bluuebunny/crossref_metadata_2025 huggingface dataset:
Modeling and finite element formulation of piezoelectric fiber compositebeams
Authors: Lammering Rolf , Brockmann Tobias H.
Published: June 2004

Piezoelectric fiber composites with their dynamic characteristics, tailorable anisotropic properties, and high degree of integration provide excellent prospects for structural actuation tasks. An active beam concept with such a material system can be applied to helicopter rotor blades in order to reduce vibrations and noise. The most effective way to actively influence the blade dynamics is to make use of the aerodynamic forces by changing the angle of attack. Thus the goal is to investigate the potential of induced torsion and its different possible actuation schemes on the dynamic behavior of the rotating system. For this purpose a finite beam element formulation is derived and tested successfully.
Finite Element Simulation of Smart Structures for Active Vibration andAcoustic Control
Authors: Lefèvre Jean , Gabbert Ulrich
Published: June 2004

The design process of engineering smart structures using piezoelectric patches as distributed sensors and actuators requires a virtual overall model, which includes the main functional parts. In the paper a suitable software tool based on the FEM is presented to simulate coupled electro‐mechanical‐acoustical problems regarding interior noise problems. The modal truncation technique is used to design a LQ‐controller as well as to study the time‐depending behaviour of a clamed smart plate.
Aspects of Computational Modeling of Discontinuities with Enriched Triangular Finite Elements
Authors: Löblein J. , Schröder J.
Published: June 2004

In this paper the simulation of discrete cracks using triangular finite elements with an embedded interface is discussed. The formulation based on [2] is extended to geometric nonlinearity. The derivation starting from the kinematics for a divided body and the corresponding weak form of equilibrium is briefly described. Furthermore, some details concerning the numerical implementation are outlined. Finally, a three‐point bending test is analyzed.
On a Surface‐Related Multi‐Layer Shell Theory and its Application to CompoundStructures
Authors: Matheas Jan , Schlebusch Rainer , Zastrau Bernd W.
Published: June 2004

The paper is concerned with the analytical formulation of a multi‐layer surface‐related shell theory and with the basic concepts of the used contact formulation.
Discrete methods for soil modelling
Authors: Nardin A. , Schrefler B. A. , Zavarise G.
Published: June 2004

The interaction of the cutting tools with different geological settings determines a different wear and consequently different economical costs for the excavation. We apply here a strategy for soil modelling which is based on discretization of the continuum with rigid disks and suitable contact models. We concentrate at contact level the real mechanical behaviour of the soil. In order to carry out this strategy a “micro” and a “macro” level are established. This paper focuses on the micromechanical model.
Beanspruchungen des Unterkiefers bei unterschiedlichen Implantatverteilungen und unter unterschiedlichen Lasten
Authors: Rues Stefan , Lenz Jürgen , Schindler Hans J. , Rong Qiguo , Schweizerhof Karl , Riediger Dieter
Published: June 2004

Mit Hilfe der Methode der Finiten Elemente werden für unterschiedliche, häufig verwendete (symmetrische und nicht‐symmetrische) Implantatverteilungen im Unterkiefer die Spannungen im periimplantären Knochenbett analysiert, insbesondere um klinisch‐kritische Beanspruchungen zu bewerten. Die Analyse zeigt, dass die Druckspannungen mit wachsendem Atrophiegrad des Kiefers ansteigen und dass eine zusätzliche Schleimhautabstützung zu einer beträchtlichen Reduktion der Spannungen im Implantatbett beitragen kann.
Bending design of reinforced concrete circular cross sections after EC2 standard for strain εc2 smaller than 1.35‰
Authors: Skrinar M.
Published: June 2004

The paper discusses the bending analysis of a concrete circular cross section using the bilinear stress distribution for the design stress‐strain relationship of the concrete according to the EC2 standard for the case when the absolute maximal strain in the concrete does not exceed the value of 1.35‰
Fixed‐point type iterations in numerical simulations for static and dynamic elastoplasticity
Authors: Vetyukov Yury , Gerstmayr Johannes , Irschik Hans
Published: June 2004

Dynamics of the elastoplastic media is stated in terms of plastic eigenstrains acting upon a background elastic problem with fixed (initial) stiffness. The plastic flow is described by specifically introduced plastic multipliers, which minimizes the number of unknown variables to be determined within the time step. A fixed‐point type iteration strategy is suggested for the computation of the plastic multipliers, which has been implemented for the finite element spatial discretization. Numerical experiments show the correctness and the effectiveness of the developed algorithm.
Consistent Transition of Beam‐Shell Structures within the FE Method
Authors: Wenzel Michael
Published: June 2004

In this paper we present a finite transition element for a consistent coupling of beam and shell structures. Often thin‐walled beam structures are calculated with beam elements. In order to achieve low modelling and calculation costs this is a useful procedure. For some reasons, e.g. local buckling or global collapse like torsional‐flexural buckling, it is necessary to model high loaded regions of a structure with shell elements within the beam model. For this kind of dimensional adaptivity the transition element is developed.
A Procedure for Identification of Friction Parameters in Constrained Robots
Authors: Fenili A. , Schäfer B.
Published: June 2004

