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- 2010 (105) (remove)
Models in the context of engineering can be classified in process based and data based models. Whereas the process based model describes the problem by an explicit formulation, the data based model is often used, where no such mapping can be found due to the high complexity of the problem. Artificial Neuronal Networks (ANN) is a data based model, which is able to “learn“ a mapping from a set of training patterns. This paper deals with the application of ANN in time dependent bathymetric models. A bathymetric model is a geometric representation of the sea bed. Typically, a bathymetry is been measured and afterwards described by a finite set of measured data. Measuring at different time steps leads to a time dependent bathymetric model. To obtain a continuous surface, the measured data has to be interpolated by some interpolation method. Unlike the explicitly given interpolation methods, the presented time dependent bathymetric model using an ANN trains the approximated surface in space and time in an implicit way. The ANN is trained by topographic measured data, which consists of the location (x,y) and time t. In other words the ANN is trained to reproduce the mapping h = f(x,y,t) and afterwards it is able to approximate the topographic height for a given location and date. In a further step, this model is extended to take meteorological parameters into account. This leads to a model of more predictive character.
Die Behandlung von geometrischen Singularitäten bei der Lösung von Randwertaufgaben der Elastostatik stellt erhöhte Anforderungen an die mathematische Modellierung des Randwertproblems und erfordert für eine effiziente Auswertung speziell angepasste Berechnungsverfahren. Diese Arbeit beschäftigt sich mit der systematischen Verallgemeinerung der Methode der komplexen Spannungsfunktionen auf den Raum, wobei der Schwerpunkt in erster Linie auf der Begründung des mathematischen Verfahrens unter besonderer Berücksichtigung der praktischen Anwendbarkeit liegt. Den theoretischen Rahmen hierfür bildet die Theorie quaternionenwertiger Funktionen. Dementsprechend wird die Klasse der monogenen Funktionen als Grundlage verwendet, um im ersten Teil der Arbeit ein räumliches Analogon zum Darstellungssatz von Goursat zu beweisen und verallgemeinerte Kolosov-Muskhelishvili Formeln zu konstruieren. Im Hinblick auf die vielfältigen Anwendungsbereiche der Methode beschäftigt sich der zweite Teil der Arbeit mit der lokalen und globalen Approximation von monogenen Funktionen. Hierzu werden vollständige Orthogonalsysteme monogener Kugelfunktionen konstruiert, infolge dessen neuartige Darstellungen der kanonischen Reihenentwicklungen (Taylor, Fourier, Laurent) definiert werden. In Analogie zu den komplexen Potenz- und Laurentreihen auf der Grundlage der holomorphen z-Potenzen werden durch diese monogenen Orthogonalreihen alle wesentlichen Eigenschaften bezüglich der hyperkomplexen Ableitung und der monogenen Stammfunktion verallgemeinert. Anhand repräsentativer Beispiele werden die qualitativen und numerischen Eigenschaften der entwickelten funktionentheoretischen Verfahren abschließend evaluiert. In diesem Kontext werden ferner einige weiterführende Anwendungsbereiche im Rahmen der räumlichen Funktionentheorie betrachtet, welche die speziellen Struktureigenschaften der monogenen Potenz- und Laurentreihenentwicklungen benötigen.
In this paper the influence of changes in the mean wind velocity, the wind profile power-law coefficient, the drag coefficient of the terrain and the structural stiffness are investigated on different complex structural models. This paper gives a short introduction to wind profile models and to the approach by Davenport A. G. to compute the structural reaction of wind induced vibrations. Firstly with help of a simple example (a skyscraper) this approach is shown. Using this simple example gives the reader the possibility to study the variance differences when changing one of the above mentioned parameters on this very easy example and see the influence of different complex structural models on the result. Furthermore an approach for estimation of the needed discretization level is given. With the help of this knowledge the structural model design methodology can be base on deeper understanding of the different behavior of the single models.
