal energy is given instead of assigning the flux on the fixed face. The approximating scheme is shown to converge to the unique solution of the problem uniformly on arbitrary subsets of the parabolic domain, D. An estimate for the rate of convergence as ϑ → 0 is given which turns out to be of order of ϑ1/2 on every compact set C ⊂ D, and of order of ϑ1/2–α for every α > 0 on D, when the distance of C from ϑD goes to zero with the rate ϑα.
Application of Bloch Analysis to the Stability Investigation of Hamiltonian Systems of Linear Differential Equations with Periodic Coefficients
Authors: Stoffel A. 
Published: May 2007

AbstractThe direct integral decomposition of the self‐adjoint operator associated with the differential equation is used to determine the set of parameters for which the equilibrium solution is stable. For systems with more than one degree of freedom even parameters in the interior of the spectrum may give rise to instability. The possibility of approximation of the eigenvalues without numerical solution of the differential equation, the qualitative behaviour considering small perturbations and the relation to Krein's stability theory are outlined. The described method is applied to models of two‐bladed wind turbines.
On Methods of Structure Identification for the Class of Polynomials within Mechanical Systems
Authors: Natke H. G. , Zamirowski M. 
Published: May 2007

AbstractStructure identification with respect to linear mechanical systems in general is reduced to identification of the type of damping and the order of the model, taking into account the principles of mechanics for the equations of motion. It is more difficult to model the nonlinear behavior of a system than a linear one. Often the structure of a model is chosen and its adequacy is then tested by physical and statistical significance.The nonlinearity under consideration is assumed to be modelled within the class of polynomials. Nonlinearities of mechanical systems then deal with the restoring and damping forces. Instead of the usual parameter estimation of the polynomials with a priori assumed maximum powers, the powers of the polynomials are to be determined along with their coefficients. One approach is based on approximation theory, the other defines a recursive procedure using a ratio test. The proposed techniques are illustrated through application to examples by simulation with different noise levels and it is shown that, even with noise corrupted data, the given methods yield satisfactory results.
Variably Inclined MHD Parallel Flows
Authors: Chandna O. P. , Labropulu F. , Husain Iqbal 
Published: May 2007

AbstractFür geradlinige, parallele, ebene MHD‐Strömungen werden Magnetfelder mit allen möglichen verschiedenen Winkeln zur Strömungsgeschwindigkeit bestimmt, und die genauen Lösungen für die sich ergebenden Strömungsprobleme werden angegeben.
Hard and Soft Fingered Robot Grippers. The Linear Complementarity Approach
Authors: Al‐Fahed A. M. , Stavroulakis G. E. , Panagiotopoulos P. D. 
Published: May 2007

AbstractThis paper deals with the problem of grasping work pieces with frictional multifingered grippers. The two types of frictional fingers „hard finger”︁ and „soft finger”︁ are treated. Hard fingers have the ability to constraint the object displacements on the normal and tangential directions to the object boundary, whereas soft fingers have in addition the ability to constraint the rotation of the object about the normal axis through the point of contact. The unilateral contact problem and the frictional problem are formulated in a compact form as a nonsymmetric Linear Complementarity Problem (LCP). Necessary and sufficient conditions which guarantee the solvability of the problem are derived. Also numerical examples computing the normal and tangential reactions, the slip Lagrange multiplier and the rigid body displacements and rotations are given.
Algebraische Approximationen hoher Ordnung an die Exponentialfunktion
Authors: Fuchs P. M. 
Published: May 2007

AbstractIm Zusammenhang mit der numerischen Behandlung von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen führt der Begriff der absoluten Stabilität bei sogenannten einwertigen Verfahren auf gewisse rationale Approximationen der Exponentialfunktion, wie z. B. Padé‐Approximationen. Aus der Untersuchung dieser rationalen Approximationen haben sich verschiedene Theorien entwickelt, als Beispiel sei die Theorie der Ordnungssterne von Wanner, Hairer und Nørsett genannt. Im selben Zusammenhang ergeben sich bei der Anwendung von mehrwertigen Verfahren algebraische Approximationen der Exponentialfunktion. In der vorliegenden Arbeit wird für Butchers verallgemeinerte implizite Runge‐Kutta Methoden untersucht, von welcher Ordnung die zugeordneten algebraischen Approximationen an die Exponentialfunktion sein können.
On Transformations and Perturbations of Orthogonal r‐Frames
Authors: Sherif N. 
Published: May 2007

AbstractA decomposition of Cn into a finite direct sum of orthogonal subspaces can be conveniently represented by its orthogonal projector frame, which is the collection of the corresponding orthogonal projectors. Two such decompositions whose frames are close, are known to be linearly homeomorphic and homotopic. In a recent work we compared the resulting geodesic arcs with naturally arising paths, resulting from interpolating the balanced transformation and found them cubically close. In this work we describe an efficient algorithm to compute the balanced transformation.
Pitching Response of an Anchored Viscous Liquid Bridge to Bottom and/or Top Disc Excitation
Authors: Bauer H. F. , Eidel W. 
Published: May 2007

