bluuebunny/crossref_metadata_2025 huggingface dataset:
A General View of Minimally Extended Systems for Simple Bifurcation Points
Authors: Allgower E. L. , Schwetlick H.
Published: May 2007

A simple bifurcation point y* of the nonlinear equation F(y) = 0 with a function F : ℝn + 1 → ℝn can be characterized by a so‐called minimally extended system G(z) = 0 where G : ℝn + 2 → ℝn + 2 is chosen such that z* = (y*, 0) is a regular solution of this system in the sense that the Jacobian ∂zG(z*) is nonsingular. Hence, y* can be computed by applying superlinearly convergent Newton type methods. A general principle for obtaining such minimally extended systems is described which, as special cases, yields the systems proposed in the literature by Griewank and Reddien [5], Pönisch [9], and Janovský [7]. Moreover, an improvement of Pönisch's method is given, and some numerical aspects of implementing the methods and optimally choosing free parameters are discussed.
Transporting and Mixing Gasses with Different Qualities
Authors: Ten Kate H. , van Der Hoeven T. , Sierksma G.
Published: May 2007

The Dutch gas company “Gasunie” has as one of its main policies, always meeting fluctuating demands, even in case of sudden changes of temperature. Gas originates roughly from three locations which have different gas qualities. A fast and flexible algorithm is needed to determine the quantities of gasses to be mixed and transported. In this paper the advantages of piecewise linear and network programming are combined to a simplex‐like algorithm, that speeds up the recently used algorithms with at least a factor 50.
Time Estimation of Disturbance Occurrences in Monitoring Systems
Authors: Banek T. , Batko W.
Published: May 2007

The paper presents a method of estimating the exit time of vibratory signals in monitoring systems into areas assigned to emergency states. It refers to the methods of the analysis of dynamic systems' stochastic trajectories, including the method of “functionals supporting the availability areas”. A simple model of a system “rotorbearing” was accepted as the basis for the derivation of the estimation dependencies of the time of the disturbance occurrences in a monitored bearing nod. The system is given by a model of an elastic, symmetrical rotor with the mass concentrated in the centre, and supported by two identical slide bearings.
Transport Properties of Double‐Periodic Arrays of Circular Cylinders
Authors: Mityushev V. V.
Published: May 2007

The paper is concerned with the problem of the conductivity of double‐periodic composite materials with circular inclusions. Rayleigh's sum S2 has been calculated for each double‐periodic structure. An exact formula for the tensor of effective conductivity is given.
Transmission Loss in the Far Field over a One‐layer Seabed Assuming the Biot Sediment Model
Authors: Buchanan J. L. , Gilbert R. P.
Published: May 2007

A system of differential equations is derived from Biot's constitutive and motion equations for a poroelastic material and a model for a one‐layer seabed is constructed. A normal modes representation for pressure in the far field is found in the case of constant parameters. The model's prediction for transmission loss is examined for five different types of sediments and compared to the predictions of a solid elastic halfspace model.
Geometric Aspects of the Co‐Rotational Derivative of a Continuous Motion
Authors: Kadianakis N.
Published: May 2007

In this work we use a frame‐independent version of the co‐rotational derivative of a motion, and study the geometry defined by this derivative on classical space‐time. This is done in the general framework of derivatives, called Spins, which define a rigid parallel translation of space‐like vectors. We express the Spin itself in terms of this translation, and show that for a non‐uniform Spin this translation depends on the path. Since the co‐rotational derivative is a Spin, its geometry is studied in this context. After showing that the relative vorticity of two motions is the difference of their co‐rotational derivatives, we prove that the translation defined by the co‐rotational derivative of a motion is path‐independent, if and only if the motion is homogeneous.
On the Stabilization of a Parametrically Driven Inverted Double Pendulum
Authors: Schiele K.
Published: May 2007

The stability of a two state process periodically driven inverted double pendulum is considered by Floquet's theory. A stability criterion is derived and numerically analysed. For some values of the excitation a stabilization is indeed possible. The corresponding parameter region is inside of the parameter region where a single pendulum is stabilized.
Conjugate Film Flow Down a Heated Vertical Wall
Authors: Pop I. , Ingham D. B. , Lesnic D.
Published: May 2007

The conjugate flow of a film down a heated vertical wall of finite length is investigated theoretically. It is shown that the momentum boundary‐layer equation leads to an exact solution for the velocity field, but the energy equation is nonsimilar. Solutions of this nonsimilar equation, subject to appropriate boundary conditions, are obtained numerically using an efficient finite‐difference scheme. Series solutions which are valid near the leading edge of the wall and far downstream are also obtained and compared with the corresponding numerical solutions. The distribution of the surface wall temperature and in the film region are also determined for values of the Prandtl number of 0.6 (air) and 6.7 (water).
Rißausbreitungsvorgänge in thermomechanisch belasteten Zweikomponentenmedien: Analysis und Experiment
Authors: Herrmann K. P.
Published: May 2007