Precise manipulation of objects in space by robotics requires the knowledge of contact parameters. These physical parameters change with outer space environmental impacts. On‐orbit experiments for in situ parameters identification are being prepared, and a simplified problem regarding the identification of friction coefficients is addressed in this paper. The development of a reliable contact model, that includes a complete knowledge about the robot parameters is adressed here. The parameters identification is based on a least square algorithm.
Wavelet‐based nonparametric identification technique for nonlinear dynamic systems
Authors: Glabisz Wojciech , Koźbiał Tomasz , Napiórkowska Magdalena
Published: June 2004

New parametric and non‐parametric identification techniques, based on wavelet expansion, for dynamic systems is shown. The identification results of the parameters of models obtained by the least‐squares method using the Haar wavelet packet analysis of randomly disturbed displacement signal is presented. New differentiation procedure of the measured data exploiting the properties of the wavelet packet analysis of a signal is applied. The non‐parametric identification results of models are known in the form of the restoring force surfaces.
Experimental Identification of a Surface Delamination of a Laminated Sandwich Beam
Authors: Müller I. , Schmieg H.
Published: June 2004

The oscillation properties of a laminate structure yields information about its structural integrity. Unilateral constraints and impacts dominate the oscillation properties of delaminated structures. These phenomena give rise to a nonlinear system response, whereas the degree of the nonlinearity augments with increasing intensity of excitation. The distribution of the nonlinearity on various test points allows the localisation of a delamination, exemplarily shown here on a laminated beam with a surface delamination.
Estimation of Partial Frequency Response Functions of Periodic Time‐Variant Systems under Broadband Excitation
Authors: Prothmann Thorsten
Published: June 2004

Mechanical systems, which are described by linear periodic time‐variant differential equations, show essential differences in their dynamic behaviour compared to systems, which are described by linear time‐invariant differential equations. In case of time‐invariant systems the dynamic behaviour in the frequency domain is uncorrelated, i.e. a harmonic excitation at one frequency yields a system response at the respective frequency. Opposite to that periodic systems respond not only with the excitation frequency but also with additional side bands shifted by multiples of the parameter frequency. Thus the dynamic behaviour of periodic systems is correlated in the frequency domain, i.e. the frequency response functions (FRFs) in terms of commonly considered time‐invariant mechanical systems depend on the excitation configuration. Therefore unique partial FRFs are defined, which are independent from the excitation configuration. An estimator for the partial FRFs is introduced, which represents a decisive extension of the possibilities of experimental testing of linear periodic systems.
Dedicated analytical formulation for an experimental set‐up to determine thermomechanical properties ‐ sensitivity and inverse analyses
Authors: Wawrzynek A. , Bartoszek M. , Delpak R. , Ching‐Wen Hu.
Published: June 2004

Computational analysis of new experiment is presented here. It is realized within two main tasks: 1. an application of inverse thermal analysis supported by thermovision measurements into evaluation of thermomechanical parameters of non‐homogeneous materials (like concrete), 2. an application of sensitivity analysis in a new experiment design process.
Dissipation of vortices in CFD‐simulations
Authors: Krieger Michael , Wimmer Peter
Published: June 2004

The aim of this investigation is to find out the crucial factors for the meshing of a wing and especially the area behind the wingtip with the intention to keep numerical vortex‐dissipation low to be able to analyse the trailing edge vortices of the wing in inviscid CFD‐simulations. In a series of basic test‐simulations spatial vortex propagation is observed for different cell types, mesh sizes and vorticities. A numerical viscosity is determined by comparing numerical results with an analytical solution for vortex‐decay. The information gained is applied to a numerical analysis of a trailing edge vortex of a rectangular wing. The results of the numerical calculations are compared to PIV‐measurements of trailing edge vortices and analytic results of linear wing theory.
Simulation of flow and mass transport in a meander micro‐channel subject to electroosmotic driving
Authors: Barz Dominik P.J. , Ehrhard Peter
Published: June 2004

The aim of this work is the investigation of the flow and mass transport in a meander micro‐channel caused by pressure and electroosmotic forces. Two‐dimensional, time dependent Finite Element simulations are employed to obtain information about the suitability of the structure for electrophoretic separation. Analytical solutions valid within the electrical double layers are asymptotically matched to the numerical solution of the core flow. The electroosmotic flow is realized for two idealized and two realistic electrical fields and the results are compared with the pressure‐driven case. The different driving methods lead to different velocity profiles and thus to different concentration profiles of a sample plug. We find that for the most of the electroosmotically‐driven cases complex flow fields with recirculation regions are present. These recirculation regions increase dispersion of the sample plug. According to the simulation results, we conclude that an improvement of the channel geometry for this electroosmotically‐driven device is needed.
Blow‐up phenomena in marginally separated boundary layer type flows
Authors: Braun S. , Kluwick A.
Published: June 2004

