bluuebunny/crossref_metadata_2025 huggingface dataset:
A vanishing viscosity approach to the evolution of microstructures in finite plasticity
Authors: Günther Christina , Hackl Klaus
Published: December 2012

Material microstructures in finite single‐slip crystal plasticity occur and evolve due to deformation. Their formation is not arbitrary, they tend to form structured spatial patterns. This hints at a universal underlying process. As in the approach of D. Kochmann and K. Hackl, we use a variational framework, focusing on the Lagrange functional to describe the evolving mircrostructure. We modify this approach by introducing a small smooth transition zone between the domains in order to improve the numerical treatment. We present explicit time‐evolution equations for the volume fractions and the internal variables. We outline a numerical scheme. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the direct connection of rheological elements in nonlinear continuum mechanics
Authors: Landgraf Ralf , Ihlemann Jörn
Published: December 2012

The structure of complicated phenomenological material models at finite strains is often exemplified with the help of rheological elements. Thereby, simple material behaviour, i.e. elasticity or viscous and plastic flow, are composes by components. In our approach, we directly apply this concept to obtain material models at finite strains. Towards this end, the thermodynamically consistent material behaviour of single elements is defined first. Subsequently, the elements are connected by evaluation of stress equilibria equations formulated on interconnecting configurations. The basic equations of this concept are presented using the example of nonlinear viscoelasticity of Maxwell type. The model results from a series connection of an elastic and a viscous element, whereas both are formulated in a thermodynamically consistent way within the framework on nonlinear continuum mechanics. Furthermore, an approach of numerical implementation using the stress equilibria is suggested. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multi‐phase modeling of shape memory polymers
Authors: Hempel Nico , Böl Markus
Published: December 2012

In the present work, we propose a model for shape memory polymers based on the idea of the multiplicative decomposition of the deformation gradient. Evolution equations for the several deformation components are presented that provide for the storage of the entropy‐elastic strain and its recovery during the transition between the frozen phase and the active phase. First characteristic shape memory cycles for small and large deformations will be shown as a last point. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Formulation of Finite Gradient Crystal Plasticity with Systematic Separation of Long‐ and Short‐Range States
Authors: Mauthe Steffen , Hildebrand Felix , Miehe Christian
Published: December 2012

With the ongoing trend of miniaturization and nanotechnology, the predictive modeling of size effects plays an increasingly important role in metal plasticity. The description of such size effects requires gradient‐extended theories of crystal plasticity. We outline a new viscous regularized formulation of rate‐independent gradient crystal plasticity for full multislip scenarios. To this end, we exploit in a systematic manner the long‐ and short‐range nature of the involved variables. It is shown that the evolution of the short‐range state is fully determined by the evolution of the long‐range state. This separation into long‐ and short‐range states is systematically exploited in the algorithmic treatment by a new update structure, where the short‐range variables play the role of a local history base. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical modeling of a non‐linear viscous flow in order to determine how parameters in constitutive relations influence the entropy production
Authors: Müller Wolfgang H. , Abali B. Emek
Published: December 2012

Some rheological materials, such as melting polymers, cosmetic creams, ketchup, toothpaste, can be modeled as non‐NEWTONian fluids by using a non‐linear constitutive relation. An incompressible flow of this kind of amorphous matter can be considered as a thermodynamic process, and a solution for the pressure, velocity and temperature fields describe it fully. Since such flow processes are generally irreversible, entropy is produced leading to dissipation in the system. This energy loss can be measured indirectly in a cone/plate viscometer which is used to determine viscosity of a BINGHAM fluid. While dissipation is an observable quantity we also want to be able to calculate it. Thus the goal of this work is to explain briefly how to compute a transient flow of a viscous fluid in two‐dimensional channel under a sinusoidal traction and calculate the dissipated energy for non‐NEWTONian fluids. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of Healing Processes in a Polymer Matrix
Authors: Specht Steffen , Bluhm Joachim , Schröder Jörg
Published: December 2012

In this article, a macroscopic 4‐phase model, based on the Theory of Porous Media, is presented to simulate healing processes in a polymere matrix. The healing process is described by the phase transition of two constituents, i.e., from liquid like healing agents to solid like healed material. As a first step, the healing mechanism begins at a certain time and is not driven by a healing criterion. A numerical example will be presented to demonstrate the applicability of the model in view of the description of healing processes. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modifications of hypergraphs of subsystems of mechatronic system as an effect of their analysis by means of different methods
Authors: Buchacz Andrzej
Published: December 2012