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitean (or h-) monogenic functions, of two Hermitean Dirac operators which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Clifford-Cauchy integral formula has proven to be a corner stone of the function theory, as is the case for the traditional Cauchy formula for holomorphic functions in the complex plane. Previously, a Hermitean Clifford-Cauchy integral formula has been established by means of a matrix approach. This formula reduces to the traditional Martinelli-Bochner formula for holomorphic functions of several complex variables when taking functions with values in an appropriate part of complex spinor space. This means that the theory of Hermitean monogenic functions should encompass also other results of several variable complex analysis as special cases. At present we will elaborate further on the obtained results and refine them, considering fundamental solutions, Borel-Pompeiu representations and the Teoderescu inversion, each of them being developed at different levels, including the global level, handling vector variables, vector differential operators and the Clifford geometric product as well as the blade level were variables and differential operators act by means of the dot and wedge products. A rich world of results reveals itself, indeed including well-known formulae from the theory of several complex variables.
In the context of finite element model updating using vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the order of natural frequencies and mode shapes is important. As only limited spatial information is available and noise is present in the measurements, the automatic selection of the most likely numerical mode shape corresponding to a measured mode shape is a difficult task. The most common criterion to indicate corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases. In this paper, the pure mathematical modal assurance criterion will be enhanced by additional physical information of the numerical model in terms of modal strain energies. A numerical example and a benchmark study with real measured data are presented to show the advantages of the enhanced energy based criterion in comparison to the traditional modal assurance criterion.
The advent of high-performance mobile phones has opened up the opportunity to develop new context-aware applications for everyday life. In particular, applications for context-aware information retrieval in conjunction with image-based object recognition have become a focal area of recent research. In this thesis we introduce an adaptive mobile museum guidance system that allows visitors in a museum to identify exhibits by taking a picture with their mobile phone. Besides approaches to object recognition, we present different adaptation techniques that improve classification performance. After providing a comprehensive background of context-aware mobile information systems in general, we present an on-device object recognition algorithm and show how its classification performance can be improved by capturing multiple images of a single exhibit. To accomplish this, we combine the classification results of the individual pictures and consider the perspective relations among the retrieved database images. In order to identify multiple exhibits in pictures we present an approach that uses the spatial relationships among the objects in images. They make it possible to infer and validate the locations of undetected objects relative to the detected ones and additionally improve classification performance. To cope with environmental influences, we introduce an adaptation technique that establishes ad-hoc wireless networks among the visitors’ mobile devices to exchange classification data. This ensures constant classification rates under varying illumination levels and changing object placement. Finally, in addition to localization using RF-technology, we present an adaptation technique that uses user-generated spatio-temporal pathway data for person movement prediction. Based on the history of previously visited exhibits, the algorithm determines possible future locations and incorporates these predictions into the object classification process. This increases classification performance and offers benefits comparable to traditional localization approaches but without the need for additional hardware. Through multiple field studies and laboratory experiments we demonstrate the benefits of each approach and show how they influence the overall classification rate.
A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES
(2010)
Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.
The application of a recent method using formal power series is proposed. It is based on a new representation for solutions of Sturm-Liouville equations. This method is used to calculate the transmittance and reflectance coefficients of finite inhomogeneous layers with high accuracy and efficiency. Tailoring the refraction index profile defining the inhomogeneous media it is possible to develop very important applications such as optical filters. A number of profiles were evaluated and then some of them selected in order to perform an improvement of their characteristics via the modification of their profiles.
MICROPLANE MODEL WITH INITIAL AND DAMAGE-INDUCED ANISOTROPY APPLIED TO TEXTILE-REINFORCED CONCRETE
(2010)
The presented material model reproduces the anisotropic characteristics of textile reinforced concrete in a smeared manner. This includes both the initial anisotropy introduced by the textile reinforcement, as well as the anisotropic damage evolution reflecting fine patterns of crack bridges. The model is based on the microplane approach. The direction-dependent representation of the material structure into oriented microplanes provides a flexible way to introduce the initial anisotropy. The microplanes oriented in a yarn direction are associated with modified damage laws that reflect the tension-stiffening effect due to the multiple cracking of the matrix along the yarn.
In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.
