Publikationen nach Jahren

This paper is concerned with the numerical examination of acoustically driven flows within the inner ear on the basis of a computational model. For this purpose, a comprehensive system of differential equations and boundary conditions is deduced, which takes, to a satisfactory extent, the complexity of the main biophysical mechanisms of the cochlea into account. Beside an appropriate representation of the fluid dynamics, also the biomechanical properties of the basilar membrane as well as the internal amplification mechanism caused by the outer hair cell motility are considered in order to get realistic estimates of the structure and magnitude of the mean flow field. The present paper introduces a two-stage approach for the numerical evaluation of the solutions on the basis of the finite element method. The first step deals with the calculation of the linear acoustic reaction whereas the second step is associated with the determination of a first-order approximation of the acoustic streaming field. It is shown that the results are essentially consistent with measurements as well as analytical and experimental considerations. In addition, the numerical estimates of the acoustically driven flows provide an instrument for a more profound discussion on their physiological impact. Keywords: Acoustic streaming; cochlea; fluid-structure interaction.

In the present work, we extend the theoretical and numerical discussion of the well-known Laplace–Beltrami operator by equipping the underlying manifolds with additional structure provided by vector bundles. Focusing on the particular class of flat complex line bundles, we examine a whole family of Laplacians including the Laplace–Beltrami operator as a special case. To demonstrate that our proposed approach is numerically feasible, we describe a robust and efficient finite-element discretization, supplementing the theoretical discussion with first numerical spectral decompositions of those Laplacians.

Our method is based on the concept of introducing complex phase discontinuities into the finite element basis functions across a set of homology generators of the given manifold. More precisely, given an m-dimensional manifold M and a set of n generators that span the relative homology group H_m-1(M, ∂ M), we have the freedom to choose n phase shifts, one for each generator, resulting in a n-dimensional family of Laplacians with associated spectra and eigenfunctions. The spectra and absolute magnitudes of the eigenfunctions are not influenced by the exact location of the paths, depending only on their corresponding homology classes.

Employing our discretization technique, we provide and discuss several interesting computational examples highlighting special properties of the resulting spectral decompositions. We examine the spectrum, the eigenfunctions and their zero sets which depend continuously on the choice of phase shifts.

The well-known Laplace-Beltrami operator, established as a basic tool in shape processing, builds on a long history of mathematical investigations that have induced several numerical models for computational purposes. However, the Laplace-Beltrami operator is only one special case of many possible generalizations that have been researched theoretically. Thereby it is natural to supplement some of those extensions with concrete computational frameworks. In this work we study a particularly interesting class of extended Laplacians acting on sections of flat line bundles over compact Riemannian manifolds. Numerical computations for these operators have recently been accomplished on two-dimensional surfaces. Using the notions of line bundles and differential forms, we follow up on that work giving a more general theoretical and computational account of the underlying ideas and their relationships. Building on this we describe how the modified Laplacians and the corresponding computations can be extended to three-dimensional Riemannian manifolds, yielding a method that is able to deal robustly with volumetric objects of intricate shape and topology. We investigate and visualize the two-dimensional zero sets of the first eigenfunctions of the modified Laplacians, yielding an approach for constructing characteristic well-behaving, particularly robust homology generators invariant under isometric deformation. The latter include nicely embedded Seifert surfaces and their non-orientable counterparts for knot complements.

We introduce the 3D-segmentation and -visualization software YaDiV to the mineralogical application of rock texture analysis. YaDiV has been originally designed to process medical DICOM datasets. But due to software advancements and additional plugins, this open-source software can now be easily used for the fast quantitative morphological characterization of geological objects from tomographic datasets.In this paper, we give a summary of YaDiV's features and demonstrate the advantages of 3D-stereographic visualization and the accuracy of 3D-segmentation for the analysis of geological samples. For this purpose, we present a virtual and a real use case (here: experimentally crystallized and vesiculated magmatic rocks, corresponding to the composition of the 1991-1995 Unzen eruption, Japan). Especially the spacial representation of structures in YaDiV allows an immediate, intuitive understanding of the 3D-structures, which may not become clear by only looking on 2D-images. We compare our results of object number density calculations with the established classical stereological 3D-correction methods for 2D-images and show that it was possible to achieve a seriously higher quality and accuracy.The methods described in this paper are not dependent on the nature of the object. The fact, that YaDiV is open-source and users with programming skills can create new plugins themselves, may allow this platform to become applicable to a variety of geological scenarios from the analysis of textures in tiny rock samples to the interpretation of global geophysical data, as long as the data are provided in tomographic form.