In dieser Arbeit wird eine Übersicht über bruchmechanische Untersuchungen zur Entstehung und Ausbreitung von Wärmespannungsrissen in einem Segment oder in der Materialgrenzfläche von zwei‐ und dreidimensionalen eingespannten Verbundstrukturen gegeben. Die resultierenden Randwertprobleme der stationären Thermoelastizitätstheorie für ungerissene und gerissene 2‐D‐ und 3‐D‐Zweikomponentenverbunde werden dabei mit Hilfe von Muskhelishvilis Methode der komplexen Potentiale sowie der FE‐Methode gelöst. Für die 2‐D‐Bimaterialien konnten dabei in den entsprechenden Querschnitten orthogonale Scharen von Hauptspannungstrajektorien erhalten werden, die einen Überblick über die thermisch induzierten Eigenspannungsfelder in den Verbundstrukturen vermitteln. Bei Anwendung eines geeigneten Rißausbreitungskriteriums, das auf der numerischen Berechnung der Gesamtenergiefreisetzungsrate einer Mixed‐Mode‐Rißausbreitung beruht, konnten schließlich die Rißwege von Wärmespannungsrissen in 2‐D‐ und 3‐D‐Bimaterialien vorhergesagt werden, die an der Schnittlinie von Materialgrenzfläche und spannungsfreier äußerer Oberfläche entstehen. Dabei zeigten im Fall der scheibenförmigen Zweikomponentenverbunde die theoretisch vorausgesagten Rißwege eine sehr gute Übereinstimmung mit aus zugehörigen Abkühlungsexperimenten erhaltenen Rißpfaden. Die bruchmechanischen Untersuchungen wurden für verschiedene Probengeometrien mit unterschiedlichen Materialkombinationen durchgeführt, die sowohl gleichförmigen als auch ungleichförmigen Temperaturverteilungen unterworfen waren. Als Ergebnis dieser Untersuchungen kann festgestellt werden, daß Wärmespannungsrisse, die sich vollständig in einem Segment eines Bimaterials ausbreiten, der Bedingung GII = 0 an der jeweiligen Rißspitze genügen, während im Falle der Grenzflächenrisse stets eine Mixed‐Mode‐Rißausbreitung vorliegt, bei der die GII‐Werte eine wichtige Rolle spielen. Weiterhin konnte bei Anwendung des vorgeschlagenen Rißausbreitungskriteriums auch der mögliche Rißablenkungswinkel ϑ* einer Grenzflächenrißspitze aus der Grenzfläche ermittelt werden, wobei auch die Dicke der Grenzschicht (interphase) berücksichtigt werden konnte.

Schließlich wurden die Einflüsse dreidimensionaler Effekte auf die Wärmespannungsrißausbreitung in rotationssymmetrischen Bimaterialien unter Heranziehung der FE‐Methode sowie des bereits erwähnten Rißausbreitungskriteriums studiert. Dabei weisen die erzielten Ergebnisse für die ermittelten Rißwege sowie die zugehörigen bruchmechanischen Parameter auf einige bemerkenswerte Unterschiede zwischen den 2‐D‐ und 3‐D‐Bimaterialien hin.
State Space Approach to Viscoelastic Fluid Flow of Hydromagnetic Fluctuating Boundary‐Layer through a Porous Medium
Authors: Ezzat M. A. , Abd‐Elaal M. Z.
Published: May 2007

The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the non‐dimensional equations of a viscoelastic fluid flow of hydromagnetic fluctuating boundary‐layer through a porous medium bounded by an infinite non‐magnetic vertical plate. The formulation is valid for one‐dimensional problems. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solution to a problem of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field and to a problem for the flow between two parallel fixed plates is obtained. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the velocity distribution and the induced magnetic field are given and illustrated graphically for each problem.
The Long‐Time Behavior of Solutions of a Nonlinear Fourth Order Wave Equation, Describing the Dynamics of Marine Risers
Authors: Kalantarov V. K. , Kurt A.
Published: May 2007

The fourth order nonlinear equation describing the dynamics of marine risers is considered. It is established that the zero solution of the boundary value problem for the considered equation is globally asymptotically stable. Moreover, an estimate of the rate of decay of the solutions is obtained.
Stochastic Reconstruction of Loading Histories from a Rainflow Matrix
Authors: Dressler K. , Hack M. , Krüger W.
Published: May 2007

This paper is devoted to the mathematical description of the solution of the so‐called rainflow reconstruction problem, i.e. the problem of constructing a time series with an a priori given rainflow matrix. The algorithm we present is mathematically exact in the sense that no approximations or heuristics are involved. Furthermore, it generates a uniform distribution of all possible reconstructions and thus an optimal randomization of the reconstructed series. The algorithm is a genuine on‐line scheme. It is easy adjustable to all variants of rainflow such as symmetric and asymmetric versions and different residue techniques.
Eigenfrequencies and Simplified Models of Semi‐Infinite Cascades with Variable Boundary Mass
Authors: Dieterman H. A. , Metrikine A.
Published: May 2007

The eigenfrequencies of a semi‐infinite cascade of mass‐spring systems with variable boundary mass are studied. The investigation shows that real eigenfrequencies only occur for a boundary mass equal to or smaller than half the mass of the bodies in the cascade. For values of the boundary mass between a half mass and a full mass the cascade shows to have no eigenfrequencies. For a boundary mass larger than the internal masses only imaginary eigenfrequencies are present. Frequency‐response functions for the different cases are derived. Some simplified models for the semi‐infinite system are given and a comparison is made with the dynamic behaviour of continuous systems.
Identification of Weakly Singular Memory Kernels in Heat Conduction
Authors: Janno J. , Von Wolfersdorf L.
Published: May 2007