Seit 1969 werden für die Bundesrepublik kontinuierlich Berechnungen zu den Gesamtkosten des Straßenverkehrs der Bundesfernstraßen und deren Verteilung auf die Verkehrsteilnehmer durchgeführt. Die Ergebnisse der Wegekostenrechnungen der Jahre 2002 und 2007 sind die Grundlage für die mittlerweile für das deutsche Autobahnnetz eingeführte fahrleistungsbezogene Benutzungsgebühr für Lkw mit einem zulässigen Gesamtgewicht von mindestens zwölf Tonnen. Damit wird die Forderung der EU-Richtlinie 1999/62/EG umgesetzt, nach der sich die durchschnittlichen Straßenbenutzungsgebühren an den Kosten für den Bau, den Betrieb und den Ausbau des betreffenden Verkehrswegenetzes orientieren sollen. Mit der EU-Richtlinie 2006/38/EG kündigt sich die weitere Entwicklung bei der Berechnung von Straßenbenutzungsgebühren an. Zukünftig sollen auch externe Kosten in die Berechnung einfließen. Ein erster Schritt zur Berücksichtigung dieser externen Kosten erfolgte mit Erstellung eines Handbuchs im Rahmen eines EU-Forschungsprojektes. Das Handbuch enthält aufgrund der unterschiedlichen Rahmenbedingungen in den Mitgliedsstaaten der EU keine exakten Berechnungsvorschriften, sondern stellt verschiedene methodische Ansätze bisher durchgeführter Studien zu externen Kosten vor, gibt Empfehlungen hinsichtlich der Methodenwahl und beinhaltet Schätzungen über die Höhe der externen Kosten. Die im europäischen Raum in den vergangenen Jahren durchgeführten Studien zur Ermittlung externer Kosten des Verkehrs zeichnen sich durch einander ähnelnde Vorgehensweisen aus, die aber vor allem hinsichtlich der Kostenrechnungsart und der verwendeten Kostensätze aus Sicht des Verfassers der vorliegenden Arbeit kritische Aspekte aufweisen. In der vorliegenden Dissertationsschrift wird daher eine alternative Berechnungsmethodik zur Ermittlung abschnitts-, fahrzeugklassen- und fahrleistungsbezogener externer Kosten für Autobahnen entwickelt und an einem ausgewählten Beispielnetz zur Anwendung gebracht. Dabei wird in einigen wesentlichen Punkten von der in aktuellen Studien überwiegend gewählten Vorgehensweise abgewichen, um eine andere Sichtweise darzustellen. Damit trägt die vorliegende Arbeit substanziell zur Erweiterung des Erkenntnisstands zu Berechnungsmethoden externer Kosten des Straßenverkehrs bei. Die hier entwickelte Berechnungsmethodik ist außerdem als Grundlage für ein in der Praxis anwendbares Verfahren zu verstehen und zeichnet sich auch daher durch eine einfach zu handhabende Übertragbarkeit auf das gesamte Autobahnnetz Deutschlands aus. Die Abschnitte entsprechen den Teilstrecken zwischen zwei Autobahnanschlussstellen. Es wird zwischen den beiden Fahrzeugklassen "Lkw ab 12 t zulässigem Gesamtgewicht" und "Sonstigen Fahrzeugen" unterschieden. Obwohl momentan nur eine Benutzungsgebühr für Lkw ab 12 t zulässigem Gesamtgewicht erhoben wird, ist es mit der entwickelten Methodik möglich, fahrleistungsbezogene externe Kosten für alle Kfz angeben zu können. Die Einbeziehung externer Nutzen wird in diesem Zusammenhang andiskutiert; der Schwerpunkt liegt allerdings auf den externen Kosten. Im Rahmen der Arbeit werden zunächst Definitionen wesentlicher Terminologien dargestellt, soweit diese für das Verständnis der sich anschließenden Diskussion und Festlegung der Grundlagen der entwickelten Berechnungsmethodik notwendig erscheinen. Diese Diskussion und Festlegung umfasst die Bereiche Kostenrechnungsart, Bewertungsverfahren zur Ermittlung des Wertegerüsts, Diskontrate, zu betrachtende Kostenbereiche, Mengengerüst und Allokationsrechnung. Darauf folgend werden die betrachteten Kostenbereiche anhand vorliegender Studien und eigener Überlegungen detailliert dargestellt und das Wertegerüst bestimmt. Außerdem wird die Allokationsrechnung und das für die Berechnung heranzuziehende Mengengerüst für jeden Bereich separat vorgestellt. Anschließend wird die entwickelte Berechnungsmethodik auf ein Beispielnetz (Autobahnnetz Thüringen) angewendet. Neben der Vorstellung des Untersuchungsgebiets, der Berechnung der externen Kosten und der disaggregierten Ergebnisdarstellung wird die Einteilung des Beispielnetzes in unterschiedliche Preiskategorien auf der Grundlage der abschnittsbezogen vorliegenden Ergebnisse diskutiert, auf deren Basis die externen Kosten über Straßenbenutzungsgebühren internalisiert werden könnten. Im Rahmen einer Sensitivitätsanalyse werden einzelne Annahmen der Berechnungsmethodik bzw. Kostensätze des Wertegerüsts variiert. Die Auswirkungen dieser Variationen werden wiederum am Beispielnetz, für das erneute Kostenberechnungen vorgenommen werden, dargelegt. Abschließend werden offen gebliebene Fragestellungen und Empfehlungen für weitere Untersuchungen benannt.