AbstractThe response of an anchored viscous liquid bridge to different pitching top and/or bottom excitation has been determined. The pressure, the velocity distribution and free surface displacement are obtained for synchronous, counter‐excited and one‐sided pitching excitation as a function of the dimensionless forcing frequency Ωa2/v. The contactlines at the rim of the upper and lower discs are considered to be anchored there. In synchronous pitching excitation only the even resonances show response peaks, while in a counter‐excited system only odd resonances appear, which is in contrast to axial excitation modes. For one‐sided excitation all resonances appear.
Finite Elements Based on Differential Equations
Authors: Poceski A. 
Published: May 2007

AbstractSimple but efficient quadrilateral and hexahedronal elements for the analysis of plane stress, and three‐dimensional plate bending and shell problems are derived explicitly. The high order derivatives of the differential equations are approximated by a product of lower order derivatives. The integration of the equations yields the element matrix. It is composed of constant submatrices, multiplied by variable coefficients. The numerical results indicate very good accuracy of the applied method.
Finite Element Methods for Nonlinearly Viscous Fluids
Authors: Belonosov M. S. , Litvinov W. G. 
Published: May 2007

AbstractThe problem of stationary flow of a nonlinearly viscous fluid is studied under the “velocity‐pressure” mixed formulation, the surface forces are prescribed on one portion of the boundary and the velocities are given on the other portion. The problem is considered under Stokes approximation, i.e., the inertia forces are neglected. Existence and uniqueness are proved, and finite element approximation for velocity and pressure as well as iterative methods are studied.
Diffraktion von Wasserwellen an einer Kugel
Authors: Dorfmann A. 
Published: May 2007

AbstractIn Rahmen der linearen Wellentheorie wurde die analytische Lösung der Diffraktion von Wasserwellen an der Kugel — die sich in unendlich tiefer Flüssigkeit befindet, während sich Kugel‐ und Wasseroberfläche berühren — ermittelt. Dabei verwendet man krummlinige Koordinaten und das Integraltransformationsverfahren.
Effects of Initial Stresses and Wall Thickness on Wave Characteristics in Elastic Tubes
Authors: Demiray H. , Antar N. 
Published: May 2007

AbstractEmploying the theory of small deformations superimposed on large initial static deformations, the propagations of harmonic waves in an initially stressed thick elastic tube filled with a viscous fluid is studied. Due to variability of the coefficients of the resulting differential equation of the tube, the field equations are solved by a power series method. Utilizing the properly posed boundary conditions that characterize the reaction of fluid with the tube wall, the dispersion relation is obtained as a function of initial deformations and the geometrical characteristics. The dispersion equation is examined analytically, whenever it is possible, and numerically, and the results are depicted on some graphs. It is observed that wave speeds increase with thickness parameter.
On the Determination of the Solutions for the Kinetic State of Single‐Freedom Multi‐Body Systems with Friction
Authors: Klepp H. J. 
Published: May 2007

AbstractA single‐freedom multi‐body system with determinate structure having friction‐affected sliders and hinges is considered. For the determination of the solutions of initial value problems the governing equations are put in the form of a system of linear algebraic equations having the absolute values of the friction forces as unknowns. The coefficients of these equations contain the signs of the unknown normal reactions, and the unknown friction torques are included in the right‐hand‐sides of these equations. With all possible sets of assumptions for the signs of the normal reactions and approaches of the friction torques these equations are solved, and the solutions, which are approaches of the friction forces, are selected. With these approaches of the friction forces new approaches of the friction torques can be established, which can be used for repeating the calculations, until the desired accuracy is reached. The determination of the accelerations and reaction forces of a five‐body system with three sliders and four hinges with this method evidenced advantages in comparison with pure iteration schemes.
The Use of Defect Correction for the Solution of Parabolic Singular Perturbation Problems
Authors: Hemker P. W. , Shishkin G. I. , Shishkina L. P. 
Published: May 2007

AbstractWe construct discrete approximations for a class of singularly perturbed boundary value problems, such as the Dirichlet problem for a parabolic differential equation, for which the coefficient multiplying the highest derivatives can take an arbitrarily small value from the interval (0, 1]. Discretisation errors for classical discrete methods depend on the value of this parameter and can be of a size comparable with the solution of the original problem. We describe how to construct special discrete methods for which the accuracy of the discrete solution does not depend on the value of the parameter, but only on the number of mesh points used. Moreover, using defect correction techniques, we construct a discrete method that yields a high order of accuracy with respect to the time variable. The approximation, obtained by this special method, converges in the discrete l∞‐norm to the true solution, independent of the small parameter. For a model problem we show results for our scheme and we compare them with results obtained by the classical method.
The Hermite Equation and the Generalised Laplace Transform
Authors: Deakin M. A. B. 
Published: May 2007