It is well‐known that unsteady effects may lead to finite time break‐down of the solutions to the fundamental equation following from the interaction theory of marginal separation which describes e.g. the leading edge flow of a slender airfoil at a small angle of attack. Recent studies dealing with the analysis of a bifurcation problem associated with this integral equation which arises if the angle of attack reaches a critical value showed that this equation can be simplified significantly for small deviations from this limiting value. The resulting evolution equation is a nonlinear partial differential equation whose local blow‐up behaviour is analyzed in detail. The existence of singular travelling waves strongly suggests the possible continuation of the solution beyond the blow‐up time.
Numerical Investigation of the Reorientation of a Free Liquid Interface upon Step Reduction in Gravity
Authors: Gerstmann J. , Michaelis M. , Dreyer M. , Rath H.J.
Published: June 2004

In this study we consider numerically the natural frequencies of a free liquid interface in a partly filled right circular cylinder at microgravity conditions. The dependence on the static contact angle, the fill height ratio and the boundary condition at the contact line was investigated. A formula for the calculation of the natural frequency is provided.
Contribution to the simultaneous measurements of the gas–mixture velocity and concentration
Authors: Jonáš P. , Mazur O. , Šarboch J. , Uruba V.
Published: June 2004

Fundamental relations are described of the heat transfer in flow of He / air mixture from the heated sensors of the dual hot wire / film probe working in a very weak interference regime.
On a new form of marginal separation
Authors: Kinell Mats , Kluwick Alfred
Published: June 2004

Incompressible high Reynolds number flows past a slender airfoil have the distinguishing property that there exists a critical value of the angle of attack where the wall shear stress on the suction side vanishes in a single point but immediately recovers. This phenomenon is now commonly refered to as marginal separation. In the present study it is shown that a laminar boundary layer on a flat plate subjected to a linearly retarded external flow may experience a similar behaviour if the molecular complexity of the medium is sufficiently large. The role of the critical angle of attack is played by the critical value of the freestream density ρc∞ on a given isentrope. As in the case of a slender airfoil it is possible to construct an asymptotic theory which allows to calculate small separation bubbles which form if ρ∞ becomes smaller than ρc∞.
Shear stress on the surface of a circular cylinder at rest in a moving fluid in axially symmetric flow using the Padé approximation technique
Authors: Redmond Brendan , Spillane Sandra
Published: June 2004

Following the asymptotic series solution of Seban & Bond [1], this paper evaluates the shear stress on the surface of a circular cylinder of radius a at rest in a fluid moving with steady velocity U0 parallel to the axis of the cylinder. The boundary layer builds up from the front of the cylinder and its thickness increases with increasing ξ, where ξ is a non‐dimensional variable representing axial distance from the front of the cylinder. The Seban & Bond solution is valid for small ξ only, near the front of the cylinder where the boundary layer thickness is small compared with a. Curle [2] extended the Seban & Bond results, thus making them valid for larger ξ. Glauert & Lighthill [3] used an asymptotic series to solve the problem in the region where ξ is large. They also used an approximate Pohlhausen method valid for small and large ξ. It is the purpose of this paper to extend the results given by the exact asymptotic series of Seban & Bond so that they are valid for both small and large ξ. This will be done using a Padé approximation technique, which will be compared with the historical results above. It will be seen that the region of validity of the series solution is extended without the need for Curle's extensive analysis and interpolation as in the other cases.
Charakterisierung von viskoelastischen Fluiden mittels Staupunktströmung und Fano‐Strömung
Authors: Wilkes C. , Gampert B.
Published: June 2004

Es wurde ein Dehnrheomat entwickelt, mit dem es möglich ist, Dehnströmungen von Polymerlösungen nach dem Prinzip der Staupunktmethode zu untersuchen. Die Konzentration kann bei diesem Anlagentyp unterhalb der kritischen Konzentration liegen, die für die Ausbildung einer transienten Netzwerkstruktur unter Strömungsbedingungen angegeben werden kann. Mit einer weiteren Versuchsanlage, mit der nach dem Prinzip der Fano‐Strömung Dehnstr ömungen erzeugt werden können, wurden im Rahmen dieser Arbeit viskoelastische Fluide untersucht. Für die Untersuchungen wurden kommerzielle Polyacrylamide, gelöst in wässerigen Lösungsmitteln, verwendet.
A comparison of algebraic Reynolds stress models for the prediction of the turbulent flow inside a turbomachine rotor
Authors: Antonello Marco , Masi Massimo , Navarro Giampaolo
Published: June 2004

An algebraic Reynolds stress model has been developed and tested simulating the turbulent flow inside a centrifugal impeller. The prediction of the model are compared with those of other algebraic turbulent stress models, in order to analyse the capability of properly account for effects such as flow curvature, flow separation, and solid wall rotation.
Large‐eddy simulation of shock‐turbulence interaction with finite volumes and the Approximate Deconvolution Model
Authors: von Kaenel R. , Kleiser L. , Adams N. A. , Vos J. B.
Published: June 2004

The supersonic flow over a compression corner is computed by Large‐Eddy Simulation (LES) using the Approximate Deconvolution Model (ADM) and a finite volume method. Results are in excellent agreement with DNS.
Solving functions in problems of mathematical physics
Authors: Al Khatib M.J. , Grysa K.
Published: June 2004