Purpose of this paper is creating of the hypergraphs of the beam concerning of two methods of analysis of vibrating beam by the exact and approximate methods. This approach make possible to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies‐poles of beams characteristics. The main subject of the research is the continuous free‐sliding (F‐S) beam as a subsystems of vibrating beam‐system. Findings this approach is a fact, that approximate solutions fulfill all conditions for vibrating beams and can be introduction to synthesis of these systems modeled by hypergraphs. Research limitation is that linear continuous transverse vibrating (F‐S) beam is considered. Practical implications of this study is the main point is the introduction to synthesis of transverse vibrating continuous beam‐systems. Originality of this approach considers the application Galerkin's method which concerns the analysis of beams and modeling them of transformed hypergraphs. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Effects of different crack‐face boundary conditions on the dynamic intensity factors in linear magnetoelectroelastic solids
Authors: Wünsche Michael , Zhang Chuanzeng
Published: December 2012

New multifield materials for the development of smart devices and structures are receiving increasing attentions. Composite materials consisting of piezoelectric and piezomagnetic phases with an additional magnetoelectric coupling effect [1] offer advanced opportunities and may be used for broadband sensing, actuating devices and many other smart devices and structures which are required in engineering sciences. The dynamic crack analysis of magnetoelectroelastic solids is of special importance because such materials are often very brittle and the corresponding results have a direct relevance to the design and optimization of smart structures. The boundary element method (BEM) has been shown to be very attractive and efficient for solving dynamic crack problems in linear magnetoelectroelastic solids [3]. A critical issue in the numerical simulation of crack problems in linear magnetoelectroelastic solids is a realistic description of the mechanical and electromagnetical crack‐face boundary conditions, which is considered in this paper. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A projection method for phase field models in micromagnetics
Authors: Ethiraj Gautam , Miehe Christian
Published: December 2012

Magnetic materials have been finding increasingly wider areas of application in industry and therefore, as indicated by the reviews [1], [2] and [3], there is an increased interest in the efficient modeling of such materials that have an inherent coupling between the magnetic and mechanical characteristics. A particular challenge in the modeling of such materials is the algorithmic preservation of the geometric constraint on the magnetization field, that remains constant in magnitude [4]. In earlier works, [5] and [6], we presented a phase field model within a geometrically exact incremental variational framework where the geometric property of the magnetization director is exactly preserved pointwise by nonlinear rotational updates at the nodes. In the current work however, we present an alternative approach that involves an operator split along with a projection step for the magnetization vector. This method provides significant advantages in terms of speed and ease of implementation at the cost of the maximum time step size used. The current work therefore presents comparative study of the the two methods. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental evaluation of phase velocities and tortuosity in fluid saturated highly porous media
Authors: Gueven Ibrahim , Kurzeja Patrick , Luding Stefan , Steeb Holger
Published: December 2012

In the current contribution, we present a novel method for the determination of the high frequency tortuosity parameter, α∞ in high porous media. Therefore, time‐domain measurements of ultrasonic signals are performed with a transmission technique. Aluminium foams with different pore fluids will be under the scope of experimental investigation. Finally, the experimental results are compared with analytical wave propagation tests. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical assessment of disorder effects in metal foam core sandwich beams based on a local homogenization procedure
Authors: Beckmann Carla , Hohe Jörg
Published: December 2012

The present study is concerned with a numerical procedure for prediction of uncertainty effects in sandwich structures with disordered cores. The approach is based on probability distributions of different material properties and their spatial correlation which are the results of the multiple homogenization analysis of testing volume elements. In order to illustrate the essential difference in the results of material uncertainties between computations using random fields and a deterministic approach both methods are applied to a single edge clamped sandwich beam with a metal foam core which is loaded by a force at the free end. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Data‐driven estimation of atomistic support for continuum stress using the Gaussian mixture model
Authors: Moran Sean J. , Ulz Manfred H.
Published: December 2012

The notion of stress being an inherent continuum concept has been a matter of discussion at the atomistic level. The atomistic stress measure at a given spatial position contains a space averaging volume over nearby atoms to provide an averaged macroscopic stress measure. Previous work on atomistic stress measures introduce the characteristic length as an a priori given parameter. In this contribution we learn the characteristic length directly from the atomistic data itself. Central to our proposed approach is the grouping of atoms with highly similar values of position and stress into the same atomistic sub‐population. We hypothesise that atoms with similar values for position and stress are those atoms which harbour the greatest influence over each other and therefore should be contained within the same space averaging volume. Consequently the characteristic length can be computed directly from the discovered sub‐populations by averaging over the maximum extent of each sub‐population. We motivate the Gaussian mixture model (GMM) as a principled probabilistic method of estimating the similarity between atoms within position‐stress space. The GMM parameters are learnt from the atomistic data using the Expectation Maximization (EM) algorithm. To form a parsimonious representation of the dataset we regularise our model using the Bayesian Information Criterion (BIC) which maintains a balance between too few and too many atomistic sub‐populations. We use the GMM to segment the atoms into homogeneous sub‐populations based on the probability of each atom belonging to a particular sub‐population. Thorough evaluation is conducted on a numerical example of an edge dislocation in a single crystal. We derive estimates of the space averaging volume which are in very close agreement to the corresponding analytical solution. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Selective Damping for Weakly Coupled FE‐MD models
Authors: Shan Wenzhe , Nackenhorst Udo
Published: December 2012

