## Fraunhofer (ITWM)

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#### Year of publication

- 2008 (16) (remove)

#### Keywords

- energy minimization (2)
- 3d imaging (1)
- Asymptotic homogenization (1)
- Electrophysiology (1)
- Eulerian-Lagrangian formulation (1)
- FETI (1)
- Gradual Covering (1)
- Heuristics (1)
- Integer programming (1)
- Kirchhoff\\\'s geometrically theory (1)

We develop a framework for analyzing an executive’s own-company stockholding and work effort preferences. The executive, characterized by risk aversion and work effectiveness parameters, invests his personal wealth without constraint in the financial market, including the stock of his own company whose value he can directly influence with work effort. The executive’s utility-maximizing personal investment and work effort strategy is derived in closed-form, and an indifference utility rationale is demonstrated to determine his required compensation. Our results have implications for the practical and theoretical assessment of executive quality and the benefits of performance contracting. Assuming knowledge of the company’s non-systematic risk, our executive’s unconstrained own-company investment identifies his work effectiveness (i.e. quality), and also reflects work effort that establishes a base-level that performance contracting should seek to exceed.

We propose a constraint-based approach for the two-dimensional rectangular packing problem with orthogonal orientations. This problem is to arrange a set of rectangles that can be rotated by 90 degrees into a rectangle of minimal size such that no two rectangles overlap. It arises in the placement of electronic devices during the layout of 2.5D System-in-Package integrated electronic systems. Moffitt et al. [8] solve the packing without orientations with a branch and bound approach and use constraint propagation. We generalize their propagation techniques to allow orientations. Our approach is compared to a mixed-integer program and we provide results that outperform it.

Open cell foams are a promising and versatile class of porous materials. Open metal foams serve as crash absorbers and catalysts, metal and ceramic foams are used for filtering, and open polymer foams are hidden in every-day-life items like mattresses or chairs. Due to their high porosity, classical 2d quantitative analysis can give only very limited information about the microstructure of open foams. On the other hand, micro computed tomography (μCT) yields high quality 3d images of open foams. Thus 3d imaging is the method of choice for open cell foams. In this report we summarise a variety of methods for the analysis of the resulting volume images of open foam structures developed or refined and applied at the Fraunhofer ITWM over a course of nearly ten years: The model based determination of mean characteristics like the mean cell volume or the mean strut thickness demanding only a simple binarisation as well as the image analytic cell reconstruction yielding empirical distributions of cell characteristics.

The problem discussed in this paper is motivated by the new recycling directiveWEEE of the EC. The core of this law is, that each company which sells electrical or electronic equipment in a European country has the obligation to recollect and recycle an amount of returned items which is proportional to its market share. To assign collection stations to companies, in Germany for one product type a territory design approach is planned. However, in contrast to classical territory design, the territories should be geographically as dispersed as possible to avoid that a company, resp. its logistics provider responsible for the recollection, gains a monopoly in some region. First, we identify an appropriate measure for the dispersion of a territory. Afterwards, we present a first mathematical programming model for this new problem as well as a solution method based on the GRASP methodology. Extensive computational results illustrate the suitability of the model and assess the effectiveness of the heuristic.

A Lattice Boltzmann Method for immiscible multiphase flow simulations using the Level Set Method
(2008)

We consider the lattice Boltzmann method for immiscible multiphase flow simulations. Classical lattice Boltzmann methods for this problem, e.g. the colour gradient method or the free energy approach, can only be applied when density and viscosity ratios are small. Moreover, they use additional fields defined on the whole domain to describe the different phases and model phase separation by special interactions at each node. In contrast, our approach simulates the flow using a single field and separates the fluid phases by a free moving interface. The scheme is based on the lattice Boltzmann method and uses the level set method to compute the evolution of the interface. To couple the fluid phases, we develop new boundary conditions which realise the macroscopic jump conditions at the interface and incorporate surface tension in the lattice Boltzmann framework. Various simulations are presented to validate the numerical scheme, e.g. two-phase channel flows, the Young-Laplace law for a bubble and viscous fingering in a Hele-Shaw cell. The results show that the method is feasible over a wide range of density and viscosity differences.