Public Private Partnership (PPP) setzt sich zunehmend als alternative Beschaffungsvariante für die öffentliche Hand durch. Im Krankenhausbereich bestehen erste Erfahrungen mit PPP, allerdings kann hier im Gegensatz zu anderen öffentlichen Bereichen noch nicht von einer Etablierung gesprochen werden. In vielen Krankenhäusern besteht Unklarheit über dieses neue Organisationskonzept. Was steckt hinter diesem Begriff, der teilweise synonym zur „Privatisierung“ verwendet wird? Ausgehend von dieser Fragestellung wird in der vorliegenden Arbeit gezeigt, dass PPP bei richtiger Anwendung eine Alternative zum Verkauf eines öffentlichen Krankenhauses darstellt. PPP ist ein Instrument, mit dem privates Know-how und Kapital für den öffentlichen Krankenhausträger nutzbar gemacht wird. Die öffentliche Trägerschaft des Krankenhauses bleibt dabei, im Gegensatz zu einer materiellen Privatisierung, erhalten. Die Rahmenbedingungen des Gesundheitswesens stellen insbesondere die öffentlichen Krankenhäuser vor große Herausforderungen. Die Lage ist zunehmend geprägt von Mittelknappheit, Sanierungsstau und stetig steigendem Wettbewerbsdruck um die Patienten. Die Reformbemühungen der Bundesregierung zur Senkung der Gesundheitsausgaben haben in den letzten Jahrzehnten zu immer neuen Gesetzesregelungen in immer kürzeren Zeitabständen geführt. Den bisher letzten großen Schritt in dieser Entwicklung stellt die Umstellung der Krankenhausvergütung auf DRG-Fallpauschalen dar. Die Auswirkungen sind insbesondere in den öffentlichen Krankenhäusern zu spüren. Defizitäre Einrichtungen, die bisher durch Subventionen gestützt wurden, werden nun nicht mehr „künstlich am Leben“ erhalten. Alle Krankenhäuser erhalten eine leistungsorientierte Vergütung, weitgehend unabhängig von den krankenhausspezifisch anfallenden Kosten. Durch diese Entwicklungen wurde das Bestreben in den Krankenhäuser, die internen Leistungsprozesse zu optimieren, weiter forciert. Dabei kommt den mit der Gebäudesubstanz verbundenen Leistungen eine besondere Bedeutung zu. Aufgrund hoher Investitionskosten und bedeutender Aufwendungen in der Nutzungsphase erreichen die nicht-medizinischen Leistungen in einem Krankenhaus einen beachtlichen Anteil an den Gesamtkosten. Fast ein Drittel der Krankenhaus-Kosten steht nicht in direkter Beziehung zum Heilungsprozess. In Deutschland macht dieser Anteil der nicht-medizinischen Abläufe jährlich rd. 18 Mrd. Euro aus. Das Optimierungspotenzial des nicht-medizinischen Leistungsbereichs, der auch die bau- und immobilienwirtschaftlichen Leistungen umfasst, wird bisher oft noch unterschätzt und ist in den meisten Fällen noch nicht ausgeschöpft. Allein schon aufgrund dessen finanzieller Bedeutung bedarf es einer verstärkten wissenschaftlichen Auseinandersetzung. Dieser Notwendigkeit ist bisher noch unzureichend Rechnung getragen wurden. Die vorliegende Arbeit will mit der Erforschung der Anwendbarkeit von PPP für Krankenaus-Immobilien einen Beitrag dazu leisten, diese Lücke zu schließen. Mit dieser für den deutschen Krankenhausbereich neuartigen Beschaffungsvariante wird ein Weg aufgezeigt, wie bei den nicht-medizinischen Leistungen nachhaltig Effizienzpotenziale erschlossen werden können und auf diese Weise ein Beitrag zum wirtschaftlichen Erfolg des gesamten Krankenhauses erzielt werden kann.