AbstractThe second order Laplace equation (i.e. the linear o.d.e. with linear coefficients) may be reduced to one of a number of standard forms. One of these is the Hermite equation which has hitherto been thought not to be treatable by the Laplace transform. This is true because the defining integral for that transform diverges in this case. However this problem does not arise with a generalised Laplace transform. This paper gives the detailed working out of the theory from this point of view, and in the process derives results for the parabolic cylinder functions; these derivations are simpler than the standard ones or else produce these (known) results in a somewhat different form.
The Lifting Line Equation for a Curved Wing in Oscillatory Motion
Authors: Chiocchia G. , Tordella D. , Prössdorf S. 
Published: May 2007

AbstractAn unsteady linear lifting line method for the determination of the circulation and lift distribution along the span of a curved wing subject to harmonic small amplitude oscillations is presented. The method relies on the Pistolesi‐Weissinger 3/4‐chord steady lifting line theory and couples it to the unsteady theory developed by Possio for the motion of lifting surfaces. It leads to an integro‐differential equation of a modified Prandtl's type, where the unknown is the circulation. This equation has been carefully analysed in order to evidence all the singularities and to treat them in the most convenient way. The numerical procedure consists of a gaussian quadrature technique based on Chebyshev's polynomial approximation of the unknown function. The method has been appraised through the comparison of a number of solutions, pertaining to different wing configurations, with existing solutions based on lifting surface theory.
Mechanics of Multiphase Materials
Authors: Fischer F. D. , Werner E. 
Published: May 2007

AbstractFirst the observation levels for materials are discussed. Then a material is modelled as a heterogeneous continuum consisting of grains, each of them being a tiny continuum in its turn. As demonstration material steel consisting of two phases is selected. In the case of duplex steel the material consists a priori of two phases at fixed volume fractions. Subsequently, the martensitic transformation in a Fe‐Ni steel is investigated as an example for a material with changing volume fractions of the phases. It is shown how continuum mechanics and thermodynamics can help to explain the some‐what unexpected deformation behavior of those materials.Vorerst werden die verschiedenen Beobachtungsmaßstäbe für Werkstoffe erörtert. In der Folge wird ein Werkstoff als heterogenes Kontinuum im Sinne einer Ansammlung von Körnern betrachtet. Jedes Korn für sich stellt wiederum ein kleines Kontinuum dar. Als Demonstrationsmaterial wird Stahl ausgewählt, der aus zwei Phasen besteht. Im Falle des Duplexstahles besitzt das Material zwei Phasen mit fixer Volumsfraktion. Weiters wird die martensitische Umwandlung in einem Fe‐Ni‐Stahl behandelt, die zu einer veränderlichen Volumsfraktion der beiden Phasen führt. Es wird gezeigt, wie die Kontinuumsmechanik und Thermodynamik beitragen können, um das doch merkwürdige Verformungsverhalten dieser beiden Werkstoffe aufzuklären.
On the Localization and Computation of Zeros of Bessel Functions
Authors: Vrahatis M. N. , Grapsa T. N. , Ragos O. , Zafiropoulos F. A. 
Published: May 2007

AbstractThe topological degree of a continuous mapping is implemented for the calculation of the total number of the simple real zeros within any interval of the Bessel functions of first and second kind and their derivatives. A new algorithm, based on this implementation, is given for the localization and isolation of these zeros. Furthermore, a second algorithm is presented for their computation employing a modified bisection method. The only information required for this computation is the algebraic signs of function values. Moreover, lower and upper bounds of a zero can also be obtained.
On the Existence of Positive Solutions to a Three‐Point Boundary Value Problem for the One‐Dimensional p‐Laplacian
Authors: Wang J.‐Y. , Zheng D.‐W. 
Published: May 2007

AbstractThe existence of positive solutions to a three‐point boundary value problem for the one‐dimensional p‐Laplacian is proved by a simple application of a Fixed Point Theorem in cones due to Krasnoselskii and the Arzela‐Ascoli Theorem.
On Hybrid High Resolution Upwind Methods for Multicomponent Flows
Authors: Ivings M. J. , Causon D. M. , Toro E. F. 
Published: May 2007

