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The fact that long fibre reinforced thermoplastic composites (LFT) have higher tensile
strength, modulus and even toughness, compared to short fibre reinforced
thermoplastics with the same fibre loading has been well documented in literature.
These are the underlying factors that have made LFT materials one of the most
rapidly growing sectors of plastics industry. New developments in manufacturing of
LFT composites have led to improvements in mechanical properties and price
reduction, which has made these materials an attractive choice as a replacement for
metals in automobile parts and other similar applications. However, there are still
several open scientific questions concerning the material selection leading to the
optimal property combinations. The present work is an attempt to clarify some of
these questions. The target was to develop tools that can be used to modify, or to
“tailor”, the properties of LFT composite materials, according to the requirements of
automobile and other applications.
The present study consisted of three separate case studies, focusing on the current
scientific issues on LFT material systems. The first part of this work was focused on
LGF reinforced thermoplastic styrenic resins. The target was to find suitable maleic
acid anhydride (MAH) based coupling agents in order to improve the fibre-matrix
interfacial strength, and, in this way, to develop an LGF concentrate suitable for
thermoplastic styrenic resins. It was shown that the mechanical properties of LGF
reinforced “styrenics” were considerably improved when a small amount of MAH
functionalised polymer was added to the matrix. This could be explained by the better fibre-matrix adhesion, revealed by scanning electron microscopy of fracture surfaces.
A novel LGF concentrate concept showed that one particular base material can be
used to produce parts with different mechanical and thermal properties by diluting the
fibre content with different types of thermoplastic styrenic resins. Therefore, this
concept allows a flexible production of parts, and it can be used in the manufacturing
of interior parts for automobile components.The second material system dealt with so called hybrid composites, consisting of
long glass fibre reinforced polypropylene (LGF-PP) and mineral fillers like calcium
carbonate and talcum. The aim was to get more information about the fracture
behaviour of such hybrid composites under tensile and impact loading, and to
observe the influence of the fillers on properties. It was found that, in general, the
addition of fillers in LGF-PP, increased stiffness but the strength and fracture
toughness were decreased. However, calcium carbonate and talcum fillers resulted
in different mechanical properties, when added to LGF-PP: better mechanical
properties were achieved by using talcum, compared to calcium carbonate. This
phenomenon could be explained by the different nucleation effect of these fillers,
which resulted in a different crystalline morphology of polypropylene, and by the
particle orientation during the processing when talc was used. Furthermore, the
acoustic emission study revealed that the fracture mode of LGF-PP changed when
calcium carbonate was added. The characteristic acoustic signals revealed that the
addition of filler led to the fibre debonding at an earlier stage of fracture sequence
when compared to unfilled LGF-PP.
In the third material system, the target was to develop a novel long glass fibre
reinforced composite material based on the blend of polyamide with thermoset
resins. In this study a blend of polyamide-66 (PA66) and phenol formaldehyde resin
(PFR) was used. The chemical structure of the PA66-PFR resin was analysed by
using small molecular weight analogues corresponding to PA66 and PFR
components, as well as by carrying out experiments using the macromolecular
system. Theoretical calculations and experiments showed that there exists a strong
hydrogen bonding between the carboxylic groups of PA66 and the hydroxylic groups
of PFR, exceeding even the strength of amide-water hydrogen bonds. This was
shown to lead to the miscible blends, when PFR was not crosslinked. It was also
found that the morphology of such thermoplastic-thermoset blends can be controlled
by altering ratio of blend components (PA66, PFR and crosslinking agent). In the
next phase, PA66-PFR blends were reinforced by long glass fibres. The studies
showed that the water absorption of the blend samples was considerably decreased,
which was also reflected in higher mechanical properties at equilibrium state.
Wie man aus zahlreichen Untersuchungen und Anwendungsbeispielen entnehmen
kann, besitzen langfaserverstärkte Thermoplaste (LFT) eine bessere Zugfestigkeit,
Biege- und Schlagzähigkeit im Vergleich zu kurzfaserverstärkten Thermoplasten. Die
Vorteile in den mechanischen Eigenschaften haben die LFT zu einem
schnellwachsenden Bereich in der Kunststoffindustrie gemacht. Neue Entwicklungen
in Bereich der Herstellung von LFT haben für zusätzliche Verbesserungen der
mechanischen Eigenschaften sowie eine Preisreduzierung der Materialien in den
vergangenen Jahren gesorgt, was die LFT zu einer attraktiven Wahl u.a. als Ersatz
von Metallen in Automobilteilen macht. Es stellen sich allerdings immer noch einige
offene wissenschaftliche Fragen in Bezug auf z.B. die Materialbeschaffenheit, um
optimale Eigenschaftskombinationen zu erreichen. Die vorliegende Arbeit versucht,
einige dieser Fragen zu beantworten. Ziel war es, Vorgehensweisen zu entwickeln,
mit denen man die Eigenschaften von LFT gezielt beeinflussen und so den
Anforderungen von Automobilen oder anderen Anwendungen anpassen oder
„maßschneidern“ kann.
Die vorliegende Arbeit besteht aus drei Teilen, welche sich auf unterschiedliche
Materialsysteme, angepasst an den aktuellen Bedarf und das Interesse der Industrie,
konzentrieren.
Der erste Teil der Arbeit richtet sich auf die Eigenschaftsoptimierung von
langglasfaserverstärkten (LGF) thermoplastischen Styrolcopolymeren und von
Blends aus diesen Materialien. Es wurden passende, auf Maleinsäureanhydride
(MAH) basierende Kopplungsmittel gefunden, um die Faser-Matrix-Haftung zu
optimieren. Weiterhin wurde ein LGF Konzentrat entwickelt, welches mit
verschiedenen thermoplastischen Styrolcopolymeren kompatibel ist und somit als
„Verstärkungsadditiv“ eingesetzt werden kann.Das Konzept für ein neues LGF-Konzentrat auf Basis des kompatiblen
Materialsystems konzentriert sich insbesondere darauf, dass ein Basismaterial für
die Herstellung von Bauteilen bereit gestellt werden kann, mit dessen Hilfe gezielt
verschiedene mechanische und thermomechanischen Eigenschaften durch das
Zumischen von verschiedenen Styrolcopoylmeren und Blends verbessert werden
können. Dieses Konzept ermöglicht eine sehr flexible Produktion von Bauteilen und
wird seine Anwendung bei der Herstellung von Bauteilen u.a. im Interieur von Autos
finden.
Das zweite Materialsystem basiert auf sogenannten hybriden Verbundwerkstoffen,
welche aus Langglasfasern und mineralischen Füllstoffen wie Kalziumkarbonat und
Talkum in einer Polypropylen (PP) - Matrix zusammengesetzt sind. Ziel war es, durch
detaillierte bruchmechanische Analysen genaue Informationen über das
Bruchverhalten dieser hybriden Verbundwerkstoffe bei Zug- und Schlagbelastung zu
bekommen, um dann die Unterschiede zwischen den verschiedenen Füllstoffen in
Bezug auf ihre Eigenschaften zu dokumentieren. Es konnte beobachtet werden, dass
bei Zugabe der Füllstoffe zum LGF-PP normalerweise die Steifigkeit weiter
verbessert wurde, jedoch die Festigkeit und Schlagzähigkeit abnahmen. Weiterhin
zeigten die verschiedenen Füllstoffe wie Kalziumkarbonat und Talkum
unterschiedliche mechanische Eigenschaften auf, wenn sie zusammen mit LGF
Verstärkung eingesetzt wurden: Bei der Zugabe von Talkum wurde u.a. eine deutlich
bessere Schlagzähigkeit als bei der Zugabe von Kalziumkarbonat festgestellt. Dieses
Phänomen konnte durch das unterschiedliche Nukleierungsverhalten des PPs erklärt
werden, welches in einer unterschiedlichen Kristallmorphologie von Polypropylen
resultierte. Weiterhin konnte man durch Messungen der akustischen Emmissionen
während der Zugbelastung eines bruchmechanischen Versuchskörpers aufzeigen,
dass die höhere Bruchzähigkeit von LGF-PP ohne Füllstoffe daraus resultiert, dass
Faser-Pullout schon bei geringeren Kräften vorhanden war.

