Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Identification and dissolution behavior of the secondary uranium minerals in the corrosion products of Depleted Uranium (DU) ammunition formed in soils

In der vorliegenden Studie wurden verschiedene Techniken eingesetzt um drei Proben (4, 7, and 8) die aus denrnKorrosionsprodukten von aus dem Kosovo Krieg stammenden Munitionskugeln, bestehend aus abgereichertem Uranrn(Depleted Uranium - DU), zu untersuchen. Als erstes Verfahren wurde die Raman-Spektroskopie eingesetzt. Hierbeirnzeigte sichin den Proben, charakterisiert durch einen Doppelpeak, die Anwesenheit von Schoepitrn(UO2)8O2(OH)12(H2O)12. Der erste und zweite Peakzeigte sich im Spektralbereich von 840,3-842,5 cm-1rnbeziehungsweise 853,6-855,8 cm-1. Diese Werte stimmen mit den Literaturwerten für Raman-Peaks für Schoepitrnüberein. Des Weiteren wurde bei dieser Untersuchungsmethode Becquerelite Ca(UO2)6O4(OH)6(H2O)8 mit einemrnPeak im Bereich zwischen 829 to 836 cm-1 gefunden. Aufgrund des Fehlens des Becquerelitespektrums in derrnSpektralbibliothek wurde eine in der Natur vorkommende Variante analysiert und deren Peak bei 829 cm-1 bestimmt,rnwas mit den Ergebnissen in den Proben korrespondiert. Mittels Röntgenbeugung (X-Ray Diffraction, XRD) zeigtenrnsich in allen Proben ähnliche Spektren. Das lässt darauf schließen, dass das pulverisierte Material in allen Probenrndas gleiche ist. Hierbei zeigte sich eine sehr gute Übereinstimmung mit Schoepit und/oder meta-rnSchoepit(UO2)8O2(OH)12(H2O)10, sowie Becquerelite. Weiterhin war weder Autunit, Sabugalit noch Uranylphosphatrnanwesend, was die Ergebnisse einer anderen Studie, durchgeführt an denselben Proben, wiederlegt. DiernAnwesenheit von P, C oder Ca im Probenmaterial konnte ausgeschlossen werden. Im Falle von Calciumkann diesrnmit der Anwesenheit von Uran erklärt werden, welches aufgrund seines Atomradius bevorzugt in Becquerelite (1:6)rneingebaut wird. Die beiden Hauptpeaks für Uran lagen im Falle von U 4f 7/2 bei 382.0 eV und im Falle von U 4f 5/2rnbei 392 eV. Diese Werte mit den Literaturwerten für Schoepit und meta-Schoepitüberein. Die Ergebnissernelektronenmikroskopischen Untersuchung zeigen U, O, Ca, Ti als dominante Komponenten in allen Messungen.rnElemente wie Si, Al, Fe, S, Na, und C wurden ebenfalls detektiert; allerdings kann nicht ausgeschlossen werden,rndass diese Elemente aus dem Boden in der unmittelbaren Umgebung der Munitionsgeschosse stammen. Gold wurdernebenfalls gemessen, was aber auf die Goldarmierung in den Probenaufbereitungsbehältern zurückgeführt werdenrnkann. Die Elektronenmikroskopie zeigte außerdem einige Stellen in denen elementares Uran und Bodenmineralernsowie sekundäre Uranminerale auftraten. Die Elementübersicht zeigt einen direkten Zusammenhang zwischen U andrnCa und gleichzeitig keine Korrelation zwischen U und Si, oder Mg. Auf der anderen Seite zeigte sich aber einrnZusammenhang zwischen Si und Al da beide Konstituenten von Bodenmineralen darstellen. Eine mit Hilfe derrnElektronenstrahlmikroanalyse durchgeführte quantitative Analyse zeigte den Massenanteil von Uran bei ca. 78 - 80%,rnwas mit den 78,2% and 79,47% für Becquerelite beziehungsweise Schoepit aufgrund ihrer Summenformelrnkorrespondiert. Zusätzlich zeigt sich für Calcium ein Massenanteil von 2% was mit dem Wert in Becquerelite (2.19%)rnrecht gut übereinstimmt. Der Massenanteil von Ti lag in einigen Fällen bei 0,77%, was auf eine noch nicht korrodierternDU-Legierung zurückzuführen ist. Ein Lösungsexperiment wurde weiterhin durchgeführt, wobei eine 0,01 M NaClO4-rnLösung zum Einsatz kam in der die verbliebene Probensubstanz der Korrosionsprodukte gelöst wurde;rnNatriumperchlorate wurde hierbei genutzt um die Ionenstärke bei 0,01 zu halten. Um Verunreinigungen durchrnatmosphärisches CO2 zu vermeiden wurden die im Versuch für die drei Hauptproben genutzten 15 Probenbehälterrnmit Stickstoffgas gespült. Eine Modelkalkulation für den beschriebenen Versuchsaufbau wurde mit Visual MINTEQrnv.3.0 für die mittels vorgenannten Analysemethoden beschriebenen Mineralphasen im pH-Bereich von 6 – 10 imrnFalle von Becquerelite, und Schoepit berechnet. Die modellierten Lösungskurven wurden unter An- und Abwesenheitrnvon atmosphärischem CO2 kalkuliert. Nach dem Ende des Lösungsexperiments (Dauer ca. 6 Monate) zeigten diernKonzentrationen des gelösten Urans, gemessen mittels ICP-OES, gute Übereinstimmung mit den modelliertenrnSchoepit und Becquerelite Kurven. Auf Grund des ähnlichen Löslichkeitverhaltens war es nicht möglich zwichen denrnbeiden Mineralen zu unterscheiden. Schoepit kontrolliert im sauren Bereich die Löslichkeit des Urans, währendrnbecquerelit im basichen am wenigsten gelöst wird. Des Weiteren bleibt festzuhalten, dass ein Anteil an CO2 in diernverschlossenen Probenbehälter eingedrungen ist, was sich mit der Vorhersage der Modeldaten deckt. Die Löslichkeitrnvon Uran in der Lösung als Funktion des pH-Wertes zeigte die niedrigsten Konzentrationen im Falle einer Zunahmerndes pH-Wertes von 5 auf 7 (ungefähr 5,1 x 10-6 mol/l) und einer Zunahme des pH-Wertes auf 8 (ungefähr 1,5 x 10-6rnmol/l bei). Oberhalb dieses Bereichs resultiert jeder weitere Anstieg des pH-Wertes in einer Zunahme gelösten Uransrnin der Lösung. Der ph-Wert der Lösung wie auch deren pCO2-Wert kontrollieren hier die Menge des gelösten Urans.rnAuf der anderen Seite zeigten im Falle von Becquerelite die Ca-Konzentrationen höhere Werte als erwartet, wobeirnwahrscheinlich auf eine Vermischung der Proben mit Bodensubstanz zurückgeführt werden kann. Abschließendrnwurde, unter Berücksichtigung der oben genannten Ergebnisse, eine Fallstudie aus Basrah (Irak) diskutiert, wo inrnzwei militärischen Konflikten Uranmunition in zwei Regionen unter verschiedenen Umweltbedingungen eingesetztrnwurden.