Inverse problems of identification of memory kernels in linear heat conduction are dealt with in case of weakly singular kernels in the space Lp and of continuous kernels with power singularity. The problems are reduced to nonlinear Volterra integral equations of convolution type for which by the method of contraction with weighted norms global existence and stability of solutions are proved.
On the Unsteady Potential Plane Flow Past a Porous Circle
Authors: Keglević I.
Published: May 2007

We consider a nonstationary plane flow which is an ideal flow on the whole plane except on a circle. On the circle we assume inhomogeneous in time and position linear dependence between normal velocity and pressure difference. We reduce the problem to an operator differential equation with an initial condition and by use of partial differential equation theory from Lions and Magenes we prove the existence and uniqueness of a solution for t ϵ [0, ∞). For periodic in time input conditions we prove the existence and uniqueness of a periodic solution of the problem. We also consider the solution by time independent input conditions. In this case the solution has a limit in infinity and tends exponentially to this limit.
On Dynamic Multi‐Rigid‐Body Contact Problems with Coulomb Friction
Authors: Trinkle J. C. , Pang J.‐S. , Sudarsky S. , Lo G.
Published: May 2007

This paper is a summary of a comprehensive study of the problem of predicting the accelerations of a set of rigid, three‐dimensional bodies in contact in the presence of Coulomb friction. We begin with a brief introduction of this problem and its governing equations. This is followed by the introduction of complementarity formulations for the contact problem under two friction laws: Coulomb's Law of quadratic friction and an approximated pyramid law. Existence and uniqueness results for the complementary problems are presented. Algorithms for solving these problems are proposed and their convergence properties are discussed. Computational results are presented and conclusions are drawn.
Exact Piezothermoelastic Solution for Simply Supported Laminated Flat Panel in Cylindrical Bending
Authors: Kapuria S. , Dube G. P. , Dumir P. C.
Published: May 2007

The three‐dimensional exact solution is presented for infinite simply supported, cross‐ply laminated flat panel with piezoelectric layers in cylindrical bending. The variables are expanded in Fourier series to satisfy the boundary conditions at the simply supported ends. The governing equations reduce to ordinary differential equations with constant coefficients. For each layer, the general solutions of the thermal and the piezoelastic problems involve two and six arbitrary constants, respectively. These are determined from the boundary and interface conditions. The response of panels consisting of cross‐ply laminated substrate of graphite‐epoxy composite with a PVDF layer bonded to its one face has been determined for prescribed sinusoidal surface temperature distributions and electric potential difference applied to the piezoelectric layer. The effect of span to thickness ratio on the response has been investigated. The feasibility of reducing deflection and stresses by applying potential difference to the piezoelectric layer is reported.
Solution of a Hypersingular Integral Equation of the Second Kind
Authors: Chakrabarti A. , Mandal B. N. , Basu U. , Banerjea S.
Published: May 2007

A straightforward analysis involving the complex function‐theoretic method is employed to determine the closed‐form solution of a special hypersingular integral equation of the second kind, and its known solution is recovered.
The Application of Tensor Algebra on Manifolds to Nonlinear Continuum Mechanics — Invited Survey Article
Authors: Stumpf H. , Hoppe U.
Published: May 2007

Some properties of the tensor algebra on manifolds are discussed with respect to the classical tensor algebra of continuum mechanics. Basic definitions and relations of linear maps are briefly recalled and applied to tensor spaces, where special attention is focused to the definition of dual and transposed maps. As application to nonlinear continuum mechanics, algebraic pull‐back and push‐forward maps, and Lie‐like time derivatives associated with linear maps are defined and used to build up commutative schemes for deformation measures, objective deformation rates, stresses, and frame‐invariant forms of the stress power. The transition to the classical formulation of tensor algebra by identifying vector spaces and their duals is examined. It is shown how this concept enables a straight‐forward derivation of the Doyle‐Ericksen formula and its possible variants.
A Rational Deduction of Plate Theories from the Three‐Dimensional Linear Elasticity
Authors: Bisegna P. , Sacco E.
Published: May 2007

In this paper a general procedure for a rational derivation of plate theories is proposed. The methodology is based on the conjecture that plate theories can be carried out from the three‐dimensional elasticity by imposing suitable constraints on the strain and stress fields. The powerful Lagrange multipliers theory is adopted to derive the variational principles, based on the Hu‐Washizu functional, governing the constrained elasticity problems. Both the first‐order shear deformation plate theory, and the higher‐order Lo‐Christensen‐Wu plate theory are derived. The governing equations are recovered, and the reactive fields, arising as a consequence of the imposed constraints, are carried out. When these reactive fields are taken into account, the equilibrium, congruence, and constitutive equations turn out to be exactly satisfied.
Numerical Algorithms for Dynamics of Thermopiezoceramic Bars
Authors: Altay G. Aşkar , Dökmeci M. C.
Published: May 2007