For any linear partial differential equation the solving functions are such ones that satisfy the equation and form a complete set of functions. In the paper the heat polynomials (i.e. solving functions for the heat conduction equation) are discussed as a representative example. They are used to construct an approximate solution of a given problem in a form of linear combination of the polynomials.
On the Thermoregulation in the Human Microvascular System
Authors: Deuflhard Peter , Hochmuth Reinhard
Published: June 2004

The bio‐heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. So far the derivation of the Helmholtz term arising in the bio‐heat transfer equation is not completely satisfactory. Our results show that this term may be understood as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. In view of a future integration of the bio‐heat transfer equation in a heterogeneous heat distribution model we present also asymptotic estimtates for first order correctors.
3D Particle Tracking Thermometry for Thermo‐Convective Flow Analysis
Authors: Heiland Hans Georg , Wozniak Günter
Published: June 2004

A new optical measurement technique for the investigation of thermo‐convective flow processes is the 3D particle tracking thermometry (3D PTT). This method is based on a combination of particle tracking velocimetry and liquid crystal tracer technique. Within observation volumes in fluids velocity and temperature fields can be determined simultaneously.
Freezing and thawing at the high hydrostatic pressure conditions ‐ modelling and numerical simulation
Authors: Kowalczyk Wojciech , Hartmann Christoph , Delgado Antonio
Published: June 2004

In this paper the modelling and numerical simulation of the freezing and thawing processes of water under high hydrostatic pressure up to 200 MPa is presented. The system of equation consists of the conservation laws of mass, momentum and energy. Moreover, it contains also the equation of phase change and the equations of state for water and ice. In order to model the phase transitions the enthalpy‐porosity method is used. The finite‐volume method is used to solve the system of equations and to simulate different cases of phase transitions. After analysing the results from our numerical simulations it can be seen that the fluid flow in a vessel at high pressure differs from that at normal pressure. The spatial ice developing depends more strongly on convection than on conduction in larger high pressure chambers. Very good agreement between results from numerical simulation and experiment is obtained.
A Joule‐Thomson process with condensation and evaporation
Authors: Loimer Thomas
Published: June 2004

The one‐dimensional flow of a fluid near saturation through a porous plug is considered. Upstream of the plug, the vapor is in the state of saturation. It is assumed that (i) the vapor cools down in a throttling process and (ii) it is in the unsaturated state downstream of the plug. At the upstream surface of the plug, the saturated vapor releases heat by partial or full condensation. If the permeability of the plug lies above a critical value the vapor condenses partially, otherwise full condensation occurs and a liquid film appears in front of the plug. In a small range of permeabilities above the critical value, the vapor condenses partially at the upstream surface, then it condenses fully at a front within the plug. Consuming the heat conducted downstream, the fluid evaporates fully at an evaporation front within the plug. The value of the critical permeability is a function of thermodynamic and transport properties of the fluid and of the thermal conductivity of the plug. The values of the permeabilities where the transitions between the different types of the process occur depend on the pressure difference across the porus plug.
Numerical Simulation of Fluid Flow and Enzyme Catalysed Substrate Conversion in a Packed‐bed Enzyme Reactor
Authors: Özmutlu Ö. , Hartmann C. , Delgado A.
Published: June 2004

This numerical study evaluates the momentum and mass transfer in an immobilized enzyme reactor. The simulation gives detailed information of the local substrate and product concentrations with respect to external and internal transport limitations. The flow field characterization of the system makes it possible to understand fluid mechanical properties and its importance on transport processes. With the obtained data it is also possible to detect zones of high, low and latent enzymatic activity and to determine whether the conversion is limited due to mass transfer or reaction resistances.
Grid convergence in large scale reactive flow calculations
Authors: Bielert Ulrich
Published: June 2004

Numerical simulations of turbulent combustion experiments in a large scale test facility (total length 35m) were performed solving the compressible Navier‐Stokes equations together with an k‐ϵ turbulence model and an eddybreakup combustion model. In the simulations the cell size and the model parameters of the combustion model were varied. The numerical results were compared to experimental data. The results indicate that rather coarse grids are sufficient to resolve essential features of the experiment, but user experience is required to choose good values for the model parameters.
Coupling of deterministic and stochastic simulation methods for gas‐solid‐flows
Authors: Kanther Wolfgang , Grüner Christof , Götz Sören , Strauß Karl
Published: June 2004

A new simulation method is proposed coupling deterministic and stochastic methods by an adaptive domain decomposition based on local granular equilibrium rating. This method reduces the computational effort compared to the fully stochastic method by roughly an order of magnitude, without significant loss of accuracy. Furthermore with this method appropriate boundary conditions for the solid phase can easily be derived.
Shear Flow of Suspensions under Wall Influence: Phenomenological Theory and Effects
Authors: Muckenfuss Silke , Buggisch Hans
Published: June 2004

The influence of solid boundary walls in shear flow of suspensions leads to structure formation and particle transport. We have developed a phenomenological model to describe the wall effects such as the formation of a wall boundary layer, the occurence of pseudo wall slip as well as discontinuities of the particle concentration. Using the model particle concentration profiles, thickness of boundary layer and suitably defined wall slip velocities depending on the total particle concentration of the suspension can be determined.
Peculiarities of fully Lagrangian approach for modeling dilute two‐phase mixtures with close phase densities
Authors: Osiptsov Alexander
Published: June 2004