When dynamic problems are of interest, the high‐frequency waves reflected from the coupling boundary will pollute the solution in the MD domain quickly and render the results from the multiscale model meaningless. In this contribution, we show that by applying artificial damping only to the high‐frequency part of the displacement field in the coupling domain in the weak coupling method can significantly reduce the reflections in the MD domain while not affecting the low‐frequency part that can be transmitted into the FE domain. The frequency analysis shows the errors in the magnitudes and phases of wave components are orders of magnitudes smaller than that in the bridging domain model or undamped weak coupling model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Plane stress finite element analysis of filler reinforced polymers
Authors: Sodhani Deepanshu , Reese Stefanie
Published: December 2012

The characteristics of polymers such as force‐deformation behaviour, strength, fatigue and wear resistance, can be tailored by embedding it with filler particles. The influence of the fillers on the material behaviour significantly depends on the size and geometric form of the filler aggregates, which vary under mechanical loading. The concept of super element is used to model filler particles. This is now coupled with the polymer matrix to generate a finite element model of filler reinforced polymers. In this work, we investigate the effect of filler geometry and volume fraction of fillers on the overall stiffness of the filler reinforced polymer. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiscale failure Modeling of composites using generalized finite element method
Authors: Pal Mahendra Kumar , Rajagopal Amirtham
Published: December 2012

In this work multiscale failure modeling of composites is made using generalized finite element method (GFEM). In this method the global approximation are constructed by combining the local basis with partition of unity functions. The enrichment functions for the GFEM approximation are computed using a proper orthogonal decomposition (POD) technique. The approximation is then used in a two scale Galerkin scheme for failure modeling of composites. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An insight into the rotational stall delay
Authors: Dumitrescu Horia , Vladimir Cardos , Frunzulica Florin
Published: December 2012

Blade element momentum (BEM) theory which is based on the two‐dimensional (2D) aerodynamic properties of airfoil blade element is the most common computational engineering method for the prediction of loads and power curves of wind turbines. Although most BEM models yield acceptable results for high tip‐speed ratios where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the loads and power in stall regime for stall‐controlled turbines. Understanding of the stall delay phenomenon on wind turbines remains, to this day, incomplete. The lack of a conceptual model for the complex three‐dimensional (3D) flow field on the rotor blade, where stall is begins, how it progresses and where stall is practically terminated, has hindered the finding of a unanimously accepted solution. The paper aims at giving a better understanding of the delayed stall events and a reasonably simple correction model that complements the 2D airfoil characteristics used to a BEM method. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Allocation of the particle concentration for the SPH‐method
Authors: Stein Anika , Wünsch Olaf , Rütten Markus , Künemund Jens , Saalfeld Stefan
Published: December 2012

In this paper a method is presented to optimize the number of particles in three‐dimensional computations using the SPH method, based on the nearest neighbour. The process is presented for the breaking dam problem. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Non isothermal simulation of non‐Newtonian flow in the shot sleeve of semi‐solid die casting processes
Authors: Laouar Roudouane , Wünsch Olaf
Published: December 2012

This work present a numerical study of the non isothermal flow of metal in the semi‐solid state in the shot sleeve of horizontal die casting machine during the injection process. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Crude estimate of velocity distributions from Truckenbrodt's energy and momentum coefficients
Authors: Niessner Herbert
Published: December 2012

One of the simplest models for the velocity distribution in a pipe cross‐section dependent on two parameters consists of two layers of different thickness and velocity. Unfortunately relative thickness and velocity of the wall layer cannot be expressed analytically in terms of Truckenbrodt's energy and momentum coefficents. But relative thicknesses of a three‐layer model with wall and intermediate layer having opposite core and zero velocity can be. Reasonable in case of strong reverse wall flow only they allow a crude estimate of the parameters of the two‐layer model, which may then serve as initial values in computing them iteratively. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of bubbly flow in a vertical turbulent channel
Authors: Santarelli Claudio , Fröhlich Jochen
Published: December 2012