This paper is concerned with the numerical algorithms for the macromechanical analysis of a ceramic bar in which account is taken of mechanical, electrical, and thermal fields. In the first part of the paper, a hierarchic system of one‐dimensional equations of the thermopiezoceramic bar is deduced by a direct method of integration from the three‐dimensional equations of thermopiezoelectricity. Also, in a similar way, the method of moments is described for the macromechanical analysis. The second part is addressed to a direct method of solution which is essentially based on Kantorovich's method, as an alternative, for the macromechanical analysis. The resulting equations incorporate all the significant effects of ceramic bar under a general state of mechanical, electrical, and thermal loads. They accommodate the extensional, flexural, and torsional as well as coupled motions of thermopiezoceramic bar at both low and high frequencies. Lastly, in the third part, attention is confined to the cases involving special fields, motions, and material properties.
A Method for Determining the Lower Bound Dynamic Buckling Loads of Imperfection‐Sensitive Structures
Authors: Wu B.
Published: May 2007

A perturbation method based on the static stability criterion associated with the vanishing of the total potential energy on a certain equilibrium point on the unstable postbuckling path is presented for the determination of lower bound dynamic buckling loads of imperfection‐sensitive structures under step load of infinite duration. Attention is focused on the effect of various possible sources of structural imperfections on the dynamic buckling strength of perfect structures. Under the assumption that the effect of structural imperfections is of the first order, the method can give any desired higher‐order approximation to the lower bound dynamic buckling loads and the corresponding displacements without solving the system of differential equations of motion numerically. Especially, the method applies to finite‐degree‐of‐freedom systems as well as continuous ones. The application of the method is illustrated on two examples. The results demonstrate the significant effect of other imperfection sources, besides the shape imperfections having the shape of the classical buckling mode.
Calculation of Electrohydrodynamic Flow in a Circular Cylindrical Conduit
Authors: McKee S. , Watson R. , Cuminato J. A. , Caldwell J. , Chen M. S.
Published: May 2007

The electrohydrodynamic flow of a fluid in an “ion drag” configuration in a circular cylindrical conduit is governed by a non‐linear second‐order ordinary differential equation. The degree of non‐linearity in this equation is determined by a nondimensional parameter α and the equation can be approximated by two different linear equations for very small or very large values of α respectively. Perturbation solutions of the fluid velocities for α ≪ 1 and α ≫ 1 are developed. A Gauss‐Newton finite‐difference solver combined with the continuation method and a Runge‐Kutta shooting method are used to provide numerical results for the fluid velocity over a large range of values of α. Both numerical and analytical results are compared in order to establish the range of validity for the perturbation solutions.
The Volume Fraction Concept in the Porous Media Theory
Authors: Bluhm J. , De Boer R.
Published: May 2007

In this paper the volume fraction concept in the porous media theory is considered. First, the historical development of this important concept is traced. Thereupon, the concept of volume fractions is formulated and the transport theorems, which govern the transformations of volume elements from one placement to another, are derived. An essential feature is the incorporation of the effect of incompressibility into the transport theorems. This is only possible by the introduction of a new multiplicative decomposition of the deformation gradients of the constituents into parts describing the deformations of the realistic (true) materials and parts including the changes of the pores.
Finite‐Elemente‐Analyse gummiartiger inkompressibler Elastomere unter großen Verzerrungen und Kontaktwechselwirkungen
Authors: Itskov M.
Published: May 2007

In der vorliegenden Arbeit wird das Problem der Finite‐Elemente‐Analyse gummiartiger, strikt inkompressibler Elastomere unter großen Verzerrungen und Kontaktwechselwirkungen behandelt. Die Inkompressibilitätsbedingungen werden durch Ausschließung in expliziter Form eines Teiles von Komponenten des Verschiebungsfeldes aus dem globalen FE‐Gleichungssystem erfüllt. Numerische Aspekte dieser Vorgehensweise werden ausführlich besprochen. Zur Modellierung der reibungslosen Kontaktwechselwirkung von Oberflächen eines modellierten Körpers miteinander und mit festen Anschlägen wird die Penalty‐Methode angewandt. Numerische Beispiele und experimentelle Ergebnisse werden angeführt und verglichen.
On Tensor Functions of Second‐Order Tensors and Vectors Under N‐Gonal Classes Dnh
Authors: Zheng Q.‐S.
Published: May 2007

In three‐dimensional space there are seven series of classes, i,e., 𝒟nh, 𝒟n, 𝒟nd, 𝒞nv, 𝒞nh, 𝒞n, and 𝒞ni in general n‐gonal systems for n = integer ⩾ 1. The classes 𝒟nh are of most practical interest, they not only cover the usual orthotropy 𝒟2h, tetratropy 𝒟4h, and hexatropy 𝒟6h, but they contain the other six series of classes, too. Furthermore, one may refer to the overall material symmetry of a fibre‐reinforced composite with fibre reinforcements equivalently in the 0, π/s, 2π/s,…,(s – 1) π/s directions for s ⩾ 3 as the symmetry 𝒟2sh, and this kind of composite is known as a quasiisotropic material since its planar linear elasticity is isotropic. In this paper we establish the complete and irreducible representation for scalar‐valued, vector‐valued, and second‐order tensor‐valued functions of any finite number of second‐order tensors and vectors with respect to the infinitely many classes 𝒟nh, in supplement to the known representation with respect to the orthotropy 𝒟2h. These results allow for a general invariant formulation of constitutive equations for crystals in the tetragonal, trigonal, and hexagonal systems, as well as quasi‐isotropic fibre‐reinforced composites.
The Eigenfunctions of the Stokes Operator in Special Domains. I
Authors: Rummler B.
Published: May 2007