In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms.
THE FOURIER-BESSEL TRANSFORM
(2010)
In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of the classical tensorial Fourier transform. Moreover the L2-basis elements consisting of generalized Clifford-Hermite functions appear to be eigenfunctions of the Fourier-Bessel transform.
This paper describes the application of interval calculus to calculation of plate deflection, taking in account inevitable and acceptable tolerance of input data (input parameters). The simply supported reinforced concrete plate was taken as an example. The plate was loaded by uniformly distributed loads. Several parameters that influence the plate deflection are given as certain closed intervals. Accordingly, the results are obtained as intervals so it was possible to follow the direct influence of a change of one or more input parameters on output (in our example, deflection) values by using one model and one computing procedure. The described procedure could be applied to any FEM calculation in order to keep calculation tolerances, ISO-tolerances, and production tolerances in close limits (admissible limits). The Wolfram Mathematica has been used as tool for interval calculation.
One of the main focuses of recent Chinese urban development is the creation and retrofitting of public spaces driven by the market force and demand. However, researches concerning human and cultural influences on shaping public spaces have been scanty. There still exist many undefined ambiguous planning aspects institutionally and legislatively. This is an explanatory research to address interactions, incorporations and interrelationship between the lived environment and its peoples. It is knowledge-seeking and normative. Theoretically, public space in a Chinese context is conceptualized; empirically, a selected case is inquired. The research has unfolded a comparatively complete understanding of China’s planning evolution and on-going practices. Data collection emphasizes the concept of ‘people’ and ‘space’. First-hand data is derived from the intensive fieldwork and observatory and participatory documentations. The ample detailed authentic empirical data empowers space syntax as a strong analysis tool in decoding how human’s activities influence the public space. Findings fall into two categories but interdependent. Firstly, it discloses the studied settlement as a generic, organic and incremental development model. Its growth and established environment is evolutionary and incremental, based on its intrinsic traditions, life values and available resources. As a self-sustaining settlement, it highlights certain vernacular traits of spatial development out of lifestyles and cultural practices. Its spatial articulation appears as a process parallel to socio-economic transitions. Secondly, crucial planning aspects are theoretically summarized to address the existing gap between current planning methodology and practicalities. It pinpoints several most significant and particular issues, namely, disintegrated land use system and urban planning; missing of urban design in the planning system, loss of a human-responsive environment resulted from standardized planning and under-estimation of heritage in urban development. The research challenges present Chinese planning laws and regulations through urban public space study; and pinpoints to yield certain growth leverage for planning and development. Thus, planning is able to empower inhabitants to make decisions along the process of shaping and sustaining their space. Therefore, it discusses not only legislative issues, concerning land use planning, urban design and heritage conservation. It leads to a pivotal proposal, i.e., the integration of human and their social spaces in formulating a new spatial strategy. It expects to inform policymakers of underpinning social values and cultural practices in reconfiguring postmodern Chinese spatiality. It propounds that social context endemic to communities shall be integrated as a crucial tool in spatial strategy design, hence to strengthen spatial attributes and improve life quality.