The paper presents results of Direct Numerical Simulation of bubbly flow to analyse the interaction between the turbulent fluid and the bubbles. The simulations aim to investigate the effect of the bubble Reynolds number, related to the bubble size, and the void fraction. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of bed load transport in turbulent open channel flow
Authors: Vowinckel Bernhard , Fröhlich Jochen
Published: December 2012

The paper reports on direct numerical simulations of a particle‐laden open channel flow carried out to investigate the interaction between the dispersed and the continuous phase. The dispersed phase is represented by an immersed boundary method. The particle‐particle collisions are accounted for by a physically motivated collision model. Two cases, one with shear stress below the threshold of mobilization and the other with shear stress above the threshold are considered. The different density ratios lead to different types of modification of the flow field by the formation of density‐specific patterns of the particles. Light particles do not attain resting states but saltate evenly distributed in span‐wise direction. Heavy particles tend to form stream‐wise clusters of inactive particles. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Molecular dynamics simulation of lubricated contact between textured surfaces
Authors: Khromov Oleg , Shan Wenzhe , Nackenhorst Udo
Published: December 2012

In this contribution, the friction at atomical scale has been investigated by using molecular dynamics (MD) simulations. This work surves as a preliminary study on the influence of surface texture on the friction at atomic scale, where simple rectangular grooves are added to the contact surface. Our results suggest definite dependence of the friction on the orientation of the grooves, which decreases as the velocity increases. For a given velocity, an optimal direction of sliding which gives the minimum averaged friction coefficient can be identified. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Temperature effects in thin droplets
Authors: Boettcher Konrad , Hötzel Jonas , Ehrhard Peter
Published: December 2012

Thin droplets spreading on a solid substrate are investigated, with a special focus on temperature effects. The aim is to manipulate the fingering instability which may occur in the spreading in a spin coating process. The analysis bases on lubrication approximation, valid for flat thin droplets, which usually is the case. The dynamic of the wetting is implemented by using a generalized law of Tanner, coupling the contact angle (CA) of the droplet at the (apparent) contact line (CL) with its speed. A one‐way coupling is used to investigate, whether viscous heating has to be taken into account. It can be derived that its role is negligible in the spreading process of a thin droplet, even for a relatively large viscous influence (large capillary number). Analyzing the results of a linear stability analysis of the fingering instability and taking Marangoni‐stresses (MS) into account reveals, that the instability may be suppressed by cooling the ambient gas or heating the substrate during the spreading. Unfortunately an comparison with experiments for spreading droplets in a heated gas shows deviations for larger spreading radii. The influence of temperature on density is investigated and on the way a criteria, from which it may be obtained whether a simple Boussinesq‐approximation (BA) is appropriate or not. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Linearly implicit time discretization for free surface problems
Authors: Bänsch Eberhard , Weller Stephan
Published: December 2012

Deeper investigation of time discretization for free surface problems is a widely neglected problem. Many existing approaches use an explicit decoupling which is only conditionally stable. Only few unconditionally stable methods are known, and known methods may suffer from too strong numerical dissipativity. They are also usually of first rder only [1, 9]. We are therefore looking for unconditionally stable, minimally dissipative methods of higher order.

Linearly implicit Runge‐Kutta (LIRK) methods are a class of one‐step methods that require the solution of linear systems in each time step of a nonlinear system. They are well suited for discretized PDEs, e.g. parabolic problems [7]. They have been used successfully to solve the incompressible Navier‐Stokes equations [5]. We suggest an adaption of these methods for free surface problems and compare different approximations to the Jacobian matrix needed for such methods. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Investigation of sediment transport at the interface of a porous and a free flow domain
Authors: Reisner Timo , Steeb Holger , Renner Joerg
Published: December 2012

Sediment transport involves fluid flow in two different regions. In the free flow domain, the flow is governed by the viscous Newtonian fluid; sediment only occurs as suspended particles. In the porous domain however, the flow is governed by the pore geometry of the porous skeleton consisting of sedimented grains. In nature, the interface between these two domains is not a no‐slip boundary for the free flow. In this study, we quantify how sediment transport is affected by the interaction of the two different flows. We do this by comparing fluid flow in no‐slip bounded flow channels to fluid flow in channels containing both a free and a porous domain. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A VOF Method for Isobaric Expandable Flows
Authors: Shevchuk Illya , Rauschenberger Philipp , Janicka Johannes
Published: December 2012