We consider the eigenvalue problem of the Stokes operator in a bounded cylindrical domain of ℝ3 with homogeneous Dirichlet boundary conditions on the curved part of the boundary and periodical conditions in the main stream direction. We deduce by separation the corresponding systems of ordinary differential equations and solve them explicitly looking for bounded, solenoidal vector fields fulfilling the boundary conditions. The investigation of possible cases yields either the explicit eigenfunctions and eigenvalues, or equations for the determination of the eigenvalues, and a general representation of the eigenfunctions.
Elastic Wave Scattering on a Thin‐Walled Inclusion
Authors: Lavrov N. A.
Published: May 2007

The dynamic three‐dimensional problem of interaction between an elastic wave and a thin‐walled elastic inclusion is considered. The incident wave length is comparable to the large linear size of the inclusion. Integral equations of motion are obtained by means of the asymptotic approach proposed. The deflections of a circular plate and a fragment of a spherical shell embedded in the medium are calculated in the case of axial symmetry.
Domain Decomposition with Nonmatching Grids and Mixed Formulation in the Spaces W, p(Ω), W(Ω)
Authors: Pousin J. , Sassi T.
Published: May 2007

In this note, we deal with the domain decomposition method with nonmatching grids for the Laplace operator in the Sobolev space W(Ω) for 2 < p < ∞. Expressing the problem by a mixed formulation, the Brezzi‐Babuška theorem applies (see for example [18]), and we prove that the problem is well posed. A priori error estimates for Lagrangean finite elements of first order are given. Note that the approximate problem can be solved by elimination. This result is straightforwardly extended to the plane linearized elasticity model (see remark 4). This is important when one intents to solve plane nonlinear elasticity problems by using the domain decomposition method with nonmatching grids combined with an adaptive finite element technique based on a posteriori error estimates (see [15]). Please note that the right functional setting for stating nonlinear elasticity problems in the Sobolev space W1,p with 2 < p.
The Eigenfunctions of the Stokes Operator in Special Domains. II
Authors: Rummler B.
Published: May 2007

We investigate the eigenvalue problem of the Stokes operator in an open bounded rectangular parallelepiped of the ℝ3 supplemented with homogeneous Dirichlet boundary conditions on two face to face lying lateral surfaces and periodical conditions in the directions orthogonal to the other faces. By separation we deduce a corresponding system of ordinary differential equations. We look for solutions as solenoidal vector fields satifying the boundary conditions. The investigation of possible cases yields either the explicit eigenfunctions and eigenvalues or equations for determining the eigenvalues and a general deduced form of the eigenfunctions. In the appendix we give an example of the first eigenvalues of the Stokes operator for fixed l = 2.69.
Acoustic Field in a Shallow, Stratified Ocean with a Poro‐Elastic Seabed
Authors: Gilbert R. P. , Lin Z.
Published: May 2007

In this paper we investigate the propagating solutions of the acoustic equation in a stratified shallow ocean with a poroelastic, semi‐infinite seabed. The ocean‐seabed system is first Hankel transformed. Then the method of transmutation is used to generate the transformed solutions in the water column; whereas, the modal seabed equations are solved using the computer algebra Macsyma. In the water column the transformed solutions are first decomposed using the Mittag‐Leffler expansion for the discrete spectrum. Both the discrete and continuous spectrum are then used to give a spectral representation of the solution, from which we develop a numerical scheme. Some numerical examples are given to illustrate the method.
Stability of a Viscoelastic Pipe Filled with a Moving Fluid
Authors: Drozdov A. D.
Published: May 2007

Sufficient stability conditions are derived for transversal oscillations of a thin‐walled viscoelastic pipe filled with a moving fluid. By using two different approaches, explicit expressions are developed for the critical flow velocities. In particular, steady flow and time‐periodic flow are considered. The effect of material and geometrical parameters on the critical velocity is studied numerically.
Stress Distribution in a Long Circular Cylinder Containing an Elliptical Crack
Authors: Lee Doo‐Sung
Published: May 2007

This paper deals with the three dimensional analysis of the stress distribution in a long circular cylinder containing an elliptical crack. The surface of the crack is perpendicular to the axis of the cylinder and is subjected to a constant pressure. The equations of the classical theory of elasticity are solved in terms of an unknown function which is then shown to be the solution of an integro‐differential equation. Numerical solution of the integro‐differential equation is obtained. The resultant stress intensity magnification factors for the elliptical crack in the cylinder are presented in graphical forms for various crack aspect ratios and proximity ratios.
Some Mathematical Identities Derived from the Solution of an Elementary Potential Problem
Authors: Schieber D.
Published: May 2007

A simple potential problem leads to closed‐form expressions for some definite integrals which do not seem to be readily available in the relevant literature. The outlined approach indicates that simple problems might sometimes provide unexpected and, perhaps, even novel results.
The Fully Plastic Rotating Disk with Rigid Inclusion
Authors: Güven U.
Published: May 2007

The plane state of stress in a fully plastic rotating annular disk mounted on a rigid circular shaft is studied. The analysis is based on Tresca's yield condition, its associated flow rule, and linear strain hardening material behaviour.
Informationsverlust, abstrakte Entropie und die mathematische Beschreibung des zweiten Hauptsatzes der Thermodynamik
Authors: Ansorge R. , Sonar Th.
Published: May 2007