AbstractShock capturing numerical methods expressed in terms of conservative variables produce erroneous solutions when applied to multicomponent flows. Numerical schemes expressed in terms of primitive variables are able to provide accurate results for non‐shocked multicomponent flows. An assessment of four hybrid primitive‐conservative upwind schemes is presented for the solution of multicomponent flows involving strong shock waves. The schemes used are the MUSCL‐Hancock scheme, the Weighted Average Flux scheme, and modified versions of the Generalised Riemann Problem, and Piecewise Linear Methods. These four hybrid schemes provide accurate solutions to such problems, and numerical experiments suggest that they converge. It is also shown that conservative methods may often provide satisfactory results when applied to multicomponent problems when the flow is dominated by strong shocks.
Scalar Wave Diffraction by a Rigid Cylindrical Rod of Finite Length with Impedance Ends
Authors: Büyükaksoy A. , Polat B. 
Published: May 2007

AbstractA uniform asymptotic high frequency solution is presented for the problem of diffraction of plane harmonic sound waves by an acoustically rigid cylindrical rod of finite length with the ends characterized by the same surface impedance. This problem is described by a modified Wiener‐Hopf equation of the third kind and then solved approximately. The solution involves two infinite sets of constants satisfying two infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.
The Dirichlet Problem for the 2‐D Helmholtz Equation in a Multiply Connected Domain with Cuts
Authors: Krutitskii P. A. 
Published: May 2007

AbstractThe Dirichlet problem for the dissipative Helmholtz equation in a connected plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of second kind, which is uniquely solvable.
Hausdorff Dimension Estimates for Time‐Discrete Feedback Control Systems
Authors: Noack A. 
Published: May 2007

AbstractWe consider time‐discrete dynamical systems written as generalized feedback systems. Several results on the estimation of the Hausdorff dimension of negatively invariant sets of C1‐maps on Riemannian manifolds based on a theorem by Douady and Oesterlé are used to estimate the Hausdorff dimension of negatively invariant sets of discrete systems. In particular, conditions in the frequency domain are formulated. As a special class discrete systems acting on the cylinder are discussed.
On the Reconstruction of a Rigid Body in the Theory of Elasticity
Authors: Dassios G. , Rigou Z. 
Published: May 2007

AbstractA method is proposed for the solution of the inverse scattering problem associated with the shape reconstruction of a 3‐D, star shaped, rigid scatterer in the theory of elasticity. The inversion procedure is based on the use of elastic Herglotz functions. A key point of the method is a basic connection formula associating the scattered field and the Herglotz function on the surface of the scatterer, with the corresponding scattering amplitudes and Herglotz kernels on the unit sphere. Analytical difficulties caused by the complexity of the spectral Navier operator were overpassed by embedding the vector elastic scattering problem into a dyadic scattering problem, which absorbs the dependence of the incident field upon the transverse polarization by considering a complete incident dyadic field. The actual elastic problem is then obtained by projecting the dyadic scattering problem into the particular polarization of the assumed incident field. The method, which for the scalar case has been developed by Colton and Monk, leads to an optimization scheme which is similar, but much more complicated, to the corresponding scheme in acoustics.
Stoichiometric determination of hydroperoxides in fats and oils by fourier transform infrared spectroscopy
Authors: Ma K. , van de Voort F. R. , Sedman J. , Ismail A. A. 
Published: May 2007

AbstractA primary Fourier transform infrared (FTIR) spectroscopic method for the determination of peroxide value (PV) in edible oils was developed based on the stoichiometric reaction of triphenylphosphine (TPP) with hydroperoxides to produce triphenylphosphine oxide (TPPO). Accurate quantitation of the TPPO formed in this reaction by measurement of its intense absorption band at 542 cm−1 provides a simple means of determining PV. A calibration was developed with TPPO as the standard; its concentration, expressed in terms of PV, covered a range of 0–15 PV. The resulting calibration was linear over the analytical range and had a standard deviation of ±0.05 PV. A standardized analytical protocol was developed, consisting of adding ∼0.2 g of a 33% (w/w) stock solution of TPP in hexanol to ∼30 g of melted fat or oil, shaking the sample, and scanning it in a 100‐µm KCI IR transmission cell maintained at 80°C. The FTIR spectrometer was programmed in Visual Basic to automate scanning and quantitation, with the reaction/FTIR analysis taking about 2 min per sample. The method was validated by comparing the analytical results of the AOCS PV method to those of the automated FTIR procedure by using both oxidized oils and oils spiked with tert‐butyl hydroperoxide. The two methods correlated well. The reproducibility of the FTIR method was superior (±0.18) to that of the standard chemical method (±0.89 PV). The FTIR method is a significant improvement over the standard AOCS method in terms of analytical time and effort and avoids solvent and reagent disposal problems. Based on its simple stoichiometry, rapid and complete reaction, and the singular band that characterizes the end product, the TPP/TPPO reaction coupled with a programmable FTIR spectrometer provides a rapid and efficient means of determining PV that is especially suited for routine quality control applications in the fats and oils industry.