In this paper a method is described to simulate isobaric multiphase flows at low Mach numbers with steep temperature gradients for fluids with non‐negligible thermal expansivity. Governing equations and solution procedure are outlined. Further, a test case is shown in order to verify the model. Single phase natural convection flows with large temperature differences and either constant or temperature dependent transport properties were simulated to prove the solution of coupled Navier‐Stokes and energy equations. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of a Nozzle‐Jet Configuration Including the Acoustic Near‐Field
Authors: Bühler S. , Kleiser L.
Published: December 2012

A numerical simulation setup is presented which allows to study a circular jet flow configuration in which the nozzle is included in the simulation domain. Direct Numerical Simulations (DNS) are performed using up to 10th order compact finite‐difference schemes which are stabilized by applying a mild low‐pass filter. A parallelization approach has been implemented which shows good weak and strong scaling behavior. At the inflow the Synthetic Eddy Method is employed to generate turbulent fluctuations in the nozzle boundary layer with prescribed statistics, which are imposed by a sponge (forcing) layer technique. Simulation results for the jet flow field obtained at Reynolds number ReD = 19000 and a Mach number Ma = 0.9 as well as for the acoustic near‐field are found to be in good agreement with recent nozzle‐jet simulation results as well as experimental findings. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the impact of thermal sources on noise generation
Authors: Hahnenkamm A. , Masood R.M.A. , Münsch M. , Lienhart H. , Lopez E. , Zhou L. , Grilliat J. , Delgado A.
Published: December 2012

Sound emission is nowadays considered as a major environmental issue. The sound emission is generated, amongst other sources, due to an increasing amount of traffic and transport, i.e. road transport, rail and air traffic. Here, sound emission presents a significant risk to public health and a major cause of stress, especially in industrial countries. In this framework the present work is dedicated to the topic of active noise control with the target of noise reduction. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variation of friction drag via spanwise transversal surface waves
Authors: Meysonnat Pascal , Klumpp Stephan , Meinke Matthias , Schröder Wolfgang
Published: December 2012

Introducing spanwise velocity components into the near‐wall flow field of a turbulent boundary layer has shown to be an effective mean of influencing the wall shear stress. The underlying physical mechanisms leading to the drag reduction have however not been fully understood. The presented investigation uses sinusoidal transversal travelling surface waves to influence the near‐wall turbulence to achieve drag reduction. Two distinct wave configurations are analysed in detail and compared to an unactuated turbulent flat plate boundary layer flow to gain inside into the drag reducing mechanisms. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Flow rate measurements in turbulent liquid metal channel flow using Time‐of‐Flight Lorentz force velocimetry
Authors: Jian Dandan , Karcher Christian
Published: December 2012

Non‐contact flow control and flow measurements in hot and aggressive metal melts are big challenges in metallurgical applications. Time‐of‐Flight Lorentz force velocimetry (ToF LFV) is an electromagnetic measurement technique to meet these challenges. Our experimental results demonstrate that this method is well suited to measure flow rate in turbulent liquid metal channel flow without knowledge of both melt and magnetic field properties. Moreover, the measured flow profiles are in very good agreement with predictions of numerical simulations using the commercial program Package FLUENT MHD. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Sufficient conditions for second order L2‐convergence of the fractional step theta method
Authors: Zanger Florian
Published: December 2012

We consider the fractional step theta time stepping procedure for the non‐stationary incompressible linear Stokes equations in a cylindrical domain (0, T) × Ω, where Ω is a bounded domain in ℝn. Using energy estimates and assuming a certain degree of regularity for the data, we show second order L2‐convergence. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Love's problem for hyperbolic thermoelasticity
Authors: Gawinecki Jerzy August , Rafa Józef , Łazuka Jaroslaw
Published: December 2012

In our paper we investigated the initial‐boundary value problem for elastic layer situated on half space of another elastic medium. In this medium the thermomechanical interactions were taken into consideration. The system of equations with initial‐boundary conditions describes the phenomenon of wave propagation with finite speed. In our problem there are two surfaces ie. free surface and contact surface between layer and half space. On the free surface are setting boundary conditions for normal and tangent surface force. We consider two types of contact between layer and half‐space: rigid contact and slip contact. The initial‐boundary value problem was solved by using integral transformations and Cagniard‐de Hoope methods. From the solution of this problem follows that in layer and half space exist some kind of thermoelastic waves. We investigated moreover the conditions which should be fullfiled for propagation of Rayleigh and Love's type waves on the contact surface between layers and half space. The results obtained in our investigation were used in technical applications especially engineering design and diagnostics of roads and airfields. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On asymptotic behavior for 1‐dimensional functional of Ginzburg‐Landau type with internally‐externally created oscillations of minimizers
Authors: Raguz Andrija
Published: December 2012