Materials in general can be divided into insulators, semiconductors and conductors,
depending on their degree of electrical conductivity. Polymers are classified as
electrically insulating materials, having electrical conductivity values lower than 10-12
S/cm. Due to their favourable characteristics, e.g. their good physical characteristics,
their low density, which results in weight reduction, etc., polymers are also
considered for applications where a certain degree of conductivity is required. The
main aim of this study was to develop electrically conductive composite materials
based on epoxy (EP) matrix, and to study their thermal, electrical, and mechanical
properties. The target values of electrical conductivity were mainly in the range of
electrostatic discharge protection (ESD, 10-9-10-6 S/cm).
Carbon fibres (CF) were the first type of conductive filler used. It was established that
there is a significant influence of the fibre aspect ratio on the electrical properties of
the fabricated composite materials. With longer CF the percolation threshold value
could be achieved at lower concentrations. Additional to the homogeneous CF/EP
composites, graded samples were also developed. By the use of a centrifugation
method, the CF created a graded distribution along one dimension of the samples.
The effect of the different processing parameters on the resulting graded structures
and consequently on their gradients in the electrical and mechanical properties were
systematically studied.
An intrinsically conductive polyaniline (PANI) salt was also used for enhancing the
electrical properties of the EP. In this case, a much lower percolation threshold was
observed compared to that of CF. PANI was found out to have, up to a particular
concentration, a minimal influence on the thermal and mechanical properties of the
EP system.
Furthermore, the two above-mentioned conductive fillers were jointly added to the EP
matrix. Improved electrical and mechanical properties were observed by this
incorporation. A synergy effect between the two fillers took place regarding the
electrical conductivity of the composites.
The last part of this work was engaged in the application of existing theoretical
models for the prediction of the electrical conductivity of the developed polymer composites. A good correlation between the simulation and the experiments was
observed.
Allgemein werden Materialien in Bezug auf ihre elektrische Leitfähigkeit in Isolatoren,
Halbleiter oder Leiter unterteilt. Polymere gehören mit einer elektrischen Leitfähigkeit
niedriger als 10-12 S/cm in die Gruppe der Isolatoren. Aufgrund vorteilhafter
Eigenschaften der Polymere, wie z.B. ihren guten physikalischen Eigenschaften,
ihrer geringen Dichte, welche zur Gewichtsreduktion beiträgt, usw., werden Polymere
auch für Anwendungen in Betracht gezogen, bei denen ein gewisser Grad an
Leitfähigkeit gefordert wird. Das Hauptziel dieser Studie war, elektrisch leitende
Verbundwerkstoffe auf der Basis von Epoxidharz (EP) zu entwickeln und deren
elektrische, mechanische und thermische Eigenschaften zu studieren. Die Zielwerte
der elektrischen Leitfähigkeit lagen hauptsächlich im Bereich der Vermeidung
elektrostatischer Aufladungen (ESD, 10-9-10-6 S/cm).
Bei der Herstellung elektrisch leitender Kunststoffen wurden als erstes
Kohlenstofffasern (CF) als leitfähige Füllstoffe benutzt. Bei den durchgeführten
Experimenten konnte man beobachten, dass das Faserlängenverhältnis einen
bedeutenden Einfluss auf die elektrischen Eigenschaften der fabrizierten
Verbundwerkstoffe hat. Mit längeren CF wurde die Perkolationsschwelle bereits bei
einer niedrigeren Konzentration erreicht. Zusätzlich zu den homogenen CF/EP
Verbundwerkstoffen, wurden auch Gradientenwerkstoffe entwickelt. Mit Hilfe einer
Zentrifugation konnte eine gradierte Verteilung der CF entlang der Probenlängeachse
erreicht werden. Die Effekte der unterschiedlichen Zentrifugationsparameter
auf die resultierenden Gradientenwerkstoffe und die daraus
resultierenden, gradierten elektrischen und mechanischen Eigenschaften wurden
systematisch studiert.
Ein intrinsisch leitendes Polyanilin-Salz (PANI) wurde auch für das Erhöhen der
elektrischen Eigenschaften des EP benutzt. In diesem Fall wurde eine viel niedrigere
Perkolationsschwelle verglichen mit der von CF beobachtet. Der Einsatz von PANI hat bis zu einer bestimmten Konzentration nur einen minimalen Einfluß auf die
thermischen und mechanischen Eigenschaften des EP Systems.
In einem dritte Schritt wurden die zwei oben erwähnten, leitenden Füllstoffe
gemeinsam der EP Matrix hinzugefügt. Erhöhte elektrische und mechanische
Eigenschaften wurden in diesem Fall beobachtet, wobei sich ein Synergie-Effekt
zwischen den zwei Füllstoffen bezogen auf die elektrische Leitfähigkeit der
Verbundwerkstoffe ergab.
Im letzten Teil dieser Arbeit fand die Anwendung von theoretischen Modelle zur
Vorhersage der elektrischen Leitfähigkeit der entwickelten Verbundwerkstoffe statt.
Dabei konnte eine gute Übereinstimmung mit den experimentellen Ergebnissen
festgestellt werden .

We present a methodology to augment system safety step-by-step and illustrate the approach by the definition of reusable solutions for the detection of fail-silent nodes - a watchdog and a heartbeat. These solutions can be added to real-time system designs, to protect against certain types of system failures. We use SDL as a system design language for the development of distributed systems, including real-time systems.

We propose a framework for the synthesis of temporal logic programs which are formulated in a simple temporal logic programming language from both positive and negative examples. First we will prove that results from the theory of first order inductive logic programming carry over to the domain of temporal logic. After this we will show how programs formulated in the presented language can be generalized or specialized in order to satisfy the specification induced by the sets of examples.

Approximating illumination by point light sources, as done in many professional applications, suffers from the problem of the weak singularity: Numerical exceptions caused by the division by the squared distance between the point light source and the point to be illuminated must be avoided. Multiple importance sampling overcomes these problems by combining multiple sampling techniques by weights. Such a set of weights is called a heuristic. So far the estimators resulting from a heuristic only have been analyzed for variance. Since the cost of sampling is not at all constant for different sampling techniques, it is possible to find more efficient heuristics, even though they may hove higher variance. Based on our new stratification heuristic, we present a robust and unbiased global illumination algorithm. By numerical examples, we show that it is more efficient than previous heuristics. The algorithm is as simple as a path tracer, but elegantly avoids the problem of the weak singularity.

Today, test methods for communication protocols assume, among other things, that the protocol design is specified as a single, monolithic finite state machine (FSM). From this specification, test suites that are capable of detecting output and/or transfer faults in the protocol implementation are derived. Limited applicability ofthese methods is mainly because oftheir specific assumptions, and due to the size of the derived test suite and the resulting test effort for realistic protocols. In this work, the compositional test method (C-method), which exploits the available structure of a communication protocol, is proposed. The C-method first tests each protocol component separately for output and/or transfer faults, using one of the traditional test methods, then checks for composability, and finally tests the composite system for composition faults. To check for composability and to derive the test suite for the detection of composition faults, it is not required to construct the global state machine. Instead, all information is derived from the component state machines, which avoids a potential state explosion and lengthy test cases. Furthermore, the test suite checks for composition faults only. This substantially reduces the size of the test suite and thus the overall test effort.

Many applications dealing with geometry acquisition and processing produce polygonal meshes that carry artifacts like discretization noise. While there are many approaches to remove the artifacts by smoothing or filtering the mesh, they are not tailored to any specific application subject to·certain restrictive objectives. We show how to incorporate smoothing schemes based on the general Laplacian approximation to satsify all those objectives at
the same time for the results of flow simulation in the application field of car manufacturing. In the presented application setting the major restrictions come from the bounding volume of the flow simulation, the so-called installation space. In particular, clean mesh regions (without noise) should not be smoothed while at the same time the installation space must not be violated by the smoothing of the noisy mesh regions. Additionally, aliasing effects at the boundary between clean and noisy mesh regions must be prevented. To address the fact that the meshes come from flow simulation, the presented method is versatile enough to preserve their exact volume and to apply anisotropic filters using the flow information.
Although the paper focuses on the results of a specific application, most of its findings can be transferred to different settings as well.

The Chained Lin-Kernighan algorithm (CLK) is one of the best heuristics to solve Traveling Salesman Problems (TSP). In this paper a distributed algorithm is proposed, were nodes in a network locally optimize TSP instances by using the CLK algorithm. Within an Evolutionary Algorithm (EA) network-based framework the resulting tours are modified and exchanged with neighboring nodes. We show that the distributed variant finds better tours compared to the original CLK given the same amount of computation time. For instance fl3795, the original CLK got stuck in local optima in each of 10 runs, whereas the distributed algorithm found optimal tours in each run requiring less than 10 CPU minutes per node on average in an 8 node setup. For instance sw24978, the distributed algorithm had an average solution quality of 0.050% above the optimum, compared to CLK's average solution of 0.119% above the optimum given the same total CPU time (104 seconds). Considering the best tours of both variants for this instance, the distributed algorithm is 0.033% above the optimum and the CLK algorithm 0.099%.

