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In this paper a three dimensional stochastic model for the lay-down of fibers on a moving conveyor belt in the production process of nonwoven materials is derived. The model is based on stochastic diferential equations describing the resulting position of the fiber on the belt under the influence of turbulent air ows. The model presented here is an extension of an existing surrogate model, see [6, 3].

A theory of discrete Cosserat rods is formulated in the language of discrete Lagrangian mechanics. By exploiting Kirchho's kinetic analogy, the potential energy density of a rod is a function on the tangent bundle of the conguration manifold and thus formally corresponds to the Lagrangian function of a dynamical system. The equilibrium equations are derived from a variational principle using a formulation that involves null{space matrices. In this formulation, no Lagrange multipliers are necessary to enforce orthonormality of the directors. Noether's theorem relates rst integrals of the equilibrium equations to Lie group actions on the conguration bundle, so{called symmetries. The symmetries relevant for rod mechanics are frame{indierence, isotropy and uniformity. We show that a completely analogous and self{contained theory of discrete rods can be formulated in which the arc{length is a discrete variable ab initio. In this formulation, the potential energy density is dened directly on pairs of points along the arc{length of the rod, in analogy to Veselov's discrete reformulation of Lagrangian mechanics. A discrete version of Noether's theorem then identies exact rst integrals of the discrete equilibrium equations. These exact conservation properties confer the discrete solutions accuracy and robustness, as demonstrated by selected examples of application. Copyright c 2010 John Wiley & Sons, Ltd.

A prime motivation for using XML to directly represent pieces of information is the ability of supporting ad-hoc or 'schema-later' settings. In such scenarios, modeling data under loose data constraints is essential. Of course, the flexibility of XML comes at a price: the absence of a rigid, regular, and homogeneous structure makes many aspects of data management more challenging. Such malleable data formats can also lead to severe information quality problems, because the risk of storing inconsistent and incorrect data is greatly increased. A prominent example of such problems is the appearance of the so-called fuzzy duplicates, i.e., multiple and non-identical representations of a real-world entity. Similarity joins correlating XML document fragments that are similar can be used as core operators to support the identification of fuzzy duplicates. However, similarity assessment is especially difficult on XML datasets because structure, besides textual information, may exhibit variations in document fragments representing the same real-world entity. Moreover, similarity computation is substantially more expensive for tree-structured objects and, thus, is a serious performance concern. This thesis describes the design and implementation of an effective, flexible, and high-performance XML-based similarity join framework. As main contributions, we present novel structure-conscious similarity functions for XML trees - either considering XML structure in isolation or combined with textual information -, mechanisms to support the selection of relevant information from XML trees and organization of this information into a suitable format for similarity calculation, and efficient algorithms for large-scale identification of similar, set-represented objects. Finally, we validate the applicability of our techniques by integrating our framework into a native XML database management system; in this context we address several issues around the integration of similarity operations into traditional database architectures.

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6.

The modelling of hedge funds poses a difficult problem since the available reported data sets are often small and incomplete. We propose a switching regression model for hedge funds, in which the coefficients are able to switch between different regimes. The coefficients are governed by a Markov chain in discrete time. The different states of the Markov chain represent different states of the economy, which influence the performance of the independent variables. Hedge fund indices are chosen as regressors. The parameter estimation for the switching parameter as well as for the switching error term is done through a filtering technique for hidden Markov models developed by Elliott (1994). Recursive parameter estimates are calculated through a filter-based EM-algorithm, which uses the hidden information of the underlying Markov chain. Our switching regression model is applied on hedge fund series and hedge fund indices from the HFR database.

Wireless sensor networks are the driving force behind many popular and interdisciplinary research areas, such as environmental monitoring, building automation, healthcare and assisted living applications. Requirements like compactness, high integration of sensors, flexibility, and power efficiency are often very different and cannot be fulfilled by state-of-the-art node platforms at once. In this paper, we present and analyze AmICA: a flexible, compact, easy-to-program, and low-power node platform. Developed from scratch and including a node, a basic communication protocol, and a debugging toolkit, it assists in an user-friendly rapid application development. The general purpose nature of AmICA was evaluated in two practical applications with diametric requirements. Our analysis shows that AmICA nodes are 67% smaller than BTnodes, have five times more sensors than Mica2Dot and consume 72% less energy than the state-of-the-art TelosB mote in sleep mode.

Wireless Sensor Networks (WSN) are dynamically-arranged networks typically composed of a large number of arbitrarily-distributed sensor nodes with computing capabilities contributing to –at least– one common application. The main characteristic of these networks is that of being functionally constrained due to a scarce availability of resources and strong dependence on uncontrollable environmental factors. These conditions introduce severe restrictions on the applicability of classic real-time methods aiming at guaranteeing time-bounded communications. Existing real-time solutions tend to apply concepts that were originally not conceived for sensor networks, idealizing realistic application scenarios and overlooking at important design limitations. This results in a number of misleading practices contributing to approaches of restricted validity in real-world scenarios. Amending the confrontation between WSNs and real-time objectives starts with a review of the basic fundamentals of existing approaches. In doing so, this thesis presents an alternative approach based on a generalized timeliness notion suitable to the particularities of WSNs. The new conceptual notion allows the definition of feasible real-time objectives opening a new scope of possibilities not constrained to idealized systems. The core of this thesis is based on the definition and application of Quality of Service (QoS) trade-offs between timeliness and other significant QoS metrics. The analysis of local and global trade-offs provides a step-by-step methodology identifying the correlations between these quality metrics. This association enables the definition of alternative trade-off configurations (set points) influencing the quality performance of the network at selected instants of time. With the basic grounds established, the above concepts are embedded in a simple routing protocol constituting a proof of concept for the validity of the presented analysis. Extensive evaluations under realistic scenarios are driven on simulation environments as well as real testbeds, validating the consistency of this approach.

It has been observed that for understanding the biological function of certain RNA molecules, one has to study joint secondary structures of interacting pairs of RNA. In this thesis, a new approach for predicting the joint structure is proposed and implemented. For this, we introduce the class of m-dimensional context-free grammars --- an extension of stochastic context-free grammars to multiple dimensions --- and present an Earley-style semiring parser for this class. Additionally, we develop and thoroughly discuss an implementation variant of Earley parsers tailored to efficiently handle dense grammars, which embraces the grammars used for structure prediction. A currently proposed partitioning scheme for joint secondary structures is transferred into a two-dimensional context-free grammar, which in turn is used as a stochastic model for RNA-RNA interaction. This model is trained on actual data and then used for predicting most likely joint structures for given RNA molecules. While this technique has been widely used for secondary structure prediction of single molecules, RNA-RNA interaction was hardly approached this way in the past. Although our parser has O(n^3 m^3) time complexity and O(n^2 m^2) space complexity for two RNA molecules of sizes n and m, it remains practically applicable for typical sizes if enough memory is available. Experiments show that our parser is much more efficient for this application than classical Earley parsers. Moreover the predictions of joint structures are comparable in quality to current energy minimization approaches.

Annual Report 2009
(2010)

Annual Report, Jahrbuch AG Magnetismus

This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work.