In this note we provide a kind of generalization of the well‐known notion of internally (externally, resp.) created oscillations of minimizers of non‐convex integrands in the calculus of variations. As an example, we consider a class of 1‐dimensional Ginzburg‐Landau functionals (the simplest case being considered in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761–825 (2001)). We describe asymptotic behavior leading to multiple small scale separation as parameter epsilon tends to zero. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Ultra Relativistic Euler Equations
Authors: Abdelrahman Mahmoud , Kunik Matthias , Warnecke Gerald
Published: December 2012

We consider the relativistic Euler equations in isentropic fluids with the equation of state $p = {\rho \over 3}$, which is the ultra‐relativistic limit. We analyze the single shocks. We study the shock interaction, and give explicit example for the non‐backward uniqueness. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Almost Sure Stability Analysis of Parametric Roll in Random Seas Based on Top Lyapunov Exponent
Authors: Dostal Leo , Kreuzer Edwin , Sri Namachchivaya Navaratnam
Published: December 2012

Stability analysis of the upright position of a ship in random head or following seas is presented. Such seas lead to parametric excitation of roll motion due to periodic variations of the righting lever. The development of simple criteria for the occurrence of parametric induced roll motion in random seas is of major interest for improvement of the international code on intact stability provided by the International Maritime Organization. The stability analysis in random seas is based on the calculation of the top Lyapunov exponent using the fact, that a negative top Lyapunov exponent yields no roll motion. With this findings, roll motion can be excluded for specific sea states. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Analysis of Stochastic Fiber Lay‐Down Models: Geometry and Convergence to Equilibrium of the Basic Model
Authors: Grothaus Martin , Klar Axel , Maringer Johannes , Stilgenbauer Patrik
Published: December 2012

The so‐called fiber lay‐down models arise in the production process of nonwovens. We introduce the generalized version of the basic fiber lay‐down model which can precisely be formulated in abstract form as some manifold‐valued stochastic differential equation. An important criterion for the quality of the nonwoven material is how the solution to the associated Fokker‐Planck equation converges towards its stationary state. Especially, one is interested in determining the speed of convergence. Here we present some results concerning the long‐time behavior by using classical stochastic methods as well as modern analytic methods from the theory of hypocoercivity. Demanding mathematical difficulties arising since the equation is degenerate. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the two‐step method for solving nonlinear equations with nondifferentiable operator
Authors: Shakhno Stepan , Yarmola Halyna
Published: December 2012

We study a local and a semilocal convergence of the two‐step method for solving nonlinear equations with a nondifferentiable operator. Its method is based on two methods of order of convergence $1 + \sqrt{2}$. We carry out the numerical research on test problems and do the comparison of obtained results. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
How Competitive is the ADI for Tensor Structured Equations?
Authors: Mach Thomas , Saak Jens
Published: December 2012

In [1] we presented an extension of the alternating direction implicit (ADI) method for the solution of Lyapunov equations

to higher dimensional problems. The vectorized form of the Lyapunov equation is

We considered the generalization of this equation of the form

The tensor train structure is one possible generalization of the low rank factorization we find in the right hand side of (1). Therefor we assume B to be of tensor train structure. We showed that in analogy to the low rank ADI case the solution X can be generated in tensor train structure, too. Further we provided an algorithm that computes X using a generalization of the ADI method.

Here we compare our new tensor ADI method with an density matrix renormalization group (DMRG) solver for tensor train matrix equations and with matrix equation solvers to investigate the competitiveness of our new solver. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Subspace Iteration Methods in terms of Matrix Product States
Authors: Huckle Thomas , Waldherr Konrad
Published: December 2012

When dealing with quantum many‐body systems one is faced with problems growing exponentially in the number of particles to be considered. To overcome this curse of dimensionality one has to consider representation formats which scale only polynomially. Physicists developed concepts like matrix product states (MPS) to represent states of interest and formulated algorithms such as the density matrix renormalization group (DMRG) to find such states. We consider the standard Lanczos algorithm and formulate it for vectors given in the MPS format. It turns out that a restarted version which includes a projection onto the MPS manifold gives the same approximation quality as the well‐established DMRG method. Moreover, this variant is more flexible and provides more information about the spectrum. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bounds on the Range of Multivariate Rational Functions
Authors: Garloff Jürgen , Schabert Antek , Smith Andrew P.
Published: December 2012

By utilising the expansion of a polynomial into Bernstein polynomials, we construct bounds for the range of a multivariate rational function over a box. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
SPAI Preconditioners for HPC Applications
Authors: Sawyer William , Vanini Carlo , Fourestey Gilles , Popescu Radu
Published: December 2012

Iterative methods to solve systems of linear equations Ax = b usually require preconditioners M to speed convergence. But the calculation of many preconditioners can be notoriously sequential. The sparse approximate inverse preconditioner (SPAI) has particular potential for high performance computing [1]. We have ported the SPAI algorithm to graphical processing units (GPUs) within NVIDIA's CUSP library [2] for sparse linear algebra. GPUs perform well on dense linear algebra problems where data resides for long periods on the device. Since the underlying minimization problems are independent, they are mapped to separate thread‐blocks, and an optimized QR algorithm implemented using NVIDIA's CUBLAS library is employed on each.