In my doctoral thesis, I present new information about the developmental expression pattern of the potassium chloride cotransporter KCC2 in the rat auditory brain stem and the morphometrical effects caused by KCC2 gene silencing in mice. The thesis is divided into 3 Chapters. Chapter 1 is a general introduction which gives a brief outline of the primary ascending auditory pathway in mammals. Also, it provides information about the presence of a large number of inhibitory inputs in the auditory system and how these inputs develop; the involvement of inhibition in the acoustic processing is mentioned. In addition, the role of the KCC2 cotransporter in the shift of GABA/glycine transmission, and thus, in maintaining the normal level of inhibition in the mature brain, is described. The focus of Chapter 2 was to investigate the KCC2 immunofluorescent signal from postnatal day (P) 0 to P60 in four major nuclei of the rats superior olivary complex (SOC), namely the medial nucleus of the trapezoid body (MNTB), the medial superior olive (MSO), the lateral superior olive (LSO), and the superior paraolivary nucleus (SPN). The lack of a correlation between the continuous presence of KCC2 mRNA/protein in the postnatal rat brain stem on one side, and the shift in GABA/glycinergic polarity (i.e. KCC2 functionality) on the other side, prompted me to search for a specific cellular expression pattern of the KCC2 protein that might correlate with the switch in GABA/glycine signalling. To do so, the KCC2 immunoreactivity was analysed using high-resolution confocal microscopy in three cellular regions of interest: the soma surface, the soma interior, and the neuropil. In the soma surface, I observed an increase of the KCC2 immunofluorescent signal intensity, yet with a moderate magnitude (1.1 to 1.6-fold). Therefore, I conclude that the change in the soma surface signal is only of minor importance and does not explain the change in KCC2 functionality. The KCC2 signal intensity in the soma interior decreased in all nuclei (1.4 to 2-fold) with the exception of the MNTB where no statistically significant change was found. The decrease in the soma interior was probably related to the increase in the soma surface immunoreactivity and the proposed (weak) intracellular trafficking process of the KCC2 protein. The main developmental reorganization (in qualitative as well as in quantitative aspects) of the KCC2 immunofluorescence in the SOC nuclei was observed in the neuropil. The signal changed its pattern from a diffusely stained neuropil early in development (P0-P4) to a crisp and membrane-confined signal later on (P8-P60), with single dendrites becoming apparent. The exception was found in the MNTB, where the neuropil became almost unlabeled. Quantification revealed a statistically significant decrease (2.2 to 3.8-fold) in the neuropil immunoreactivity in all four nuclei, although the remaining KCC2-stained dendrites became thicker and the signal became stronger. I suppose that, at least in part, the neuropil reorganization can be explained by an age-related reduction of dendritic branches via a pruning mechanism and with the absence of an abnormal Cl- load via extrasynaptic GABAA receptors. This is consistent with the proposed additional role of KCC2, namely to maintain the cellular ionic homeostasis and to prevent dendritic swelling (Gulyás et al., 2001). In conclusion, neither the increase in the KCC2 soma surface signal intensity, nor the reorganization in the neuropil can be strictly related to the developmental switch in the GABA/glycine polarity and the onset of KCC2 function, although some correlation (the appearance of a specific membrane-confined dendritic pattern) between structure and function was found. Further implication of different molecular methods, regarding the proposed posttranslational modification of KCC2, will shed light upon the question of what leads to the functional activation of the cotransporter. In Chapter 3, the advantage of loss-of-function KCC2 mice made it possible, via manipulating the duration of the depolarizing phase of GABA/glycine transmission, to analyse the effect of disturbed Cl- regulation and, thus, the effect of disrupted GABA/glycine neurotransmission (lack of inhibition). I asked the following question: how important is the Cl- homeostasis to maintain general aspects (brain weight) and specific aspects (nucleus volume, neuron number, and soma cross-sectional area) of brain development? Brain stem slices from KCC2 knock-out animals (-/-), with a trace amount of transporter (~5%), as well as from wild type animals (+/+) at P3 and P12 were stained for Nissl substance and the analyses were performed with the help of basic morphometrical and stereological methods. In KCC2 (-/-) animals, body growth impairment was observed, in part related to the seizure activity preventing normal feeding (Woo et al., 2002). However, their brains, in terms of brain weight, were less affected. Therefore, I conclude that Cl- homeostasis is not essential per se to maintain the brain weight. Four auditory nuclei (MNTB, MSO, LSO, and ventral cochlear nucleus (VCN)), were compared with respect to the KCC2 null mutation. The SOC nuclei were not influenced by the lack of KCC2 at P3 considering the morphometric parameters. A difference in the number of neurons occurred in the VCN at P3. I suggest to perform additional immunohistochemical studies of glial presence related to its involvement in the structural and functional support of the neurons and their survival. At P12, the volume of the auditory nuclei in KCC2 (-/-) animals was smaller than in (+/+) animals. However, this is likely to be an epiphenomenon since the brain weight increase was also impaired with the same magnitude. Therefore, I suppose that the Cl- homeostasis is not crucial for the nucleus volume increase in the VCN, the MNTB and the MSO during development. An exception was found for the LSO. Regarding the other morphometric parameters at P12, the four nuclei behaved in a different way: (1) in the VCN, after P3, no parameter underwent a disproportional change due to impaired Cl- homeostasis; (2) the MNTB and the LSO showed less pronounced neuropil in mutants in comparison to age-matched controls and two reasons were proposed: first, the depolarizing GABA/glycine transmission in mutants may contribute to excessive Ca2+ load, excitotoxicity and dendrite damage; second, a decrease of some trophic factors may prevent dendrite development in addition to impaired normal body growth; (3) the MSO neurons in P12 (-/-) animals had smaller soma cross-sectional area than in P12 (+/+) animals. I conclude that the normal Cl- homeostasis is required in the MSO at older ages (P12) to achieve and maintain a proper soma size; (4) the lack of KCC2 did not prevent the process of neuronal differentiation in the VCN and the MNTB during development in both mutant and control animals. In conclusion, the various auditory nuclei have to be discussed independently regarding the influence of Cl- homeostasis on some morphometric parameters. Presumably, this is related to the different time of the shift in the GABA/glycine polarity i.e., the onset of KCC2 function (Srinivasan et al., 2004a). Taken together, my thesis accumulated data about the immunohistological expression pattern of KCC2 in various auditory brain stem nuclei and the influence of impaired Cl- homeostasis on some morphometric features in these nuclei. This information will be helpful for further investigations involved to discover the mechanisms and the events that govern the inhibition and the inhibitory pathway in the central auditory system.

Piezoelectric filters are used in telecommunication to filter electrical signals. This report deals with the problem of calculating passing and damped frequency intervals for a filter with given geometrical configurations and materials. Only periodic filters, which are widely used in practice, were considered. These filters consist of periodically arranged cells. For a small amount of cells a numerical procedure to visualise the wave propagation in the filter was developed. For a big number of cells another model of the filter was obtained. In this model it is assumed that the filter occupies an infinite domain. This leads to a differential equation, with periodic coefficients, that describes propagation of the wave with a given frequency in the filter. To analyse this equation the Spectral Theory for Periodic Operators had to be employed. Different ways -- analytical and numerical -- to apply the theory were proposed and analysed.

In this paper we introduce a multiscale technique for the analysis of deformation phenomena of the Earth. Classically, the basis functions under use are globally defined and show polynomial character. In consequence, only a global analysis of deformations is possible such that, for example, the water load of an artificial reservoir is hardly to model in that way. Up till now, the alternative to realize a local analysis can only be established by assuming the investigated region to be flat. In what follows we propose a local analysis based on tools (Navier scaling functions and wavelets) taking the (spherical) surface of the Earth into account. Our approach, in particular, enables us to perform a zooming-in procedure. In fact, the concept of Navier wavelets is formulated in such a way that subregions with larger or smaller data density can accordingly be modelled with a higher or lower resolution of the model, respectively.

Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial state (reference state) of the Boson field is either a normal state or a KMS state. The superselection sectors emerge if and only if the Boson field is infrared divergent, i. e. the bare photon number diverges and the ground state of the Boson field disappears in the continuum. The time scale of the decoherence depends on the strength of the infrared contributions of the interaction and on properties of the initial state of the Boson system. These results are first derived for a Hamiltonian with conservation laws. But in the most general case the Hamiltonian includes an additional scattering potential, and the only conserved quantity is the energy of the total system. The superselection sectors remain stable against the perturbation by the scattering processes.

Finite difference discretizations of 1D poroelasticity equations with discontinuous coefficients are analyzed. A recently suggested FD discretization of poroelasticity equations with constant coefficients on staggered grid, [5], is used as a basis. A careful treatment of the interfaces leads to harmonic averaging of the discontinuous coefficients. Here, convergence for the pressure and for the displacement is proven in certain norms for the scheme with harmonic averaging (HA). Order of convergence 1.5 is proven for arbitrary located interface, and second order convergence is proven for the case when the interface coincides with a grid node. Furthermore, following the ideas from [3], modified HA discretization are suggested for particular cases. The velocity and the stress are approximated with second order on the interface in this case. It is shown that for wide class of problems, the modified discretization provides better accuracy. Second order convergence for modified scheme is proven for the case when the interface coincides with a displacement grid node. Numerical experiments are presented in order to illustrate our considerations.

In traditional portfolio optimization under the threat of a crash the investment horizon or time to maturity is neglected. Developing the so-called crash hedging strategies (which are portfolio strategies which make an investor indifferent to the occurrence of an uncertain (down) jumps of the price of the risky asset) the time to maturity turns out to be essential. The crash hedging strategies are derived as solutions of non-linear differential equations which itself are consequences of an equilibrium strategy. Hereby the situation of changing market coefficients after a possible crash is considered for the case of logarithmic utility as well as for the case of general utility functions. A benefit-cost analysis of the crash hedging strategy is done as well as a comparison of the crash hedging strategy with the optimal portfolio strategies given in traditional crash models. Moreover, it will be shown that the crash hedging strategies optimize the worst-case bound for the expected utility from final wealth subject to some restrictions. Another application is to model crash hedging strategies in situations where both the number and the height of the crash are uncertain but bounded. Taking the additional information of the probability of a possible crash happening into account leads to the development of the q-quantile crash hedging strategy.