On the mechanisms of shrinkage reducing admixtures in self con-solidating mortars and concretes
(2010)
Self Consolidating Concrete – a dream has come true!(?) Self Consolidating Concrete (SCC) is mainly characterised by its special rheological properties. With-out any vibration this concrete can be placed and compacted under its own weight, without segrega-tion or bleeding. The use of such concrete can increase the productivity on construction sites and en-able the use of a higher degree of well distributed reinforcement for thin walled structural members. This new technology also reduces health risks since in contrast to the traditional handling of concrete, the emission of noise and vibration are substantially decreased. The specific mix design for self consolidating concretes was introduced around the 1980s in Japan. In comparison to normal vibrated concrete an increased paste volume enables a good distribution of aggregates within the paste matrix, minimising the influence of aggregates friction on the concrete flow property. The introduction of inert and/or pozzolanic additives as part of the paste provides the required excess paste volume without using disproportionally high amounts of plain cement. Due to further developments of concrete admixtures such as superplasticizers, the cement paste can gain self levelling properties without causing segregation of aggregates. Whereas SCC differs from normal vibrated concrete in its fresh attributes, it should reach similar properties in the hardened state. Due to the increased paste volume it usually shows higher shrinkage. Furthermore, owing to strength requirements, SCC is often produced at low water to cement ratios and hence may additionally suffer from autogenous shrinkage. This means that cracking caused by drying or autogenous shrinkage is a real risk for SCC and can compromise its durability as cracks may serve as ingression paths for gases and salts or might permit leaching. For the time being SCC still exhibits increased shrinkage and cracking probability and hence may be discarded in many practical applications. This can be overcome by a better understanding of those mechanisms and the ways to mitigate them. It is a target of this thesis to contribute to this. How to cope with increased shrinkage of SCC? In general, engineers are facing severe problems related to shrinkage and cracking. Even for normal and high performance concrete, containing moderate amounts of binder, a lot of effort was put on counteracting shrinkage and avoiding cracking. For the time being these efforts resulted in the knowledge of how to distribute cracks rather to avoid them. The most efficient way to decrease shrinkage turned out to be to decrease the cement content of concrete down to a minimum but still sufficient amount. For SCC this obviously seems to be contradictory with the requirement of a high paste volume. Indeed, the potential for shrinkage reduction is limited to some small range modifications in the mix design following two major concepts. The first one is the reduction of the required paste volume by optimising the aggregate grading curve. The second one involves high volume substitution of cement, preferentially using inert mineral additives. The optimization of grading curves is limited by several severe practical issues. Problems start with the availability of sufficiently fractionated aggregates. Usually attempts fail because of the enormous effort in composing application-optimized grading curves or mix designs. Due to durability reasons, the substitution rate for cement is limited depending on the application purpose and on environmental exposure of the hardened concrete. In the early 1980s Shrinkage Reducing Admixtures (SRA) were introduced to counteract drying shrinkage of concrete. The first publications explicitly dealing with SRA go back to Goto and Sato (Japan). They were published in 1983, which is also the time when the SCC concept was introduced. SRA modified concretes showed a substantial reduction of free drying shrinkage contributing to crack prevention or at least a significant decrease of crack width in situations of restrained drying shrinkage. Will shrinkage reducing admixtures contribute to a broader application of SCC? Within the last three decades performance tests on several types of concrete proved the efficiency of shrinkage reducing admixtures. So, at least in terms of shrinkage and cracking, concretes in general and SCC in particular can benefit from SRA application. But "One man's meat is another man's poison" and with respect to long term performance of SRA modified concretes there are still several issues to be clarified. One of these concerns the impact of SRAs on cement hydration. It is therefore an issue to know if changes in the hydrated phase composition, induced by SRA, result in undesired properties or decreased durability. Another issue is that the long term shrinkage reduction has to be evaluated. For example, one can wonder if SRA leaching may diminish or even eliminate long term shrinkage reduction and if the release of admixtures could be a severe environmental issue. It should also be noted that the basic mechanism or physical impact of SRA as well as its implementation in recent models for shrinkage of concrete is still being discussed. The present thesis tries to shed light on the role of SRA in self consolidating concrete focusing on the three questions outlined above: basic mechanisms of cement hydration, physical impact on shrinkage and the sustainability of SRA-application. Which contributions result from this study? Based on an extensive patent search, commercial SRAs could be identified to be synergistic mixtures of non-ionic surfactants and glycols. This turns out to be most important information for more than one reason and is the subject of chapter 4. An abundant literature focuses on properties of these non-ionic