Traditionally the challenge has been to determine a sparsity pattern Sp(M) of the preconditioner dynamically [3], which reduces the condition number of MA to a degree where a preconditioned iterative solver such as GMRES becomes computationally viable. Due to the extremely high performance of the GPU, it is possible to consider initial sparsity patterns much denser than have been previously considered. We therefore consider a fixed sparsity patterns to simplify the GPU implementation.

We evaluate the performance of the resulting preconditioner on a standard set of sparse matrices, and compare SPAI to other preconditioners. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Shape sensitivity analysis in the extended finite element method
Authors: Barthold Franz‐Joseph , Materna Daniel
Published: December 2012

The contribution is concerned with the derivation and implementation of shape sensitivity analysis in the context of the extended finite element method (xfem). Here, the displacement approximation is enhanced in order to model strong and weak discontinuities along the interfaces and cracks. Consequently, sensitivity analysis must be accomplished for the extended formulation based on a sub‐integration technique on sub‐domains of the cut elements. This cumbersome and error‐prone work can be circumvent using a standard treatment of sub‐elements on an appropriately defined sub‐mesh. These modifications guarantee exact analytical sensitivities even for distorted finite element domains. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The bang‐bang funnel controller: An experimental verification
Authors: Hackl Christoph , Trenn Stephan
Published: December 2012

We adjust the newly developed bang‐bang funnel controller such that it is more applicable for real world scenarios. The main idea is to introduce a third “neutral” input value to account for the situation when the error is already small enough and no control action is necessary. We present experimental results to illustrate the effectiveness of our new approach in the case of position control of an electrical drive . (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficient Volumetric Anisotropic Diffusion Computation on GPUs
Authors: Kuijper Arjan , Schwarzkopf Andreas , Kalbe Thomas , Goesele Michael
Published: December 2012

We present an efficient implementation of volumetric anisotropic image diffusion on modern programmable graphics processing units (GPUs). We avoid the computational bottleneck of a time consuming eigenvalue decomposition in ℝ3. Instead, we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining two tangent space eigenvectors. We derive closed formulas to achieve this resulting in efficient GPU code. Our most complex volumetric anisotropic diffusion gains a speed up of more than 600 compared to a CPU solution [1]. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An Estimation Theoretical View on Ambrosio‐Tortorelli Image Segmentation
Authors: Krajsek Kai , Dedovic Ines , Scharr Hanno
Published: December 2012

In this paper, we examine the Ambrosio‐Tortorelli (AT) functional [1] for image segmentation from an estimation theoretical point of view. Instead of considering a single point estimate, i.e. the maximum‐a‐posteriori (MAP) estimate, we adopt a wider estimation theoretical view‐point, meaning we consider images to be random variables and investigate their distribution. We derive an effective block‐Gibbs‐sampler for this posterior probability density function (PDF) based on the theory of Gaussian Markov random fields (GMRF) [2]. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Discrete Gradient Flows on surfaces using subdivision
Authors: Grundel Sara
Published: December 2012

Gradient flows on surfaces play a role in a wide range of applications, for example in biological modelling, computer graphics and shape optimization. We present an approach to compute a discrete gradient flow by using a newly developed C2‐smooth subdivision algorithm. We will briefly present the subdivision algorithm and how we can use it to compute the mean curvature flow. This method can be used similarly for many other gradient flows. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Hybrid GPU Accelerated Mesoscopic Particle Simulation
Authors: Fischer Katrin , Ostermeyer Georg‐Peter
Published: December 2012

During the past few years, the performance enhancement of existing algorithm implementations through massive parallelization on modern graphics processing units (GPUs) based on NVIDIA's Compute Unified Device Architecture (CUDA) has become very popular in a large variety of applications. Particle methods e.g. are dedicated for parallelization because of their basic algorithmic structure. The neighbourhood search, the computation of interaction forces and the final state update via time integration can be parallelized directly among the particles.