Inappropriate speed is the most common reason for road traffic accidents world wide. Thus, a necessity for speed management exists. The so-called SUNflower states Sweden, the United Kingdom and the Netherlands - each spending strong effort in traffic safety policies - have great success in reducing mean road speeds and speed variances through speed management. However, the effect is still insufficient for gaining real traffic safety. Thus, there is a discussion to make use of technical in-vehicle devices. One of these technologies called Intelligent Speed Adaptation (ISA) reduces vehicle speeds. This is done either by warning the driver that he is speeding, or activating the accelerator pedal with a counterforce, or reducing the gasoline supply to the motor. The three ways of reducing the speed are called version 1-3. The EC-project for research on speed adaptation policies on European roads (PROSPER) deals with strategic proposals for the implementation of the different ISA-versions. This thesis includes selected results of PROSPER. In this thesis two empiric surveys were done in order to give an overview about the basic conditions (e.g. social, economic, technical aspects) for an ISA implementation in Germany. On one hand, a stakeholder analysis and questionnaire using the Delphi-method has been accomplished in two rounds. On the other hand, a questionnaire with speed offenders has been accomplished, too, in two rounds. In addition, the author created an expert pool consisting of 23 experts representing the most important fields of science and practice in which ISA is involved. The author made phone or personal interviews with most of the experts. 12 experts also produced a detailed publication on their professional point of view towards ISA. The two surveys and the professional comments on ISA led to four possible implementation scenarios for ISA in Germany. However, due to a strong political opposition against ISA it is also thinkable that ISA is not implemented or the implementation process starts after 2015 (i.e. outside the aimed period of time). The scenarios are as follows: A) Implementation of version 1 by market forces with governmental subventions. B) Implementation of version 2 by market forces supported by traffic safety institutions and image-making processes. C) Implementation of a modified version 3 by law for speed offenders instead of cancellation of the driving licence. D) Implementation of various versions in Germany because of a broad implementation of ISA in the SUNflower states. X) Non-implementation of ISA leads to the necessity of alternative speed management measures. The author prefers scenario B because - ceteris paribus - it seems to be the most likely way to implement the technology. As soon as ISA reaches technical maturity, the implementation process has to be accomplished in three steps. 1) Marketing and image making 2) Margin introduction 3) Market penetration This implementation process for ISA by market forces could effect a percentage of at least 15% of all vehicles equipped with ISA before the year 2015.

Based on the well-known results of classical potential theory, viz. the limit and jump relations for layer integrals, a numerically viable and e±cient multiscale method of approximating the disturbing potential from gravity anomalies is established on regular surfaces, i.e., on telluroids of ellipsoidal or even more structured geometric shape. The essential idea is to use scale dependent regularizations of the layer potentials occurring in the integral formulation of the linearized Molodensky problem to introduce scaling functions and wavelets on the telluroid. As an application of our multiscale approach some numerical examples are presented on an ellipsoidal telluroid.

A spectral theory for constituents of macroscopically homogeneous random microstructures modeled as homogeneous random closed sets is developed and provided with a sound mathematical basis, where the spectrum obtained by Fourier methods corresponds to the angular intensity distribution of x-rays scattered by this constituent. It is shown that the fast Fourier transform applied to three-dimensional images of microstructures obtained by micro-tomography is a powerful tool of image processing. The applicability of this technique is is demonstrated in the analysis of images of porous media.

No doubt: Mathematics has become a technology in its own right, maybe even a key technology. Technology may be defined as the application of science to the problems of commerce and industry. And science? Science maybe defined as developing, testing and improving models for the prediction of system behavior; the language used to describe these models is mathematics and mathematics provides methods to evaluate these models. Here we are! Why has mathematics become a technology only recently? Since it got a tool, a tool to evaluate complex, "near to reality" models: Computer! The model may be quite old - Navier-Stokes equations describe flow behavior rather well, but to solve these equations for realistic geometry and higher Reynolds numbers with sufficient precision is even for powerful parallel computing a real challenge. Make the models as simple as possible, as complex as necessary - and then evaluate them with the help of efficient and reliable algorithms: These are genuine mathematical tasks.

The inverse problem of recovering the Earth's density distribution from data of the first or second derivative of the gravitational potential at satellite orbit height is discussed for a ball-shaped Earth. This problem is exponentially ill-posed. In this paper a multiscale regularization technique using scaling functions and wavelets constructed for the corresponding integro-differential equations is introduced and its numerical applications are discussed. In the numerical part the second radial derivative of the gravitational potential at 200 km orbitheight is calculated on a point grid out of the NASA/GSFC/NIMA Earth Geopotential Model (EGM96). Those simulated derived data out of SGG (satellite gravity gradiometry) satellite measurements are taken for convolutions with the introduced scaling functions yielding a multiresolution analysis of harmonic density variations in the Earth's crust. Moreover, the noise sensitivity of the regularization technique is analyzed numerically.

The mathematical formulation of many physical problems results in the task of inverting a compact operator. The only known sensible solution technique is regularization which poses a severe problem in itself. Classically one dealt with deterministic noise models and required both the knowledge of smoothness of the solution function and the overall error behavior. We will show that we can guarantee an asymptotically optimal regularization for a physically motivated noise model under no assumptions for the smoothness and rather weak assumptions on the noise behavior which can mostly obtained out of two input data sets. An application to the determination of the gravitational field out of satellite data will be shown.

In the filling process of a car tank, the formation of foam plays an unwanted role, as it may prevent the tank from being completely filled or at least delay the filling. Therefore it is of interest to optimize the geometry of the tank using numerical simulation in such a way that the influence of the foam is minimized. In this dissertation, we analyze the behaviour of the foam mathematically on the mezoscopic scale, that is for single lamellae. The most important goals are on the one hand to gain a deeper understanding of the interaction of the relevant physical effects, on the other hand to obtain a model for the simulation of the decay of a lamella which can be integrated in a global foam model. In the first part of this work, we give a short introduction into the physical properties of foam and find that the Marangoni effect is the main cause for its stability. We then develop a mathematical model for the simulation of the dynamical behaviour of a lamella based on an asymptotic analysis using the special geometry of the lamella. The result is a system of nonlinear partial differential equations (PDE) of third order in two spatial and one time dimension. In the second part, we analyze this system mathematically and prove an existence and uniqueness result for a simplified case. For some special parameter domains the system can be further simplified, and in some cases explicit solutions can be derived. In the last part of the dissertation, we solve the system using a finite element approach and discuss the results in detail.

In this paper we generalize the classical shortest path problem in two ways. We consider two objective functions and time-dependent data. The resulting problem, called the time-dependent bicriteria shortest path problem (TdBiSP), has several interesting practical applications, but has not gained much attention in the literature.

In soil mechanics assumption of only vertical subsidence is often invoked and this leads to the one-dimensional model of poroelasticity. The classical model of linear poroelasticity is obtained by Biot [1], detailed derivation can be found e.g., in [2]. This model is applicable also to modelling certain processes in geomechanics, hydrogeology, petroleum engineering (see, e.g., [3, 8], in biomechanics (e.g., [9, 10]), in filtration (e.g., filter cake formation, see [15, 16, 17]), in paper manufacturing (e.g., [11, 12]), in printing (e.g., [13]), etc. Finite element and finite difference methods were applied by many authors for numerical solution of the Biot system of PDEs, see e.g. [3, 4, 5] and references therein. However, as it is wellknown, the standard FEM and FDM methods are subject to numerical instabilities at the first time steps. To avoid this, discretization on staggered grid was suggested in [4, 5]. A single layer deformable porous medium was considered there. This paper can be viewed as extension of [4, 5] to the case of multilayered deformable porous media. A finite volume discretization to the interface problem for the classical one-dimensional Biot model of consolidation process is applied here. Following assumptions are supposed to be valid: each of the porous layers is composed of incompressible solid matrix, it is homogeneous and isotropic. Furthermore, one of two following assumptions is valid: porous medium is not completely saturated and ﬂuid is incompressible or porous medium is completely saturated and fluid is slightly compressible. The reminder of the paper is organised as follows. Next section presents the mathematical model. Third section is devoted to the dicsretization of the continuous problem. Fourth section contains the results from the numerical experiments.

In this work the problem of fluid flow in deformable porous media is studied. First, the stationary fluid-structure interaction (FSI) problem is formulated in terms of incompressible Newtonian fluid and a linearized elastic solid. The flow is assumed to be characterized by very low Reynolds number and is described by the Stokes equations. The strains in the solid are small allowing for the solid to be described by the Lame equations, but no restrictions are applied on the magnitude of the displacements leading to strongly coupled, nonlinear fluid-structure problem. The FSI problem is then solved numerically by an iterative procedure which solves sequentially fluid and solid subproblems. Each of the two subproblems is discretized by finite elements and the fluid-structure coupling is reduced to an interface boundary condition. Several numerical examples are presented and the results from the numerical computations are used to perform permeability computations for different geometries.