In hot die forging processes, the selection of an ideal preform is of great importance with respect to cavity filling and mechanical load. The common procedure in order to define an adequate preform is the usage of Finite-Element-Analysis (FEA), usually as an iterative process in which various preforms are tested with regard to their suitability. An approach that aims at reducing the number of trials by proposing a first estimation of a suitable preform is presented in this paper. It is conjectured that the material flow paths and resistance can be described by the cavity shape using the Medial Axis Transformation. Based on this, a local inverse material flow for time discrete steps is calculated. The result is a first estimation of an adequate preform shape within a few minutes as an input for further FEA. FE-based parametric design optimization procedure is then presented and compared to the inverse approach, which is identified as a useful complement for the forward simulation technique.

Editorial of the special edition of The Visual Computer, which contains the best 35 papers of the Computer Graphics International 2013 (CGI 2013) held in Hanover, at the Leibniz University of Hanover in Germany.

In this paper we present a novel haptic rendering method for exploration of volumetric data. It addresses a recurring flaw in almost all related approaches, where the manipulated object, when moved too quickly, can go through or inside an obstacle. Additionally, either a specific topological structure for the collision objects is needed, or extra speed-up data structures should be prepared. These issues could make it difficult to use a method in practice. Our approach was designed to be free of such drawbacks. An improved version of the method presented here does not have the issues of the original method – oscillations of the interaction point and wrong friction force in some cases. It uses the ray casting technique for collision detection and a path finding approach for rigid collision response. The method operates directly on voxel data and does not use any precalculated structures, but uses an implicit surface representation being generated on the fly. This means that a virtual scene may be both dynamic or static. Additionally, the presented approach has a nearly constant time complexity independent of data resolution.

We introduce the 3D-segmentation and -visualization software YaDiV to the mineralogical application of rock texture analysis. YaDiV has been originally designed to process medical DICOM datasets. But due to software advancements and additional plugins, this open-source software can now be easily used for the fast quantitative morphological characterization of geological objects from tomographic datasets. In this paper, we give a summary of YaDiV's features and demonstrate the advantages of 3D-stereographic visualization and the accuracy of 3D-segmentation for the analysis of geological samples. For this purpose, we present a virtual and a real use case (here: experimentally crystallized and vesiculated magmatic rocks, corresponding to the composition of the 1991–1995 Unzen eruption, Japan). Especially the spacial representation of structures in YaDiV allows an immediate, intuitive understanding of the 3D-structures, which may not become clear by only looking on 2D-images. We compare our results of object number density calculations with the established classical stereological 3D-correction methods for 2D-images and show that it was possible to achieve a seriously higher quality and accuracy. The methods described in this paper are not dependent on the nature of the object. The fact, that YaDiV is open-source and users with programming skills can create new plugins themselves, may allow this platform to become applicable to a variety of geological scenarios from the analysis of textures in tiny rock samples to the interpretation of global geophysical data, as long as the data are provided in tomographic form.

Both future air traffic management programs SESAR and NextGen foresee trajectory based operations as one of the major enablers for more efficient handling of air traffic. Furthermore, both initiatives claim to support user preferred trajectories. Using a common airspace it is unlikely to get a conflict-free scenario from independently optimized preferred trajectories. This paper investigates if the concept of user preferred trajectories is feasible, and what constraints are necessary to reach a conflict-free global scenario. Restricting aircraft’s trajectories a priori by forcing them to fly on pre-defined en-route segments, respect semi-circular routes, or apply given departure and arrival times reduces the achievable efficiency, but helps to avoid conflicts and keep the concept simple. On the other hand, trying to combine independently optimized trajectories to a full traffic scenario needs a lot of adaptations to achieve conflict-free operations. Even though the good answer to a problem lies often in-between the extreme solutions, this paper investigates the second approach. Based on a real day of actual traffic over Europe, an optimized sample is generated applying user’s preferred trajectory for each flight. Based on an individually optimized traffic scenario yielding nearly 29,000 conflicts, strategic resolution is performed generating least possible penalties for involved aircraft. The main technique of solving conflicts applied is shifting whole flights in time by a few minutes. Direct and recursive algorithms are presented; a focus is put on solving airport-related conflicts first. The efficiency of the original optimized scenario stays untouched, as lateral, vertical, and speed profiles remain identical; flights are only rescheduled to a slightly earlier or later departure (and arrival) slot in order to minimize conflicts. More than 94% of all conflicts can be solved by shifting whole flights in time respecting a maximum offset of 10 minutes. In a subsequent step, lateral and vertical maneuvers are facilitated; resulting in a resolution for more than 97% of all conflicts.