In order to evaluate the potential of such a GPU implementation compared to the single CPU execution, a parallel and hybrid implementation with OpenMP and CUDA has been developed for a special particle method, the so‐called mesoscopic particle method. This method takes into account mechanical as well as thermodynamical degrees of freedom. On the basis of a hybrid implementation, the performances on different types of execution architectures (sequential on single CPU core, parallel on multi‐core CPU, parallel on GPU) can be determined and compared. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Well‐posedness and Conservativity for Linear Control Systems (Part 1)
Authors: Picard Rainer , Trostorff Sascha , Waurick Marcus
Published: December 2012

We discuss a class of linear control systems in a Hilbert space setting. The aim is to show that these control systems fit in a particular class of evolutionary equations such that the discussion of well‐posedness becomes easily accessible. We exemplify our findings by a system with unbounded control and observation operator. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Uncertainty Quantification in numerical Aerodynamic via low‐rank Response Surface
Authors: Litvinenko Alexander , Matthies Hermann G.
Published: December 2012

With the example from numerical aerodynamic we illustrate how uncertainties in the input data: parameters and computational domain propagate into the solution. The mathematical model is described via a Navier‐Stokes system of equations with a k‐ω turbulence model. The computing domain is the RAE‐2822 airfoil. To reduce storage requirement and computing time, we introduce a low‐rank approximation of the whole set of realisations of the uncertain solution. This approximation allows us to compute a low‐rank approximation of the response surface and then perform post‐processing with a linear complexity and with drastically reduced memory requirements. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Approximation of the stochastic Galerkin matrix in the low‐rank canonical tensor format
Authors: Wähnert Philipp , Litvinenko Alexander , Espig Mike , Matthies Hermann G. , Hackbusch Wolfgang
Published: December 2012

In this article we describe an efficient approximation of the stochastic Galerkin matrix which stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed to be a log‐normal random field with given covariance and mean functions. The approximation is done in the canonical tensor format and then compared numerically with the tensor train and hierarchical tensor formats. It will be shown that under additional assumptions the approximation error depends only on smoothness of the covariance function and does not depend either on the number of random variables nor the degree of the multivariate Hermite polynomials. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Two model formulations for gradient crystal plasticity
Authors: Klusemann Benjamin , Bargmann Swantje , Svendsen Bob
Published: December 2012

The purpose of the current work is the formulation of two different (algorithmic) models for multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The two models are compared with each other, depending in particular on how the inelastic deformation and dislocation density are modeled. The work is a first extension of the investigation in Klusemann et al. [1] to two‐dimensions. In the first model, the corresponding displacement and inelastic local deformation are modeled as global via weak field relations, and the dislocation density is a local quantity and solved for via a strong field relation. In the second model, displacement and dislocation density are modeled as global, and the inelastic deformation as local, in this sense. The influence for the modeling results is discussed. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Production simulation by means of a structure tensor‐based framework of anisotropic plasticity
Authors: Vladimirov Ivaylo N. , Reese Stefanie
Published: December 2012

In this work, we discuss a hyperelasticity‐based concept of finite strain plasticity with combined hardening using evolving structure tensors to represent the evolution of elastic and plastic anisotropy. By defining the Helmholtz free energy density and the yield surface as functions of the evolving structure tensors, we are able to describe both evolving elastic and plastic anisotropy, respectively. The model considers also nonlinear kinematic and isotropic hardening and is derived from a thermodynamic framework based on the multiplicative split of the deformation gradient. Exploiting the dissipation inequality leads to the important result that the model includes only symmetric tensor‐valued internal variables. Evolution of anisotropy is investigated by means of simulations of cylindrical deep drawing of metal sheets. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Reduction of Plasticizer Leaching from PVC by Barrier Coatings Deposited Using DBD Processes at Atmospheric Pressure
Authors: Barreto Mercedes Cerezuela , Borris Jochen , Thomas Michael , Hänsel Renate , Stoll Michael , Klages Claus‐Peter
Published: December 2012

Barrier coatings against plasticizer leaching are deposited on flexible polyvinylchloride (PVC) films typically used in flooring or in the automotive industry. Octamethylcyclotetrasiloxane (OMCTS) and hexamethyldisiloxane (HMDSO) are plasma polymerized using plasma‐activated CVD (PA‐CVD) based on an atmospheric pressure (AP) dielectric barrier discharge (DBD). A reduction in plasticizer leaching higher than 80% is achieved with these coatings. The effect of the monomer flow rate, discharge power, and oxygen flow rate on the barrier efficiency is investigated. The coating composition of the best barrier coating has been identified and the long‐time barrier efficiency in contact with an organic solvent has been studied.

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