In this paper, we discuss approaches related to the explicit modeling of human beings in software development processes. While in most older simulation models of software development processes, esp. those of the system dynamics type, humans are only represented as a labor pool, more recent models of the discrete-event simulation type require representations of individual humans. In that case, particularities regarding the person become more relevant. These individual effects are either considered as stochastic variations of productivity, or an explanation is sought based on individual characteristics, such as skills for instance. In this paper, we explore such possibilities by recurring to some basic results in psychology, sociology, and labor science. Various specific models for representing human effects in software process simulation are discussed.

Nowadays one of the major objectives in geosciences is the determination of the gravitational field of our planet, the Earth. A precise knowledge of this quantity is not just interesting on its own but it is indeed a key point for a vast number of applications. The important question is how to obtain a good model for the gravitational field on a global scale. The only applicable solution - both in costs and data coverage - is the usage of satellite data. We concentrate on highly precise measurements which will be obtained by GOCE (Gravity Field and Steady State Ocean Circulation Explorer, launch expected 2006). This satellite has a gradiometer onboard which returns the second derivatives of the gravitational potential. Mathematically seen we have to deal with several obstacles. The first one is that the noise in the different components of these second derivatives differs over several orders of magnitude, i.e. a straightforward solution of this outer boundary value problem will not work properly. Furthermore we are not interested in the data at satellite height but we want to know the field at the Earth's surface, thus we need a regularization (downward-continuation) of the data. These two problems are tackled in the thesis and are now described briefly. Split Operators: We have to solve an outer boundary value problem at the height of the satellite track. Classically one can handle first order side conditions which are not tangential to the surface and second derivatives pointing in the radial direction employing integral and pseudo differential equation methods. We present a different approach: We classify all first and purely second order operators which fulfill that a harmonic function stays harmonic under their application. This task is done by using modern algebraic methods for solving systems of partial differential equations symbolically. Now we can look at the problem with oblique side conditions as if we had ordinary i.e. non-derived side conditions. The only additional work which has to be done is an inversion of the differential operator, i.e. integration. In particular we are capable to deal with derivatives which are tangential to the boundary. Auto-Regularization: The second obstacle is finding a proper regularization procedure. This is complicated by the fact that we are facing stochastic rather than deterministic noise. The main question is how to find an optimal regularization parameter which is impossible without any additional knowledge. However we could show that with a very limited number of additional information, which are obtainable also in practice, we can regularize in an asymptotically optimal way. In particular we showed that the knowledge of two input data sets allows an order optimal regularization procedure even under the hard conditions of Gaussian white noise and an exponentially ill-posed problem. A last but rather simple task is combining data from different derivatives which can be done by a weighted least squares approach using the information we obtained out of the regularization procedure. A practical application to the downward-continuation problem for simulated gravitational data is shown.

The hypoxia inducible factor-1 (HIF-1), a heterodimer composed of HIF-1alpha and HIF-1beta, is activated in response to low oxygen tension and serves as the master regulator for cells to adapt to hypoxia. HIF-1 is usually considered to be regulated via degradation of its a-subunit. Recent findings, however, point to the existence of alternative mechanisms of HIF-1 regulation which appear to be important for down-regulating HIF-1 under prolonged and severe oxygen depletion. The aims of my Ph.D. thesis, therefore, were to further elucidate mechanisms involved in such down-regulation of HIF-1. The first part of the thesis addresses the impact of the severity and duration of oxygen depletion on HIF-1alpha protein accumulation and HIF-1 transcriptional activity. A special focus was put on the influence of the transcription factor p53 on HIF-1. I found that p53 only accumulates under prolonged anoxia (but not hypoxia), thus limiting its influence on HIF-1 to severe hypoxic conditions. At low expression levels, p53 inhibits HIF-1 transactivity. I attributed this effect to a competition between p53 and HIF-1alpha for binding to the transcriptional co-factor p300, since p300 overexpression reverses this inhibition. This assumption is corroborated by competitive binding of IVTT-generated p53 and HIF-1alpha to the CH1-domain of p300 in vitro. High p53 expression, on the other hand, affects HIF-1alpha protein negatively, i.e., p53 provokes pVHL-independent degradation of HIF-1alpha. Therefore, I conclude that low p53 expression attenuates HIF-1 transactivation by competing for p300, while high p53 expression negatively affects HIF-1alpha protein, thereby eliminating HIF-1 transactivity. Thus, once p53 becomes activated under prolonged anoxia, it contributes to terminating HIF-1 responses. In the second part of my study, I intended to further characterize the effects induced by prolonged periods of low oxygen, i.e., hypoxia, as compared to anoxia, with respect to alterations in HIF-1alpha mRNA. Prolonged anoxia, but not hypoxia, showed pronounced effects on HIF-1alpha mRNA. Long-term anoxia induced destabilization of HIF-1alpha mRNA, which manifests itself in a dramatic reduction of the half-life. The mechanistic background points to natural anti-sense HIF-1alpha mRNA, which is induced in a HIF-1-dependent manner, and additional factors, which most likely influence HIF-1alpha mRNA indirectly via anti-sense HIF-1alpha mRNA mediated trans-effects. In summary, the data provide new information concerning the impact of p53 on HIF-1, which might be of importance for the decision between pro- and anti-apoptotic mechanisms depending upon the severity and duration of hypoxia. Furthermore, the results of this project give further insights into a novel mechanism of HIF-1 regulation, namely mRNA down-regulation under prolonged anoxic incubations. These mechanisms appear to be activated only in response to prolonged anoxia, but not to hypoxia. These considerations regarding HIF-1 regulation should be taken into account when prolonged incubations to hypoxic or anoxic conditions are analyzed at the level of HIF-1 stability regulation.

In this dissertation we consider complex, projective hypersurfaces with many isolated singularities. The leading questions concern the maximal number of prescribed singularities of such hypersurfaces in a given linear system, and geometric properties of the equisingular stratum. In the first part a systematic introduction to the theory of equianalytic families of hypersurfaces is given. Furthermore, the patchworking method for constructing hypersurfaces with singularities of prescribed types is described. In the second part we present new existence results for hypersurfaces with many singularities. Using the patchworking method, we show asymptotically proper results for hypersurfaces in P^n with singularities of corank less than two. In the case of simple singularities, the results are even asymptotically optimal. These statements improve all previous general existence results for hypersurfaces with these singularities. Moreover, the results are also transferred to hypersurfaces defined over the real numbers. The last part of the dissertation deals with the Castelnuovo function for studying the cohomology of ideal sheaves of zero-dimensional schemes. Parts of the theory of this function for schemes in P^2 are generalized to the case of schemes on general surfaces in P^3. As an application we show an H^1-vanishing theorem for such schemes.

Porous media flow of polymers with Carreau law viscosities and their application to enhanced oil recovery (EOR) is considered. Applying the homogenization method leads to a nonlinear two-scale problem. In case of a small difference between the Carreau and the Newtonian case an asymptotic expansion based on the small deviation of the viscosity from the Newtonian case is introduced. For uni-directional pressure gradients, which is a reasonable assumption in applications like EOR, auxiliary problems to decouple the micro- from the macrovariables are derived. The microscopic flow field obtained by the proposed approach is compared to the solution of the two-scale problem. Finite element calculations for an isotropic and an anisotropic pore cell geometries are used to validate the accuracy and speed-up of the proposed approach. The order of accuracy has been studied by performing the simulations up to the third order expansion for the isotropic geometry.

Algebraic Systems Theory
(2004)

Control systems are usually described by differential equations, but their properties of interest are most naturally expressed in terms of the system trajectories, i.e., the set of all solutions to the equations. This is the central idea behind the so-called "behavioral approach" to systems and control theory. On the other hand, the manipulation of linear systems of differential equations can be formalized using algebra, more precisely, module theory and homological methods ("algebraic analysis"). The relationship between modules and systems is very rich, in fact, it is a categorical duality in many cases of practical interest. This leads to algebraic characterizations of structural systems properties such as autonomy, controllability, and observability. The aim of these lecture notes is to investigate this module-system correspondence. Particular emphasis is put on the application areas of one-dimensional rational systems (linear ODE with rational coefficients), and multi-dimensional constant systems (linear PDE with constant coefficients).

In the present work, various aspects of the mixed continuum-atomistic modelling of materials are studied, most of which are related to the problems arising due to a development of microstructures during the transition from an elastic to plastic description within the framework of continuum-atomistics. By virtue of the so-called Cauchy-Born hypothesis, which is an essential part of the continuum-atomistics, a localization criterion has been derived in terms of the loss of infinitesimal rank-one convexity of the strain energy density. According to this criterion, a numerical yield condition has been computed for two different interatomic energy functions. Therewith, the range of the Cauchy-Born rule validity has been defined, since the strain energy density remains quasiconvex only within the computed yield surface. To provide a possibility to continue the simulation of material response after the loss of quasiconvexity, a relaxation procedure proposed by Tadmor et al. leading necessarily to the development of microstructures has been used. Thereby, various notions of convexity have been overviewed in details. Alternatively to the above mentioned criterion, a stability criterion has been applied to detect the critical deformation. For the study in the postcritical region, the path-change procedure proposed by Wagner and Wriggers has been adapted for the continuum-atomistic and modified. To capture the deformation inhomogeneity arising due to the relaxation, the Cauchy-Born hypothesis has been extended by assumption that it represents only the 1st term in the Taylor's series expansion of the deformation map. The introduction of the 2nd, quadratic term results in the higher-order materials theory. Based on a simple computational example, the relevance of this theory in the postcritical region has been shown. For all simulations including the finite element examples, the development tool MATLAB 6.5 has been used.