The methods of calculating dilute two‐phase flows with a collisionless dispersed phase (particles, drops, or bubbles) fall essentially in two categories: Eulerian and Lagrangian. A limitation of the Eulerian approach is the exclusion of flows with crossing particle trajectories. An effective Lagrangian method for calculating flows with the formation of caustics in particle‐trajectory patterns was proposed earlier (see, for example [1]) for the case when the interphase force contains only “local” interaction terms (aerodynamic drag, Saffman force, etc.). In this paper, the fully Lagrangian approach is generalized to the case of similar phase densities, when in the interphase momentum exchange, in addition to the Stokes drag, the differential terms (virtual‐mass and Archemedes forces) and the integral term (Basset force) should be taken into account. The use of the method is illustrated by the calculation of redistributing particles or bubbles in a rotating spherical volume of a self‐gravitating viscous fluid (a model of development of density nonuniformities in the Earth core). A substantial anisotropy in radial particle concentration distributions and the possibility of forming local particle accumulation zones in the equatorial plane is indicated in the calculations.
Numerical simulation of 2d fluid flow in an partially filled simplified extruder model
Authors: Pokriefke Gritt
Published: June 2004

A simplified partly filled two‐dimensional model of a single‐screw extruder was analyzed with a full and a limited Eulerian multiphase flow model. The numerical calculations have been validated with experimental data and a good agreement was found.
Transport in a capillary thermo‐elastic porous material
Authors: Ricken T. , de Boer R.
Published: June 2004

In this contribution, the coupled flow of liquids and gases in capillary thermo‐elastic porous materials is investigated using a continuum mechanical model based on the Theory of Porous Media (TPM). In order to describe the behaviour of the three constituents involved, the balance equations of mass, of momentum and of energy concerning to all phases must be taken into account. The aim of this investigation is to simulate the behavior of liquid and gas phases in a thermo‐elastic porous body.
On the Improvement of Efficiency and Storage Requirements of the Discontinuous Galerkin Method for Aeroacoustics
Authors: Dumbser M.
Published: June 2004

For Computational Aeroacoustics (CAA), good wave propagation properties are a crucial point for numerical schemes which solve the linearized Euler equations (LEE) in the time domain. A recently developed high order scheme with excellent wave propagation properties is the Discontinuous Galerkin (DG) method. The DG schemes are based on the Finite Element Method (FEM), using discontinuous piecewise polynomial basis functions to represent the solution. The efficiency can be highly improved for CAA applications if a quadrature‐free formulation of the DG method is used, but nevertheless the DG schemes consume much computer storage due to the Runge‐Kutta time integration procedure and the high number of degrees of freedom to be stored for each element. We managed to develop a high order single‐step quadrature‐free DG method which does not use a Runge‐Kutta time integration procedure but which applies the ADER approach of Toro, Schwartzkopff et al. and where the accuracy of the scheme can further be improved using additionally a reconstruction technique working on the degrees of freedom of the element and its neighbors.
Sound wave channeling near–critical sulfurhexafluoride (SF6)
Authors: Schlamp Stefan , Rösgen Thomas
Published: June 2004

Strong density and sound speed gradients exist in near–critical isothermal fluid columns under gravity. The sound speed profile has a minimum, allowing table–top sound channeling experiments. The three characteristic length scales (ray curvature, correlation length of critical fluctuations, wavelength) can be changed independently by adjusting the temperature, frequency, and the strength of the gravitational field.
Computational Aeroacoustics using the new FASTAder approach
Authors: Schwartzkopff T. , Munz C.‐D.
Published: June 2004

To overcome the problems of a aeroacoustical simulation in the time domain, we use a heterogenous domain decomposition where the domains can be adapted to geometrical or physical constraints. We were able to show, that the commonly used conditions of constant fluxes at the interface yields to a solution which produces reflections. The correct condition is to prescribe constant values and to allow a discontinuous flux at the interfaces. In the domain where no obstacles and nonlinear effects are present, a structured mesh is used to solve the linearized Euler equations. For these problems the FASTAder approach has been developed.
On the Stability of Solutions of a Tunnel Fire Model
Authors: Gasser I. , Steinrück H.
Published: June 2004

We consider a fluid‐dynamic model derived to describe tunnel fires. The stationary problem is discussed. The stability of the stationary solutions in the transient problem are studied.
Well‐posed and ill‐posed situations in option pricing problems when the volatility is purely time‐dependent
Authors: Hofmann Bernd , Hein Torsten
Published: June 2004

We consider an inverse problem in option pricing with time‐dependent option price and volatility functions over a finite interval. Such problems may serve as benchmark problems for studying the character of ill‐posedness in option pricing and the impact of data smoothness and no arbitrage on solution properties.
Rhombic Periodicity Lattice in Bifurcational Symmetry Breaking Problems
Authors: Konopleva Irina , Loginov Boris
Published: June 2004

General theory of symmetry breaking problems in branching theory is presented in the works [1–3]. Such problems are invariant relative to Euclidean space motions group and their solution which is invariant relatively this group is the rest state or uniform linear motion. At the stability loss cell structure solutions arise, which are invariant relative to the group of the definite period shifts along the definite directions, passing mutually under discrete subgroup transformations that is defined by the symmetry of elementary cell of the periodicity. Thus the Euclidean space motions group is changed by the symmetry of a certain crystallographic group.