The theory of the two-scale convergence was applied to homogenization of elasto-plastic composites with a periodic structure and exponential hardening law. The theory is based on the fact that the elastic as well as the plastic part of the stress field two-scale converges to a limit, which is factorized by parts, depending only on macroscopic characteristics, represented in terms of corresponding part of the homogenised stress tensor and only on stress concentration tensor, related to the micro-geometry and elastic or plastic micro-properties of composite components. The theory was applied to metallic matrix material with Ludwik and Hocket-Sherby hardening law and pure elastic inclusions in two numerical examples. Results were compared with results of mechanical averaging based on the self-consistent methods.

This paper introduces methods for the detection of anisotropies which are caused by compression of regular three-dimensional point patterns. Isotropy tests based on directional summary statistics and estimators for the compression factor are developed. These allow not only for the detection of anisotropies but also for the estimation of their strength. Using simulated data the power of the methods and the dependence of the power on the intensity, the degree of regularity, and the compression strength are studied. The motivation of this paper is the investigation of anisotropies in the structure of polar ice. Therefore, our methods are applied to the point patterns of centres of air pores extracted from tomographic images of ice cores. This way the presence of anisotropies in the ice caused by the compression of the ice sheet as well as an increase of their strength with increasing depth are shown.

Abstract. An efficient approach to the numerical upscaling of thermal conductivities of fibrous media, e.g. insulation materials, is considered. First, standard cell problems for a second order elliptic equation are formulated for a proper piece of random fibrous structure, following homogenization theory. Next, a graph formed by the fibers is considered, and a second order elliptic equation with suitable boundary conditions is solved on this graph only. Replacing the boundary value problem for the full cell with an auxiliary problem with special boundary conditions on a connected subdomain of highly conductive material is justified in a previous work of the authors. A discretization on the graph is presented here, and error estimates are provided. The efficient implementation of the algorithm is discussed. A number of numerical experiments is presented in order to illustrate the performance of the proposed method.

Determination of interaction between MCT1 and CAII via a mathematical and physiological approach
(2008)

The enzyme carbonic anhydrase isoform II (CAII), catalysing the hydration and dehydration of CO2, enhances transport activity of the monocarboxylate transporter isoform I (MCT1, SLC16A1) expressed in Xenopus oocytes by a mechanism that does not require CAII catalytic activity (Becker et al. (2005) J. Biol. Chem., 280). In the present study, we have investigated the mechanism of the CAII induced increase in transport activity by using electrophysiological techniques and a mathematical model of the MCT1 transport cycle. The model consists of six states arranged in cyclic fashion and features an ordered, mirror-symmetric, binding mechanism were binding and unbinding of the proton to the transport protein is considered to be the rate limiting step under physiological conditions. An explicit rate expression for the substrate °ux is derived using model reduction techniques. By treating the pools of intra- and extracellular MCT1 substrates as dynamic states, the time dependent kinetics are obtained by integration using the derived expression for the substrate °ux. The simulations were compared with experimental data obtained from MCT1-expressing oocytes injected with di®erent amounts of CAII. The model suggests that CAII increases the e®ective rate constants of the proton reactions, possibly by working as a proton antenna.

In this paper, the analysis of one approach for the regularization of pure Neumann problems for second order elliptical equations, e.g., Poisson’s equation and linear elasticity equations, is presented. The main topic under consideration is the behavior of the condition number of the regularized problem. A general framework for the analysis is presented. This allows to determine a form of regularization term which leads to the “natural” asymptotic of the condition number of the regularized problem with respect to mesh parameter. Some numerical results, which support theoretical analysis are presented as well. The main motivation for the presented research is to develop theoretical background for an efficient and robust implementation of the solver for pure Neumann problems for the linear elasticity equations. Such solvers usually are needed in a number of domain decomposition methods, e.g. FETI. Developed approaches are planed to be used in software, developing in ITWM, e.g. KneeMech simulation software.