Herbivory is discussed as a key agent in maintaining dynamics and stability of tropical forested ecosystems. Accordingly increasing attention has been paid to the factors that structure tropical herbivore communities. The aim of this study was (1) to describe diversity, density, distribution and host range of the phasmid community (Phasmatodea) of a moist neotropical forest in Panamá, and (2) to experimentally assess bottom-up and top-down factors that may regulate populations of the phasmid Metriophasma diocles. The phasmid community of Barro Colorado Island was poor in species and low in density. Phasmids mainly occurred along forest edges and restricted host ranges of phasmid species reflected the successional status of their host plants. Only M. diocles that fed on early and late successional plants occurred regularly in the forest understory. A long generation time with a comparably low fecundity converted into a low biotic potential of M. diocles. However, modeled potential population density increased exponentially and exceeded the realized densities of this species already after one generation indicating that control factors continuously affect M. diocles natural populations. Egg hatching failure decreased potential population growth by 10 % but was of no marked effect at larger temporal scale. Interspecific differences in defensive physical and chemical leaf traits of M. diocles host plants, amongst them leaf toughness the supposedly most effective anti-herbivore defense, seemed not to affect adult female preference and nymph performance. Alternatively to these defenses, I suggest that the pattern of differential preference and performance may be based on interspecific differences in qualitative toxic compounds or in nutritive quality of leaves. The significant rejection of leaf tissue with a low artificial increase of natural phenol contents by nymphs indicated a qualitative defensive pathway in Piper evolution. In M. diocles, oviposition may not be linked to nymph performance, because the evolutionary prediction of a relation between female adult preference and nymph performance was missing. Consequently, the recruitment of nymphs into the reproductive adult phase may be crucially affected by differential performance of nymphs. Neonate M. diocles nymphs suffered strong predation pressure when exposed to natural levels of predation. Concluding from significantly increased predation-related mortality at night, I argue that arthropods may be the main predators of this nocturnal herbivore. Migratory behavior of nymphs seemed not to reflect predation avoidance. Instead, I provided first evidence that host plant quality may trigger off-plant migration. In conclusion, I suggest that predation pressure with its direct effects on nymph survival may be a stronger factor regulating M. diocles populations, compared to direct and indirect effects of host plant quality, particularly because slow growth and off-host migration both may feed back into an increase of predation related mortality.

The present thesis deals with a novel air interface concept for beyond 3G mobile radio systems. Signals received at a certain reference cell in a cellular system which originate in neighboring cells of the same cellular system are undesired and constitute the intercell interference. Due to intercell interference, the spectrum capacity of cellular systems is limited and therefore the reduction of intercell interference is an important goal in the design of future mobile radio systems. In the present thesis, a novel service area based air interface concept is investigated in which interference is combated by joint detection and joint transmission, providing an increased spectrum capacity as compared to state-of-the-art cellular systems. Various algorithms are studied, with the aid of which intra service area interference can be combated. In the uplink transmission, by optimum joint detection the probability of erroneous decision is minimized. Alternatively, suboptimum joint detection algorithms can be applied offering reduced complexity. By linear receive zero-forcing joint detection interference in a service area is eliminated, while by linear minimum mean square error joint detection a trade-off is performed between interference elimination and noise enhancement. Moreover, iterative joint detection is investigated and it is shown that convergence of the data estimates of iterative joint detection without data estimate refinement towards the data estimates of linear joint detection can be achieved. Iterative joint detection can be further enhanced by the refinement of the data estimates in each iteration. For the downlink transmission, the reciprocity of uplink and downlink channels is used by joint transmission eliminating the need for channel estimation and therefore allowing for simple mobile terminals. A novel algorithm for optimum joint transmission is presented and it is shown how transmit signals can be designed which result in the minimum possible average bit error probability at the mobile terminals. By linear transmit zero-forcing joint transmission interference in the downlink transmission is eliminated, whereas by iterative joint transmission transmit signals are constructed in an iterative manner. In a next step, the performance of joint detection and joint transmission in service area based systems is investigated. It is shown that the price to be paid for the interference suppression in service area based systems is the suboptimum use of the receive energy in the uplink transmission and of the transmit energy in the downlink transmission, with respect to the single user reference system. In the case of receive zero-forcing joint detection in the uplink and transmit zero-forcing joint transmission in the downlink, i.e., in the case of linear unbiased data transmission, it is shown that the same price, quantified by the energy efficiency, has to be paid for interference elimination in both uplink and downlink. Finally it is shown that if the system load is fixed, the number of active mobile terminals in a SA and hence the spectrum capacity can be increased without any significant reduction in the average energy efficiency of the data transmission.

This work is concerned with a nonlinear Galerkin method for solving the incompressible Navier-Stokes equation on the sphere. It extends the work of Debussche, Marion,Shen, Temam et al. from one-dimensional or toroidal domains to the spherical geometry. In the first part, the method based on type 3 vector spherical harmonics is introduced and convergence is indicated. Further it is shown that the occurring coupling terms involving three vector spherical harmonics can be expressed algebraically in terms of Wigner-3j coefficients. To improve the numerical efficiency and economy we introduce an FFT based pseudo spectral algorithm for computing the Fourier coefficients of the nonlinear advection term. The resulting method scales with O(N^3), if N denotes the maximal spherical harmonic degree. The latter is demonstrated in an extensive numerical example.

In this text we survey some large deviation results for diffusion processes. The first chapters present results from the literature such as the Freidlin-Wentzell theorem for diffusions with small noise. We use these results to prove a new large deviation theorem about diffusion processes with strong drift. This is the main result of the thesis. In the later chapters we give another application of large deviation results, namely to determine the exponential decay rate for the Bayes risk when separating two different processes. The final chapter presents techniques which help to experiment with rare events for diffusion processes by means of computer simulations.

In recent years, more and more publications and material for studying and teaching, e. g. for Web-based teaching (WBT), appear "online" and digital libraries are built to manage such publications and online materials. Therefore, the most important concerns are related to the problem of durable, sustained storage and the management of content together with its metadata existing in heterogeneous styles and formats. In this paper, we present specific techniques and their use to support metadata-based catalog services. Such semistructured metadata (represented as XML fragments), which belong to online learning resources, need efficient XML-based query support, scalable result set processing, and comprehensive facilities for personalization purposes. We discuss the associated problems, subsequently derive the concepts of a suitable architecture, and finally outline the realization by means of our prototype system that is based on the J2EE component model.

In this paper we consider numerical algorithms for solving a system of nonlinear PDEs arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer flows through a porous medium during the filling stage. The nonlinearity of the governing system of PDEs is due to the non-Newtonian behavior of the polymer, as well as due to the moving free boundary. The latter is related to the penetration front and a Stefan type problem is formulated to account for it. A finite-volume method is used to approximate the given differential problem. Results of numerical experiments are presented. We also solve an inverse problem and present algorithms for the determination of the absolute preform permeability coefficient in the case when the velocity of the penetration front is known from measurements. In both cases (direct and inverse problems) we emphasize on the specifics related to the non-Newtonian behavior of the polymer. For completeness, we discuss also the Newtonian case. Results of some experimental measurements are presented and discussed.

Iterative solution of large scale systems arising after discretization and linearization of the unsteady non-Newtonian Navier–Stokes equations is studied. cross WLF model is used to account for the non-Newtonian behavior of the fluid. Finite volume method is used to discretize the governing system of PDEs. Viscosity is treated explicitely (e.g., it is taken from the previous time step), while other terms are treated implicitly. Different preconditioners (block–diagonal, block–triangular, relaxed incomplete LU factorization, etc.) are used in conjunction with advanced iterative methods, namely, BiCGStab, CGS, GMRES. The action of the preconditioner in fact requires inverting different blocks. For this purpose, in addition to preconditioned BiCGStab, CGS, GMRES, we use also algebraic multigrid method (AMG). The performance of the iterative solvers is studied with respect to the number of unknowns, characteristic velocity in the basic flow, time step, deviation from Newtonian behavior, etc. Results from numerical experiments are presented and discussed.

After a short introduction to the basic ideas of lattice Boltzmann methods and a brief description of a modern parallel computer, it is shown how lattice Boltzmann schemes are successfully applied for simulating fluid flow in microstructures and calculating material properties of porous media. It is explained how lattice Boltzmann schemes compute the gradient of the velocity field without numerical differentiation. This feature is then utilised for the simulation of pseudo-plastic fluids, and numerical results are presented for a simple benchmark problem as well as for the simulation of liquid composite moulding.