We intend to discuss the relations between the more abstract notion of entropy and the ideas of information using nonlinear partial differential equations as an example. Hyperbolic equations of the first order, where vanishing of the characteristics in a discontinuity may be interpreted as loss of initial information, will serve as illustration. The problem of non‐physical rarefaction shocks in discussed, and with Lax′ shock condition a first entropy condition is introduced. The approximation of a physical problem with friction by an inviscid problem leads to a demand for an entropy inequality characterizing the solutions of the model with friction in the limit, when friction vanishes. This demand for an additional condition, namely for an entropy inequality as mathematical pendant to the second fundamental law also dominates the numerics of the presented equations. It is only the fulfilment of a discrete entropy condition — i.e. of a discretized form of the second fundamental law — that provides for the convergence of finite difference procedures.
Energetic Estimates and Asymptotics for Electro‐Reaction‐Diffusion Systems
Authors: Glitzky A. , Hünlich R.
Published: May 2007

In this paper we deal with equations modelling the transport of electrically charged species in heterostructures by diffusion, drift and reaction processes. We show that for such models the free energy decays monotonously and exponentially to its equilibrium value. For this purpose we prove an estimate of the free energy from above by the corresponding dissipation rate. Exactly the same results are obtained for the fully implicit discrete‐time scheme.
Linear Complementary Problems and the Simulation of the Motion of Rigid Body Systems Subject to Coulomb Friction
Authors: Kunze M. , Neumann J.
Published: May 2007

We describe how to systematically develop an algorithm to simulate the nonsmooth dynamics of multibody systems with impacts and friction. Our approach works by using the theory of linear complementary problems.
On the Cauchy Problem for Some Elliptic Systems in a Spherical Shell in Rn
Authors: Shlapunov A. A.
Published: May 2007

Solvability conditions and a formula for solutions of the Cauchy problem for the Laplace equation, matrix factorizations of the Laplace operator and the Lamé type system in a shell D in Rn (n ≧ 2) are obtained in terms of spherical harmonics. More exactly, we consider a situation where the Cauchy data are given on the exterior surface S of a shell D the interior surface of which is a sphere in Rn.
On the Convergence of Discretizations for Set Valued Operator Equations
Authors: Lei J.
Published: May 2007

This paper is concerned with the theory of the convergence of discretizations for set‐valued operator equations. It is a continuation of investigations in [2], [7], [5], some results for one‐valued operators have been generalized herein. As an application, two examples for set‐valued differential equations are discussed.
Elastic‐Plastic Rotating Solid Disk with Rigid Casing
Authors: Güven U. , Altay O.
Published: May 2007

Subject of the present investigation is an elastic‐plastic rotating thin solid disk with constraint to the radial movement in the outer boundary. An exact solution is presented under the Tresca's yield condition, its associated flow rule, and linear strain hardening material behaviour.
Creeping Flow past a Solid Sphere in a Porous Medium
Authors: Ganapathy R.
Published: May 2007

This paper reports an analytical study of the creeping flow past a solid sphere in an unbounded sparsely‐packed porous medium assuming the validity of the Brinkman model. A closed form solution is obtained for the flow field and streamlines are drawn to demonstrate its evolution. No separation flow occurs near the rear stagnation point. In the case of low permeability media, there is an overshoot in the tangential component of velocity in the vicinity of the sphere and the total drag on the sphere is found to increase with a decrease in the value of the permeability parameter. Heat transfer due to this forced convection has been exemplified.
A Spline Difference Scheme on a Piecewise Equidistant Grid
Authors: Surla K. , Uzelac Z.
Published: May 2007

We consider singularly perturbed boundary value problems of reaction‐diffusion type and their discretization via quadratic spline difference schemes on a piecewise equidistant mesh of the Shishkin type. On such a mesh we prove that a solution to the discretisation is almost second order accurate in the discrete maximum norm, uniformly in the perturbation parameter. Numerical results are presented, which verify this rate of convergence.
The Thin‐Walled Rod of an Open Cross‐Section as an Element of a 3D‐Structure
Authors: Anisimov D. N. , Goldshtein Yu. B.
Published: May 2007

The relation for a rectilinear thin‐walled rod of an open cross‐section is established between displacements and corresponding forces applied at the ends of the rod. The problem is solved in a linear setting, taking into account a flexure, a uniform and nonuniform warping, and also an axial deformation. The calculation is conducted in the deformed configuration. Coefficients of the thin‐walled rod relation form a matrix of rigidity of this rod that allows to include a thinwalled rod of an open cross‐section in a library of a finite element method.
Speech Sound Representation in the Auditory Nerve: Computer Simulation Studies on Inner Ear Mechanisms
Authors: Rattay F. , Lutter P.
Published: May 2007

Acoustical signals are represented in the auditory nerve both by place‐rate information and by the fine structure of the time differences in the spiking pattern. For those parts of human speech which are quite aperiodic the place‐rate information is very poor, because the mechanical tuning process needs time. Computer simulation of inner ear mechanics shows that the onset of a signal moves all parts of the basilar membrane. Plenty of fibers coming from all regions will be stimulated by the first pressure wave. Because of the rapid neural adaptation process even fibers with high characteristic frequencies are systematically activated by low frequency speech components. The time structure of the firing pattern seems to be of much higher significance than previously assumed. It is also of importance for the quasiperiodic parts of speech. Irregularities in speech and sound level are the reasons, why signal processing is not governed by the sharp tuning properties of auditory fibers which are known from stimulations with pure periodic signals of low level.
On New Hydrodynamic Conservation Laws Related to the Particle Relabeling Symmetry
Authors: Albert H.‐F.
Published: May 2007