surfactants. Moreover, from this rich pool of information, the behaviour of SRAs and their interactions in cementitious systems were better understood through this thesis. For example, it could be anticipated how SRAs behave in strong electrolytes and how surface activity, i.e. surface tension, and interparticle forces might be affected. The synergy effect regarding enhanced performance induced by the presence of additional glycol in SRAs could be derived from the literature on the co-surfactant nature of glycols. Generally it now can be said that glycols ensure that the non-ionic surfactant is properly distributed onto the paste interfaces to efficiently reduce surface tension. In literature, the impact of organic matter on cement hydration was extensively studied for other admixtures like superplasticizer. From there, main impact factors related to the nature of these molecules could be identified. In addition, here again, the literature on non-ionic surfactants provides sufficient information to anticipate possible interactions of SRA with cement hydration based on the nature of non-ionic surfactants. All in all, the extensive study on the nature of non-ionic surfactants, presented in chapter 4, provides fundamental understanding of the behaviour of SRAs in cement paste. Taking a step further to relate this to the impact on drying and shrinkage required to review recent models for drying and shrinkage of cement paste as presented in chapter 3. There, it is shown that macroscopic thermodynamics of the open pore systems can be successfully applied to predict drying induced deformation, but that surface activity of SRA still has to be implemented to explain the shrinkage reduction it causes. Because of severe issues concerning the importance of capillary pressure on shrinkage, a new macroscopic thermodynamic model was derived in a way that meets requirements to properly incorporate surface activity of SRA. This is the subject of chapter 5. Based on theoretical considerations, in chapter 5 the broader impact of SRA on drying cementitious matter could be outlined. In a next step, cement paste was treated as a deformable, open drying pore system. Thereby, the drying phenomena of SRA modified mortars and concrete observed by other authors could be retrieved. This phenomenological consistency of the model constitutes an important contribution towards the understanding of SRA mechanisms. Another main contribution of this work came from introducing an artificial pore system, denominated the normcube. Using this model system, it could be shown how the evolution of interfacial area and its properties interact in presence of SRAs and how this impacts drying characteristics. In chapter 7, the surface activity of commercial SRAs in aqueous solution and synthetic pore solution was investigated. This shows how the electrolyte concentration of synthetic pore solution impacts the phase behaviour of SRA and conversely, how the presence of SRA impacts the aqueous electrolyte solution. Whilst electrolytes enhance self-aggregation of SRAs into micelles and liquid crystals, the presence of SRAs leads to precipitation of minerals as syngenite and mirabilite. Moreover, electrolyte solutions containing SRAs comprise limited miscibility or rather show miscibility gaps, where the liquid separates into isotropic micellar solutions and surfactant rich reverse micellar solutions. The investigation of surface activity and phase behaviour of SRA unravelled another important contribution. From macroscopic surface tension measurements, a relationship between excess surface concentration of SRA, bulk concentration of SRA and exposed interfacial area could be derived. Based on this, it is now possible to predict the actual surface tension of the pore fluid in the course of drying once the evolution of internal interfacial area is known. This is used later in this thesis to describe the specific drying and shrinkage behaviour of SRA modified pastes and mortars. Calorimetric studies on normal Portland cement and composite binders revealed that SRA alone show only minor impact on hydration kinetics. In presence of superplasticizer however the cement hydration can be significantly decelerated. The delaying impact of SRA could be related to a selective deceleration of silicate phase hydration. Moreover, it could be shown that portlandite precipitation in presence of SRA is changed, turning the compact habitus into more or less layered structures. Thereby, the specific surface increases, causing the amount of physically bound water to increase, which in turn reduces the maximum degree of hydration achievable for sealed systems. Extensive phase analysis shows that the hydrated phase composition of SRA modified binders re-mains almost unaffected. The appearance of a temporary mineral phase could be detected by environmental scanning electron microscopy. As could be shown for synthetic pore solutions, syngenite precipitates during early hydration stages and is later consumed in the course of aluminate hydration, i.e. when sulphates are depleted. Moreover, for some SRAs, the salting out phenomena supposed to be enhanced in strong electrolytes could also be shown to take place. The resulting organic precipitates could be identified by SEM-EDX in cement paste and by X-ray diffraction on solid residues of synthetic pore solution. The presence of SRAs could also be identified to impact microstructure of well cured cement paste. Based on nitrogen adsorption measurements and mercury intrusion porosimetry the amount of small pores is seen to increase with SRA dosage, whilst the overall porosity remains unchanged. The question regarding sustainability of SRA application is the subject of chapter 10. By means of leaching studies it could be shown that SRA can be leached significantly. The mechanism could be identified as a diffusion process and a range of effective diffusion coefficients