IMRT planning on adaptive volume structures – a significant advance of computational complexity
(2004)

In intensity-modulated radiotherapy (IMRT) planning the oncologist faces the challenging task of finding a treatment plan that he considers to be an ideal compromise of the inherently contradictive goals of delivering a sufficiently high dose to the target while widely sparing critical structures. The search for this a priori unknown compromise typically requires the computation of several plans, i.e. the solution of several optimization problems. This accumulates to a high computational expense due to the large scale of these problems - a consequence of the discrete problem formulation. This paper presents the adaptive clustering method as a new algorithmic concept to overcome these difficulties. The computations are performed on an individually adapted structure of voxel clusters rather than on the original voxels leading to a decisively reduced computational complexity as numerical examples on real clinical data demonstrate. In contrast to many other similar concepts, the typical trade-off between a reduction in computational complexity and a loss in exactness can be avoided: the adaptive clustering method produces the optimum of the original problem. This flexible method can be applied to both single- and multi-criteria optimization methods based on most of the convex evaluation functions used in practice

Characterization of neuronal activity in the auditory brainstem of rats: An optical imaging approach
(2004)

In this doctoral thesis, several aspects of neuronal activity in the rat superior olivary complex (SOC), an auditory brainstem structure, were analyzed using optical imaging with voltage-sensitive dyes (VSD). The thesis is divided into 5 Chapters. Chapter 1 is a general introduction, which gives an overview of the auditory brainstem and VSD imaging. In Chapter 2, an optical imaging method for the SOC was standardized, using the VSD RH795. To do so, the following factors were optimized: (1) An extracellular potassium concentration of 5 mM is necessary during the incubation and recording to observe synaptically evoked responses in the SOC. (2) Employing different power supplies reduced the noise. (3) Averaging of 10 subsequent trials yielded a better signal-to-noise ratio. (4) RH795 of 100 µM with 50 min prewash was optimal to image SOC slices for more than one hour. (5) Stimulus-evoked optical signals were TTX sensitive, revealing action potential-driven input. (6) Synaptically evoked optical signals were characterized to be composed of pre- and postsynaptic components. (7) Optical signals were well correlated with anatomical structures. Overall, this method allows the comparative measurement of electrical activity of cell ensembles with high spatio-temporal resolution. In Chapter 3, the nature of functional inputs to the lateral superior olive (LSO), the medial superior olive (MSO), and the superior paraolivary nucleus (SPN) were analyzed using the glycine receptor blocker strychnine and the AMPA/kainate receptor blocker CNQX. In the LSO, the known glutamatergic inputs from the ipsilateral, and the glycinergic inputs from the ipsilateral and contralateral sides, were confirmed. Furthermore, a CNQX-sensitive input from the contralateral was identified. In the MSO, the glutamatergic and glycinergic inputs from the ipsilateral and contralateral sides were corroborated. In the SPN, besides the known glycinergic input from the contralateral, I found a glycinergic input from the ipsilateral and I also identified CNQX-sensitive inputs from the contralateral and ipsilateral sides. Together, my results thus corroborate findings obtained with different preparations and methods, and provide additional information on the pharmacological nature of the inputs. In Chapter 4, the development of glycinergic inhibition for the LSO, the MSO, the SPN, and the medial nucleus of the trapezoid body (MNTB) was studied by characterizing the polarity of strychnine-sensitive responses. In the LSO, the high frequency region displayed a shift in the polarity at P4, whereas the low frequency region displayed at P6. In the MSO, both the regions displayed the shift at P5. The SPN displayed a shift in the polarity at E18-20 without any regional differences. The MNTB lacked a shift between P3-10. Together, these results demonstrate a differential timing in the development of glycinergic inhibition in these nuclei. In Chapter 5, the role of the MSO in processing bilateral time differences (t) was investigated. This was done by stimulating ipsilateral and contralateral inputs to the MSO with different t values. In preliminary experiments, the postsynaptic responses showed a differential pattern in the spread of activity upon different t values. This data demonstrates a possible presence of delay lines as proposed by Jeffress in the interaural time difference model of sound localization. In conclusion, this study demonstrates the usage of VSD imaging to analyze the neuronal activity in auditory brainstem slices. Moreover, this study expands the knowledge of the inputs to the SOC, and has identified one glycinergic and three AMPA/kainate glutamatergic novel inputs to the SOC nuclei.

The polydispersive nature of the turbulent droplet swarm in agitated liquid-liquid contacting equipment makes its mathematical modelling and the solution methodologies a rather sophisticated process. This polydispersion could be modelled as a population of droplets randomly distributed with respect to some internal properties at a specific location in space using the population balance equation as a mathematical tool. However, the analytical solution of such a mathematical model is hardly to obtain except for particular idealized cases, and hence numerical solutions are resorted to in general. This is due to the inherent nonlinearities in the convective and diffusive terms as well as the appearance of many integrals in the source term. In this work two conservative discretization methodologies for both internal (droplet state) and external (spatial) coordinates are extended and efficiently implemented to solve the population balance equation (PBE) describing the hydrodynamics of liquid-liquid contacting equipment. The internal coordinate conservative discretization techniques of Kumar and Ramkrishna (1996a, b) originally developed for the solution of PBE in simple batch systems are extended to continuous flow systems and validated against analytical solutions as well as published experimental droplet interaction functions and hydrodynamic data. In addition to these methodologies, we presented a conservative discretization approach for droplet breakage in batch and continuous flow systems, where it is found to have identical convergence characteristics when compared to the method of Kumar and Ramkrishna (1996a). Apart from the specific discretization schemes, the numerical solution of droplet population balance equations by discretization is known to suffer from inherent finite domain errors (FDE). Two approaches that minimize the total FDE during the solution of the discrete PBEs using an approximate optimal moving (for batch) and fixed (for continuous systems) grids are introduced (Attarakih, Bart & Faqir, 2003a). As a result, significant improvements are achieved in predicting the number densities, zero and first moments of the population. For spatially distributed populations (such as extraction columns) the resulting system of partial differential equations is spatially discretized in conservative form using a simplified first order upwind scheme as well as first and second order nonoscillatory central differencing schemes (Kurganov & Tadmor, 2000). This spatial discretization avoids the characteristic decomposition of the convective flux based on the approximate Riemann Solvers and the operator splitting technique required by classical upwind schemes (Karlsen et al., 2001). The time variable is discretized using an implicit strongly stable approach that is formulated by careful lagging of the nonlinear parts of the convective and source terms. The present algorithms are tested against analytical solutions of the simplified PBE through many case studies. In all these case studies the discrete models converges successfully to the available analytical solutions and to solutions on relatively fine grids when the analytical solution is not available. This is accomplished by deriving five analytical solutions of the PBE in continuous stirred tank and liquid-liquid extraction column for especial cases of breakage and coalescence functions. As an especial case, these algorithms are implemented via a windows computer code called LLECMOD (Liquid-Liquid Extraction Column Module) to simulate the hydrodynamics of general liquid-liquid extraction columns (LLEC). The user input dialog makes the LLECMOD a user-friendly program that enables the user to select grids, column dimensions, flow rates, velocity models, simulation parameters, dispersed and continuous phases chemical components, and droplet phase space-time solvers. The graphical output within the windows environment adds to the program a distinctive feature and makes it very easy to examine and interpret the results very quickly. Moreover, the dynamic model of the dispersed phase is carefully treated to correctly predict the oscillatory behavior of the LLEC hold up. In this context, a continuous velocity model corresponding to the manipulation of the inlet continuous flow rate through the control of the dispersed phase level is derived to get rid of this behavior.

Compared to our current knowledge of neuronal excitation, little is known about the development and maturation of inhibitory circuits. Recent studies show that inhibitory circuits develop and mature in a similar way like excitatory circuit. One such similarity is the development through excitation, irrespective of its inhibitory nature. Here in this current study, I used the inhibitory projection between the medial nucleus of the trapezoid body (MNTB) and the lateral superior olive (LSO) as a model system to unravel some aspects of the development of inhibitory synapses. In LSO neurons of the rat auditory brainstem, glycine receptor-mediated responses change from depolarizing to hyperpolarizing during the first two postnatal weeks (Kandler and Friauf 1995, J. Neurosci. 15:6890-6904). The depolarizing effect of glycine is due to a high intracellular chloride concentration ([Cl-]i), which induces a reversal potential of glycine (EGly) more positive than the resting membrane potential (Vrest). In older LSO neurons, the hyperpolarizing effect is due to a low [Cl-]i (Ehrlich et al., 1999, J. Physiol. 520:121-137). Aim of the present study was to elucidate the molecular mechanism behind Clhomeostasis in LSO neurons which determines polarity of glycine response. To do so, the role and developmental expression of Cl-cotransporters, such as NKCC1 and KCC2 were investigated. Molecular biological and gramicidin perforated patchclamp experiments revealed, the role of KCC2 as an outward Cl-cotransporter in mature LSO neurons (Balakrishnan et al., 2003, J Neurosci. 23:4134-4145). But, NKCC1 does not appear to be involved in accumulating chloride in immature LSO neurons. Further experiments, indicated the role of GABA and glycine transporters (GAT1 and GLYT2) in accumulating Cl- in immature LSO neurons. Finally, the experiments with hypothyroid animals suggest the possible role of thyroid hormone in the maturation of inhibitory synapse. Altogether, this thesis addressed the molecular mechanism underlying the Cl- regulation in LSO neurons and deciphered it to some extent.