In this article for the case of 4–dimensional degeneracy of the linearized Fredholm operator abstract bifurcational symmetry breaking problems both for stationary and Andronov‐Hopf bifurcation with planar rhombic periodicity lattice are considered. Applications to hydrodynamical problems are given.
Mixed Boundary Value Problem of Plate Bending
Authors: Kutnjak Milan
Published: June 2004

The bending problem of thin plates is presented through biharmonic equations expressed in terms of plate deflections. The theory of analytical functions is used to transform the problem to the Hilbert boundary value problem. The stress and deformation state of the plate is descibed by analitical functions which satisfy mixed boundary conditions. A circular plate with corresponded boundary conditions is treated.
On Regularization of Pseudoperturbation Method for Sharpening of Approximately Given Generalized Jordan Chains
Authors: Loginov Boris , Konopleva Irina
Published: June 2004

Combination of pseudoperturbation and Newton‐Kantorovich (N.‐K.) methods are applied for the sharpening of approximately given eigenvalue and generalized Jordan chains (GJChs) of linear by spectral parameter operator function.
Numerical Simulation of Pollution Dispersion over Real Terrain
Authors: Beneš Luděk , Bodnár Tomáš , Fraunié Philippe , Kozel Karel , Sládek Ivo
Published: June 2004

The paper presents a mathematical and numerical investigation of the atmospheric boundary layer (ABL) flow over coal depot. Two mathematical models have been mentioned based upon: 1) the RANS equations in the conservative form and 2) the Boussinesq approximation of RANS equations in the non–conservative form, both formulated for an incompressible flow with a simple algebraic turbulence closure and given stationary boundary conditions. Also pollution dispersion of passive pollutants has been considered.
A linear model for long‐term dosage of anticoagulant drugs
Authors: Cromme Ludwig
Published: June 2004

We discuss a stochastic linear model for effect prediction in anticoagulant therapy. The model is the basis for an expert system for correct dosage of anticoagulant drugs.
A note to the linearity proof of Lorentz transformation
Authors: Günther Helmut
Published: June 2004

The traditional proof of the linearity of Lorentz transformation makes use of a definition of simultaneity and a physical law for the propagation of light. For unravelling these two elements we use a reverse axiomatic approach to special relativity. In this case we are free, in principle, to introduce an arbitrary simultaneity. Linear coordinate transformations require a linear synchronisation. Lorentz transformation results from a special kind of linear synchronisation.
Thermodynamics of a Fluid System interacting via a “Mexican Hat”–Pair Potential
Authors: Mausbach P. , May H.‐O.
Published: June 2004

By means of three‐dimensional Monte Carlo simulations for a N,V ,T –ensemble we investigate the phasebehaviour of a fluid system interacting via a “Mexican Hat”–pair potential for a very large temperature and density range.
Numero‐Fuzzy Hybrid for Modelling and Simulation of the Fouling of Milk Heat Exchangers
Authors: Petermeier Hannes , Benning Rainer , Becker Thomas , Delgado Antonio
Published: June 2004

To overcome the lack of a selfcontained description of the fouling process in dairy industry, a fuzzy system is integrated in a process model using wellknown numerics thus resulting in a numero‐fuzzy hybrid model. Results concerning the simulation of a dairy plant and a new approach for the study of the applied fuzzy systems are presented.
A Coincidence Degree for Bifurcation Problems with Applications to Steady State Flow
Authors: Sburlan S. , Sburlan C.
Published: June 2004

In this paper we study the steady state flow of incompressible fluids treated as an eigenvalue problem. We can define a coincidence degree under some conditions weaker than the ones when the classical coincidence degree was defined, and use the properties of this degree to our problem.
Discrete and continuum models of heat conduction problems in periodic lattice structures
Authors: Szymczyk Jolanta , Wozniak Czeslaw
Published: June 2004

A new modelling approach to the hyperbolic heat conduction problems in periodic lattice structures of an arbitrary form is proposed. To this end we introduce a special description of the periodic lattice geometry which leads to the discrete lattice model governed by the system of finite difference equations. The continuum models are derived from the discrete model, by using the principle of stationary action.
Energy Conservative Methods for Numerical Solution of ODE‐s Based on Taylor series Algorithm
Authors: Miletics E.
Published: June 2004

The numerical solution of the ODE initial value problems is an intensively researched field. We have a lot of methods, eg. R‐K, Adams, symplectic but it isn't known well, how the approximate solutions behave from point of wiev of conservative quantities, for example energy [3], impulse etc. In this work we present an energy conservative algorithm based on the Taylor series method which was realized by MapleV system [2].
Overdetermined Elliptic Systems
Authors: Seiler Werner M. , Tuomela Jukka
Published: June 2004

We show that the weights classically used for the definition of ellipticity are not necessary, as any differential system that is elliptic with weights becomes elliptic without weights during its completion. Furthermore, there are systems which are not elliptic for any choice of weights but whose completed form is nevertheless elliptic.
Robustness of shortfall risk minimising strategies in the binomial model
Authors: Favero Gino , Vargiolu Tiziano
Published: June 2004