could be estimated. Thereby, the leaching of SRA can now be estimated for real structural members. However, while the admixture can be leached to high extents in tank tests, the leaching rates in practical applications can be assumed to be low because of much reduced contact with water. This could be proven by quantifying admixture loss during long term drying and rewetting cycles. Despite a loss of admixture shrinkage reduction is hardly impacted. Moreover, the cyclic tests revealed that the total deformations in presence of SRA remain low due to a lower extent of irreversibly shrinkage deformations. Another important contribution towards the better understanding of the working mechanism of SRA for drying and shrinkage came from the same leaching tests. A significant fraction of SRA is found to be immobile and does not diffuse in leaching. This fraction of SRA is probably strongly associated to cement phases as the calcium-silicate-hydrates or portlandite. Based on these findings, it is now also possible to quantify the amount of admixture active at the interfaces. This means that, the evolution of surface tension in the course of drying can be approximated, which is a fundamental requirement for modeling shrinkage in presence of SRA. The last experimental chapter of this study focuses on the working mechanism and impact of SRA on drying and shrinkage. Based on the thermodynamics of the open deformable pore system introduced in chapter 5, energy balances are set up using desorption and shrinkage isotherms of actual samples. Information on distribution of SRA in the hydrated paste is used to estimate the actual surface tensions of the pore solution. In other words, this is the first time that the surface activity of the SRA in the course of the drying is fully accounted for. From the energy balances the evolution and properties of the internal interface are then obtained. This made it possible to explain why SRAs impact drying and shrinkage and in what specific range of relative humidity they are active. Summarising the findings of this thesis it can be said that the understanding of the impact of SRAs on hydration, drying and shrinkage was brought forward. Many of the new insights came from the careful investigation of the theory of non-ionic surfactants, something that the cement community had generally overlooked up to now.
NONZONAL WAVELETS ON S^N
(2010)
In the present article we will construct wavelets on an arbitrary dimensional sphere S^n due the approach of approximate Identities. There are two equivalently approaches to wavelets. The group theoretical approach formulates a square integrability condition for a group acting via unitary, irreducible representation on the sphere. The connection to the group theoretical approach will be sketched. The concept of approximate identities uses the same constructions in the background, here we select an appropriate section of dilations and translations in the group acting on the sphere in two steps. At First we will formulate dilations in terms of approximate identities and than we call in translations on the sphere as rotations. This leads to the construction of an orthogonal polynomial system in L²(SO(n+1)). That approach is convenient to construct concrete wavelets, since the appropriate kernels can be constructed form the heat kernel leading to the approximate Identity of Gauss-Weierstra\ss. We will work out conditions to functions forming a family of wavelets, subsequently we formulate how we can construct zonal wavelets from a approximate Identity and the relation to admissibility of nonzonal wavelets. Eventually we will give an example of a nonzonal Wavelet on $S^n$, which we obtain from the approximate identity of Gauss-Weierstraß.
In nonlinear simulations the loading is, in general, applied in an incremental way. Path-following algorithms are used to trace the equilibrium path during the failure process. Standard displacement controlled solution strategies fail if snap-back phenomena occur. In this contribution, a path-following algorithm based on the dissipation of the inelastic energy is presented which allows for the simulation of snap-backs. Since the constraint is defined in terms of the internal energy, the algorithm is not restricted to continuum damage models. Furthermore, no a priori knowledge about the final damage distribution is required. The performance of the proposed algorithm is illustrated using nonlinear mesoscale simulations.
SIMULATION AND MATHEMATICAL OPTIMIZATION OF THE HYDRATION OF CONCRETE FOR AVOIDING THERMAL CRACKS
(2010)
After mixing of concrete, the hardening starts by an exothermic chemical reaction known as hydration. As the reaction rate depends on the temperature the time in the description of the hydration is replaced by the maturity which is defined as an integral over a certain function depending on the temperature. The temperature distribution is governed by the heat equation with a right hand side depending on the maturity and the temperature itself. We compare of the performance of different time integration schemes of higher order with an automatic time step control. The simulation of the heat distribution is of importance as the development of mechanical properties is driven by the hydration. During this process it is possible that the tensile stresses exceed the tensile strength and cracks occur. The goal is to produce cheap concrete without cracks. Simple crack-criterions use only temperature differences, more involved ones are based on thermal stresses. If the criterion predicts cracks some changes in the input data are needed. This can be interpreted as optimization. The final goal will be to adopt model based optimization (in contrast to simulation based optimization) to the problem of the hydration of young concrete and the avoidance of cracks. The first step is the simulation of the hydration, which we focus in this paper.