A general framework for the thermodynamics of open systems is developed in the spatial and the material setting. Special emphasis is placed on the balance of mass which is enhanced by additional source and flux terms. Different solution strategies within the finite element technique are derived and compared. A number of numerical examples illustrates the features of the proposed approach.

The following two papers present recent developments in multiscale ocean circulation modeling and multiscale gravitational field modeling that have been presented at the 2nd International GOCE User Workshop 2004 in Frascati. Part A - Multiscale Modeling of Ocean Circulation In this paper the applicability of multiscale methods to oceanography is demonstrated. More precisely, we use convolutions with certain locally supported kernels to approximate the dynamic topography and the geostrophic flow. As data sets the French CLS01 data are used for the mean sea surface topography and are compared to the EGM96 geoid. Since those two data sets have very different levels of spatial resolutions the necessity of an interpolating or approximating tool is evident. Compared to the standard spherical harmonics approach, the strongly space localizing kernels improve the possibilities of local data analysis here. Part B - Multiscale Modeling from EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, GGM01, UCPH2002_0.5, EGM96 Spherical wavelets have been developed by the Geomathematics Group Kaiserslautern for several years and have been successfully applied to georelevant problems. Wavelets can be considered as consecutive band-pass filters and allow local approximations. The wavelet transform can also be applied to spherical harmonic models of the Earth's gravitational field like the most up-to-date EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, GGM01, UCPH2002_0.5, and the well-known EGM96. Thereby, wavelet coefficients arise. In this paper it is the aim of the Geomathematics Group to make these data available to other interested groups. These wavelet coefficients allow not only the reconstruction of the wavelet approximations of the gravitational potential but also of the geoid, of the gravity anomalies and other important functionals of the gravitational field. Different types of wavelets are considered: bandlimited wavelets (here: Shannon and Cubic Polynomial (CuP)) as well as non-bandlimited ones (in our case: Abel-Poisson). For these types wavelet coefficients are computed and wavelet variances are given. The data format of the wavelet coefficients is also included.

In this thesis, the enhanced Galerkin (eG) finite element method in time is presented. The eG method leads to higher order accurate energy and momentum conserving time integrators for the underlying finite-dimensional Hamiltonian systems. This thesis is concerned with particle dynamics and semi-discrete nonlinear elastodynamics. The conservation is generally related to the collocation property of the eG method. The momentum conservation renders the Gaussian quadrature and the energy conservation is obtained by using a new projection technique. An objective time discretisation of the used strain measures avoids artificial strains for large superimposed rigid body motions. The numerical examples show the well long term performance in the presence of stiffness as well as for calculating large-strain motions.

In the delay management problem we decide how to react in case of delays in public transportation. More specific, the question is if connecting vehicles should wait for delayed feeder vehicles or if it is better to depart in time. As objective we consider the convenience over all customers, expressed as the average delay of a customer when arriving at his destination.We present path-based and activity-based integer programming models for the delay management problem and show the equivalence of these formulations. Based on these, we present a simplification of the (cubic) activity-based model which results in an integer linear program. We identify cases in which this linearization is correct, namely if the so-called never-meet property holds. Fortunately, this property is often almost satisfied in our practical data. Finally, we show how to find an optimal solution in linear time in case of the never-meet property.

In this thesis we propose an efficient method to compute the automorphism group of an arbitrary hyperelliptic function field over a given constant field of odd characteristic as well as over its algebraic extensions. Beside theoretical applications, knowing the automorphism group also is useful in cryptography: The Jacobians of hyperelliptic curves have been suggested by Koblitz as groups for cryptographic purposes, because the discrete logarithm is believed to be hard in this kind of groups. In order to obtain "secure" Jacobians, it is necessary to prevent attacks like Pohlig/Hellman's and Duursma/Gaudry/Morain's. The latter is only feasible, if the corresponding function field has an automorphism of large order. According to a theorem by Madan, automorphisms seem to allow the Pohlig/Hellman attack, too. Hence, the function field of a secure Jacobian will most likely have trivial automorphism group. In other words: Computing the automorphism group of a hyperelliptic function field promises to be a quick test for insecure Jacobians. Let us outline our algorithm for computing the automorphism group Aut(F/k) of a hyperelliptic function field F/k. It is well known that Aut(F/k) is finite. For each possible subgroup U of Aut(F/k), Rolf Brandt has given a normal form for F if k is algebraically closed. Hence our problem reduces to deciding, whether a given hyperelliptic function field F=k(x,y), y^2=D_x has a defining equation of the form given by Brandt. This question can be answered using theorem III.18: We have F=k(t,u), u^2=D_t iff x is a fraction of linear polynomials in t and y=pu, where the factor p is a rational function w.r.t. t which can be determined explicitly from the coefficients of x. This condition can be checked efficiently using Gröbner basis techniques. With additional effort, it is also possible to compute Aut(F/k) if k is not algebraically closed. Investigating a huge number of examples one gets the impression that the above motivation of getting a quick test for insecure Jacobians is partially fulfilled: The computation of automorphism groups is quite fast using the suggested algorithm. Furthermore, fields with nontrivial automorphism groups seem to have insecure Jacobians. Only fields of small characteristic seem to have a reasonable chance of having nontrivial automorphisms. Hence, from a cryptographic point of view, computing Aut(F/k) seems to make sense whenever k has small characteristic.

We consider the contact of two elastic bodies with rough surfaces at the interface. The size of the micropeaks and valleys is very small compared with the macrosize of the bodies’ domains. This makes the direct application of the FEM for the calculation of the contact problem prohibitively costly. A method is developed that allows deriving a macrocontact condition on the interface. The method involves the twoscale asymptotic homogenization procedure that takes into account the microgeometry of the interface layer and the stiffnesses of materials of both domains. The macrocontact condition can then be used in a FEM model for the contact problem on the macrolevel. The averaged contact stiffness obtained allows the replacement of the interface layer in the macromodel by the macrocontact condition.

In this thesis we show that the theory of algebraic correspondences introduced by Deuring in the 1930s can be applied to construct non-trivial homomorphisms between the Jacobi groups of hyperelliptic function fields. Concretely, we deduce algorithms to add and multiply correspondences which perform in a reasonable time if the degrees of the associated divisors of the double field are small. Moreover, we show how to compute the differential matrices associated to prime divisors of the double field for arbitrary genus. These matrices give a representation for the homomorphisms or endomorphisms in the additive group (ring) of matrices which is even faithful if the ground field has characteristic zero. As first examples for non-trivial correspondences we investigate multiplication by m endomorphisms. Afterwards we use factorisations of certain bivariate polynomials to construct prime divisors of the double field that are not equivalent to 0 in a coarser sense. Applying the theory of Deuring, these divisors yield homomorphisms between the Jacobi groups of special classes of hyperelliptic function fields. Finally, we generalise the Richelot isogeny to higher genus and by this way derive a class of hyperelliptic function fields given in terms of their defining polynomials which admit non-trivial homomorphisms. These include homomorphisms between the Jacobi groups of hyperelliptic curves of different as well as of equal genus. In addition we provide an explicit method to construct genus 2 function fields the endomorphism ring of which contains a sqrt(2) multiplication with the help of the Cholesky decomposition of a certain matrix.

A wavelet technique, the wavelet-Mie-representation, is introduced for the analysis and modelling of the Earth's magnetic field and corresponding electric current distributions from geomagnetic data obtained within the ionosphere. The considerations are essentially based on two well-known geomathematical keystones, (i) the Helmholtz-decomposition of spherical vector fields and (ii) the Mie-representation of solenoidal vector fields in terms of poloidal and toroidal parts. The wavelet-Mie-representation is shown to provide an adequate tool for geomagnetic modelling in the case of ionospheric magnetic contributions and currents which exhibit spatially localized features. An important example are ionospheric currents flowing radially onto or away from the Earth. To demonstrate the functionality of the approach, such radial currents are calculated from vectorial data of the MAGSAT and CHAMP satellite missions.

Universal Algebra
(2004)

The article is concerned with the modelling of ionospheric current systems from induced magnetic fields measured by satellites in a multiscale framework. Scaling functions and wavelets are used to realize a multiscale analysis of the function spaces under consideration and to establish a multiscale regularization procedure for the inversion of the considered vectorial operator equation. Based on the knowledge of the singular system a regularization technique in terms of certain product kernels and corresponding convolutions can be formed. In order to reconstruct ionospheric current systems from satellite magnetic field data, an inversion of the Biot-Savart's law in terms of multiscale regularization is derived. The corresponding operator is formulated and the singular values are calculated. The method is tested on real magnetic field data of the satellite CHAMP and the proposed satellite mission SWARM.

Annual Report 2003
(2004)

Annual Report, Jahrbuch AG Magnetismus