Pure particle relabeling symmetry is a special orthogonal Lie group of transformations of the labeling coordinates of Lagrangian hydrodynamics. In reversible hydrodynamics it leaves the corresponding Lagrangian function invariant. Via Noether's theory it generates a conservation law not discussed before. It not only allows to generalize the concepts of helicity and enstrophy but also yields Ertel's and Hollmann's vorticity conservation theorems. This new conservation theorem may be regarded as the base of the whole vorticity theory. A generalization to irreversible motion of arbitrary fluid is discussed briefly. Some secondary consequences are: The baroclinic fluid is isotropic only if the isentropic surfaces are spherical (§ 3); for a stationary motion the vorticity conservation theorems are special reformulations of the Bernoulli equation (end of § 4). A scaling symmetry which is the superposition of a special particle relabeling symmetry and a certain scaling of time and distance from center of gravitation is also discussed. The physical meaning of the corresponding conservation law is not completely investigated.
Point Symmetries for Lagrangian Fluid Dynamics
Authors: Albert H.‐F.
Published: May 2007

Although it is very difficult to find the whole symmetry group of the Lagrangian hydrodynamic equations of a Newtonian fluid, we are able to present all of the point symmetries of the dynamics of a non‐viscous and non‐heat conducting perfect gas in the Lagrangian (co‐moving) frame of reference. The latter possesses the structure of a Hamiltonian dynamics for which one can discuss not only Lie, but also Noether symmetries. New results are found for some kind of particle relabeling symmetry. Consequences of these symmetries, as conservation laws and invariant solutions, are discussed elsewhere. Most of the calculations have been carried out with the computer algebraic system REDUCE.
Microwave roasting and positional distribution of fatty acids of phospholipids in soybeans (Glycine max L.)
Authors: Yoshida Hiromi , Takagi Sachiko
Published: May 2007

Whole soybeans were exposed to microwave roasting for 6, 12, and 20 min at a frequency of 2,450 MHz and were studied not only for phospholipid composition but also for positional distribution of the fatty acids. During microwave roasting, the greatest rate of phospholipid losses (P<0.05) was observed in phosphatidylethanolamine (PE), followed by phosphatidylcholine (PC) and phosphatidylinositol (PI), respectively. Therefore, the effects of microwave roasting on the composition and positional distribution of the fatty acids are likely clearer in PE than in PC or PI. However, the principal characteristics for the positional distribution of fatty acids are still retained during microwave roasting: unsaturated fatty acids, especially linoleic, are predominantly concentrated in the 2‐position, and saturated fatty acids, especially palmitic, primarily occupy the 1‐position after 12 or 20 min of roasting. The results suggest that unsaturated fatty acids located in the 2‐position are significantly protected from microwave roasting.
Location of deep‐sea shark (Centrophorus squamosus) glycerol ether lipid double bonds by nitric oxide chemical ionization mass spectrometry
Authors: Sellier Nicole M. , Bordier Catherine G.
Published: May 2007

Chemical ionization mass spectrometry with nitric oxide as the reactant gas has proved to be an efficient tool for locating the double bond in monoalkenylglycerols of type HO‐CH2‐CHOH‐CH2‐O‐(CH2)n‐1‐CH=CH‐(CH2)n‐2‐CH3. These monoalkenylglycerols were extracted from the liver oil of the shark Centrophorus squamosus, which lives at depths ranging from 1000 m and deeper. The presence of characteristic acylium ions R1CO+ and/or R2CO+ allowed location of the double‐bond position.
Stereospecific analysis of triacylglycerols from vegetable oils by two procedures—II: Normal and high‐oleic sunflower oils
Authors: Damiani P. , Cossignani L. , Simonetti M. S. , Santinelli F. , Monotti M.
Published: May 2007

Triacylglycerol stereospecific analysis of normal (NOS) and high‐oleic sunflower (HOS) oils was carried out by two procedures to study the influence of variety and growing conditions. Four cultural varieties, two NOS and two HOS, were grown in seven different places of Italy. Three of the four varieties were grown both in dry conditions and with irrigation. Concerning the triacylglycerol fatty acid compositions, the results showed no significant differences between irrigated and nonirrigated samples (P>0.05), between the two NOS, and between the two HOS varieties. Between NOS and HOS varieties, only stearic acid showed no significant differences (P>0.05). The fatty acid compositions of the sn‐2 position of NOS and HOS samples showed different percentage abundances (P<0.01), especially for oleic and linoleic acids. Fatty acid distributions in the sn‐1 and sn‐3 positions indicated a certain asymmetry. The relationships between the percentage intrapositional content of each acid (one sn‐position at a time) and its percentage content in the original triacylglycerol matrix were studied. A general regression model was used to verify if the content of each acid at the three stereospecific positions changed at the same rate as the content in the intact triacylglycerols. The interpositional compositions of all varieties of NOS and HOS oils showed analogous trends for each acid.
A simple and rapid method for concurrent determination of petroselinic and oleic acids in oils
Authors: Santinelli F. , Damiani P.
Published: May 2007