In this paper we study the dependence on the loss function of the strategy which minimises the expected shortfall risk when dealing with a financial contingent claim in the particular situation of a binomial model. After having characterised the optimal strategies in the particular cases when the loss function is concave, linear or strictly convex, we analyse how optimal strategies change when we approximate a loss function with a sequence of suitable loss functions.
ℐ–invariant random strict total orderings on ℤ
Authors: Hirth Ulrich
Published: June 2004

In a recent preprint ([4]) Saul Jacka and Jon Warren develop further the ideas of Paul Ressel and myself [3], though they work without positive definite functions on semigroups. I approach the results of [4] on ℐ–invariant random strictly total orderings by semigroup methods as in [3]. These orderings are most directly related to card shuffling, cf. the rich work of Persi Diaconis. Although more concrete applications are not yet known to me, the related papers [3], [2] and [1] definitively do have a background in population genetics, so the present work on ℐ–invariant random orderings is certainly not far from real–life applications.
Ship Capsize Risk Assessment and Designing Against Capsize
Authors: Sichermann Wolfgang , Kreuzer Edwin
Published: June 2004

A promissing approach for assessing ship safety against capsize is presented by Melnikov's method. The mean zero up‐crossing rate of the dynamical system's associated Melnikov process provides an upper bound for the mean capsizing rate in a stationary sea state. Due to its moderate computational effort if low dimensional systems are considered, this approach is particularly suited for applications in ship design.
Generalizations of Optimal Control Problems by Comparison
Authors: Irrgang H. , Bittner L.
Published: June 2004

Generalizations of optimal control problems can be used for deciding the existence of solutions as well as for constructions of approximate solutions. In such cases one has to ask for gaps between the original problem and its generalizations. An overview will be given on several generalizations of a special kind of optimal control problems and the connections between them will be pointed out.

These connections allow to answer the question about gaps for special cases.
Real‐Time Trajectory Planning of the Industrial Robot IRB6400
Authors: Knauer Matthias , Büskens Christof
Published: June 2004

Path planning of industrial robots requires the calculation of trajectories with respect to different optimization criteria, e.g. time optimal, energy optimal or wear and tear optimal solutions. These optimal control problems can be solved numerically, e.g., by direct solvers. In practice, inaccuracies or perturbations in the underlying model can cause the robot to fail in following the calculated path. When deviations of the precalculated trajectory or system parameters are detected an update of the robot trajectory is required in real‐time. Therefore, a method based on the parametric sensitivity analysis of the optimal control problem is proposed to calculate admissible approximations for the solution of the perturbed robot trajectory problem in real‐time. A model of ABB's common robot IRB 6400 is used to reveal the capabilities of the proposed method.
Stability Optimization of Periodic Mechanical Systems without Feedback
Authors: Mombaur Katja , Bock Hans Georg , Schlöder Johannes , Longman Richard
Published: June 2004

The open‐loop stability of periodic mechanical systems with multiple motion phases and state discontinuities is investigated. We make the assumption that the systems do not have any active feedback, but must rely entirely on their kinematic and dynamic properties to stabilize their motion. By means of a newly developed stability optimization method we are able to determine model parameters as well as actuator inputs and cycle times for which such selfstabilizing motions are possible.
Numerical Simulation of a 1D Model of a Molten Carbonate Fuel Cell
Authors: Pesch Hans Josef , Chudej Kurt , Petzet Verena , Scherdel Sabine , Schittkowski Klaus , Heidebrecht Peter , Sundmacher Kai
Published: June 2004

Without combustion, molten carbonate fuel cells (MCFC) convert chemical energy contained in fuel and oxidizer to electric energy via electro‐chemical reaction. Performance and service life of MCFCs depends on its operating temperature. So control of the operation temperature within a specified range and reducing temperature fluctuations is highly desirable. In a first step towards this goal numerical simulations are computed.
On a Smoothing Quasi‐Newton Method for Nonlinear Complementarity Problems
Authors: Rapajić Sanja , Krejić Nataša , Lužanin Zorana
Published: June 2004

Nonlinear complementarity problems (NCP) arise from optimization theory, engineering and economic applications. These problems are usually solved applying iterative methods to equivalent systems of nonlinear equations. We consider Jacobian smoothing quasi‐Newton method for a semismooth equation reformulation of NCP based on Fisher‐Burmeister function. Some numerical experiments of Jacobian smoothing method with modification of the right‐handside vector are presented.
Optimal Control and Parametric Sensitivity Analysis in Cancer Chemotherapy
Authors: Sternberg Kati , Büskens Christof
Published: June 2004

The chemotherapeutic treatment of a tumor is based on the growth‐retarding effect of the given medicinal drug dose to a cancer cell population. Preserving the health of the patient this can be formulated as an optimal control problem. We use a modified model of Ledzewicz and Schättler and present the optimal solution calculated numerically. Especially we attend a parametric sensitivity analysis, which indicates the dependency of the optimal solution with respect to disturbances in model parameters. In detail we examine the parametric sensitivity in case of disturbances in the cell‐cycle parameters.
Optimal kinematic design of a link‐drive mechanism with prescribed velocity characteristics
Authors: Vohar Bojan , Gotlih Karl , Flašker Jože
Published: June 2004