A procedure to determine the petroselinic acid/oleic acid ratio in oils is described. The method is based on transesterification of the constituent fatty acids to methyl esters. An aliquot of the solution of the esters is then analyzed by capillary gas chromatography; another aliquot is used for epoxidation of the double bonds with 3‐chloroperoxybenzoic acid and subsequent opening of the oxirane ring with hydrochloric acid to obtain the chlorohydrin derivatives. The hydroxy groups are then silanized, and the reaction mixture is analyzed by high‐resolution gas chromatography‐mass spectrometry. The procedure is precise, rapid, and reproducible, and several samples can be analyzed in one working day.
Determination of iodine value of palm oil by differential scanning calorimetry
Authors: Haryati T. , Che Man Y. B. , Asbi A. , Ghazali H. M. , Buana L.
Published: May 2007

Iodine value (IV) is used as a parameter in process control as well as a quality parameter in traded palm oil products. IV measures the number of double bonds in the molecular structure of an oil. To form a double bond, carbon requires more energy (615 kJ/mol) than to form a single bond (350 kJ/mol). Therefore, the thermal behavior of an oil could reflect its iodine value. This study was conducted to demonstrate the use of a differential scanning calorimeter (DSC) to determine the IV of palm oil and its products as an attempt to reduce the use of chemicals in the analysis. The DSC thermograms of palm oil showed a clear separation of the substances that have low melting points (low‐T), consisting of triunsaturated, monosaturated and disaturated triglycerides, from the high ones (high‐T), consisting of trisaturated triglycerides. Regression analysis showed that the peak characteristics, namely, area and height of the low‐T group and height of the high‐T group in the heating thermogram and also the height of the high‐T group in the cooling thermogram, can predict the IV of palm oil with R2 higher than 0.99. This study concludes that DSC can be used to determine the IV of palm oil and its products.
Separation and quantitation of cholesterol oxides by HPLC with an evaporative light scattering detector in a model system
Authors: Lakritz L. , Jones K. C.
Published: May 2007

A method to analyze cholesterol and 10 of its oxidation products, ranging from the weakly polar cholest‐4‐ene‐3,6‐dione to moderately polar cholest‐5‐ene‐3β,7α‐diol, in a single run is described. The separation was achieved by normal‐phase gradient high‐performance liquid chromatography with an evaporative light‐scattering detector. This universal mass detector does not detect changes in solvent composition; this makes it possible to employ gradients, an essential technique whenever a wide range of compounds with diverse characteristics is to be separated. Standards at concentrations from 0.1–1.0 µg were separated within 37 min on an alumina/silica column with a gradient elution system that contained dichloromethane, acetonitrile, and water.
Rapid measurements of boiling point and vapor pressure of short‐chain triglycerides by thermogravimetric analysis
Authors: Goodrum J. W.
Published: May 2007

Temperature dependence of vapor pressure and the boiling points for tricaproin (Tcap) and tricaprylin (Tcpy) were measured by a new rapid thermogravimetric analysis (TGA) method. Results were in agreement with data from other references. The Clausius/Clapeyron model fitted Tcap and Tcpy vapor pressure data with errors of 6% or less for pressures ranging from ambient down to 20 mmHg. This agreement with the model suggests that the vapor of these compounds has a large degree of ideal gas behavior and that their vaporization enthalpies are nearly constant from 25 to 400°C. Comparable accuracy and precision were obtained with TGA and differential scanning calorimetry methods for the compounds tested; however, TGA plots had significantly straighter baselines, which made vapor pressure determinations more convenient.
Low‐temperature properties of alkyl esters of tallow and grease
Authors: Foglia Thomas A. , Nelson Lloyd A. , Dunn Robert O. , Marmer William N.
Published: May 2007

The low‐temperature properties of mono‐alkyl esters derived from tallow and recycled greases were determined for neat esters and 20% ester blends in No. 2 low‐sulfur diesel fuel. Properties studied included cloud point, pour point, cold filter plugging point, low‐temperature flow test, crystallization onset temperature, and kinematic viscosity. Compositional properties of the alkyl esters determined included water, residual free fatty acids, and free glycerol content. In general, the secondary alkyl esters of tallow showed significantly improved cold‐temperature properties over the normal tallow alkyl ester derivatives. The low‐temperature flow test did not show a 1:1 correlation with cloud point as previously observed with methyl soyate and methyl tallowate. For the homologous series methyl to n‐butyl tallowate, ethyl tallowate had the best broad‐spectrum low‐temperature properties, both neat and when blended in diesel fuel. For the greases studied, both the normal and branched alkyl ester derivatives showed improved properties over corresponding tallow esters, especially with neat esters.
Effect of agitation in the hydrogenation of castor oil
Authors: Trivedi Rakesh K. , Vasishtha A. K.
Published: May 2007

Castor oil was hydrogenated to evaluate the effect of agitation during hydrogenation. The turbine and propeller impellers were evaluated during hydrogenation of castor oil at various temperatures, pressures, and catalyst concentrations. The effect of impeller position in the agitator at definite oil depth was also evaluated. Hydrogenation of castor oil at 130°C, 2.0 kg/cm2 hydrogen gas pressure with 0.5% Ni catalyst for 6 h while using two turbine impellers fitted in an agitator, one close to the reactor bottom and another at a height just below the top oil layer, revolving at 350 rpm, resulted in a product of a iodine value of 4.1, hydroxyl value of 156.4, and slip point of 84°C.