The paper presents an example of a link‐drive mechanism for a deep drawing mechanical press. Because of its characteristics such a drive is much more appropriate than conventional crankshaft or eccentric drive. The existing design of the drive has proved unsatisfactory and does not meet all the demands and constraints, which are ideal for deep drawing process. Optimization of the drive is therefore necessary. The intention is to achieve the required velocity characteristics in a defined area of movement. Firstly, the drive is analyzed and a mathematical model is made and prepared for optimization procedure. The process is time‐dependent, so it cannot be used directly in the optimization algorithm. Mathematical model is transformed into a form suitable for the standard non‐linear optimization procedure and then optimization is carried out. The method used is sequential quadratic programming. The final objective of the optimization process is to find such dimensions of link‐drive members that the given requirements are satisfied in the best possible manner.
Computation of 3D exterior stationary incompressible Navier‐Stokes flowswith non‐zero velocity at infinity
Authors: Calgaro Caterina , Deuring Paul , Jennequin Delphine
Published: June 2004

We aim to find numerical approximations of stationary incompressible Navier‐Stokes flows in 3D exterior domains. To this end, we consider the Navier‐Stokes system with local artificial boundary conditions on a truncated exterior domain. This boundary value problem is solved approximately by a finite element method. The corresponding error is estimated with respect to the discretisation depth and the size of the truncated exterior domain.
Modified ℋ︁‐matrices for convection dominated problems
Authors: Le Borne Sabine
Published: June 2004

Hierarchical matrices (ℋ︁‐matrices) provide a technique for the sparse approximation of large, fully populated matrices. These matrices are constructed by using an algorithm that iteratively partitions the (block) index set until a certain admissibility condition is satisfied for an index block. For elliptic operators with L∞‐coefficients, the standard partitioning algorithm in connection with the standard admissibility condition lead to hierachical matrices that approximate the (inverse) of the stiffness matrix with an error of the same order as the discretization order while having nearly optimal storage complexity [1]. The standard partitioning and admissibility condition fail to provide satisfactory results when applied to the singularly perturbed convection‐diffusion equation. We will introduce a modified (hierarchical) partitioning of the index and block index sets together with a modified admissibility condition, both depending on the (constant) convection direction. Numerical results will illustrate the positive effect of the changes.
Artificial Multilevel Boundary Element Preconditioners
Authors: Steinbach Olaf
Published: June 2004

A hierarchical multilevel preconditioner is constructed for an efficient solution of a first kind boundary integral equation with the single layer potential operator discretized by a boundary element method. This technique is based on a hierarchical clustering of all boundary elements as used in fast boundary element methods. This hierarchy is applied to define a sequence of nested boundary element spaces of piecewise constant basis functions as used in the definition of the preconditioning multilevel operator.
MGM Optimal convergence for certain (multilevel) structured linear systems
Authors: Aricó Antonio , Donatelli Marco , Serra‐Capizzano Stefano
Published: June 2004

We present a multigrid algorithm to solve linear systems whose coefficient metrices belongs to circulant, Hartley or τ multilevel algebras and are generated by a nonnegative multivariate polynomial f.

It is known that these matrices are banded (with respect to their multilevel structure) and their eigenvalues are obtained by sampling f on uniform meshes, so they are ill‐conditioned (or singular, and need some corrections) whenever f takes the zero value. We prove the proposed metod to be optimal even in presence of ill‐conditioning: if the multilevel coefficient matrix has dimension ni at level i, i = 1, … , d, then only $ N(n) = \prod ^{d} _{i=1} n_{i} $ ni operations are required on each iteration, but the convergence rate keeps constant with respect to N(n) as it depends only on f.

The algorithm can be extended to multilevel Toeplitz matrices too.
Slow Initial Convergence of GMRES for SUPG Discretized Convection‐Diffusion Problems
Authors: Liesen Jörg , Strakoš Zdeněk
Published: June 2004

When GMRES [6] is applied to streamline upwind Petrov Galerkin (SUPG) discretized convection‐diffusion problems, its residual norms typically exhibit an initial period of slow convergence. For a model problem we offer a quantitative explanation of this behavior and relate it to the boundary conditions.
On Estimation of the A‐norm of the Error in CG and PCG
Authors: Strakoš Zdeněk , Tichý Petr
Published: June 2004

We concentrate on the preconditioned conjugate gradient method and describe a simple and numerically well‐justified way of estimation of the A‐norm of the error. In this way this note represents an extension of [5] and its aim is to mediate the analytic results from [5] to practical users of the preconditioned conjugate gradient method.
An Arnoldi type projection method for nonlinear symmetric eigenproblems
Authors: Voss Heinrich
Published: June 2004

For the nonlinear symmetric eigenproblem T(λ)x = 0 we consider an iterative projection method where the current search space is expanded by the direction governed by residual inverse iteration and the projected nonlinear eigenproblems are solved by safeguarded iteration.