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.

Sustainable improvement of water networks : to achieve best decisions for rehabilitation plans using advanced GIS and statistical techniques

Many of developing countries are facing crisis in water management due to increasing of population, water scarcity, water contaminations and effects of world economic crisis. Water distribution systems in developing countries are facing many challenges of efficient repair and rehabilitation since the information of water network is very limited, which makes the rehabilitation assessment plans very difficult. Sufficient information with high technology in developed countries makes the assessment for rehabilitation easy. Developing countries have many difficulties to assess the water network causing system failure, deterioration of mains and bad water quality in the network due to pipe corrosion and deterioration. The limited information brought into focus the urgent need to develop economical assessment for rehabilitation of water distribution systems adapted to water utilities. Gaza Strip is subject to a first case study, suffering from severe shortage in the water supply and environmental problems and contamination of underground water resources. This research focuses on improvement of water supply network to reduce the water losses in water network based on limited database using techniques of ArcGIS and commercial water network software (WaterCAD). A new approach for rehabilitation water pipes has been presented in Gaza city case study. Integrated rehabilitation assessment model has been developed for rehabilitation water pipes including three components; hydraulic assessment model, Physical assessment model and Structural assessment model. WaterCAD model has been developed with integrated in ArcGIS to produce the hydraulic assessment model for water network. The model have been designed based on pipe condition assessment with 100 score points as a maximum points for pipe condition. As results from this model, we can indicate that 40% of water pipeline have score points less than 50 points and about 10% of total pipes length have less than 30 score points. By using this model, the rehabilitation plans for each region in Gaza city can be achieved based on available budget and condition of pipes. The second case study is Kuala Lumpur Case from semi-developed countries, which has been used to develop an approach to improve the water network under crucial conditions using, advanced statistical and GIS techniques. Kuala Lumpur (KL) has water losses about 40% and high failure rate, which make severe problem. This case can represent cases in South Asia countries. Kuala Lumpur faced big challenges to reduce the water losses in water network during last 5 years. One of these challenges is high deterioration of asbestos cement (AC) pipes. They need to replace more than 6500 km of AC pipes, which need a huge budget to be achieved. Asbestos cement is subject to deterioration due to various chemical processes that either leach out the cement material or penetrate the concrete to form products that weaken the cement matrix. This case presents an approach for geo-statistical model for modelling pipe failures in a water distribution network. Database of Syabas Company (Kuala Lumpur water company) has been used in developing the model. The statistical models have been calibrated, verified and used to predict failures for both networks and individual pipes. The mathematical formulation developed for failure frequency in Kuala Lumpur was based on different pipeline characteristics, reflecting several factors such as pipe diameter, length, pressure and failure history. Generalized linear model have been applied to predict pipe failures based on District Meter Zone (DMZ) and individual pipe levels. Based on Kuala Lumpur case study, several outputs and implications have been achieved. Correlations between spatial and temporal intervals of pipe failures also have been done using ArcGIS software. Water Pipe Assessment Model (WPAM) has been developed using the analysis of historical pipe failure in Kuala Lumpur which prioritizing the pipe rehabilitation candidates based on ranking system. Frankfurt Water Network in Germany is the third main case study. This case makes an overview for Survival analysis and neural network methods used in water network. Rehabilitation strategies of water pipes have been developed for Frankfurt water network in cooperation with Mainova (Frankfurt Water Company). This thesis also presents a methodology of technical condition assessment of plastic pipes based on simple analysis. This thesis aims to make contribution to improve the prediction of pipe failures in water networks using Geographic Information System (GIS) and Decision Support System (DSS). The output from the technical condition assessment model can be used to estimate future budget needs for rehabilitation and to define pipes with high priority for replacement based on poor condition. rn

Stimuli-responsive materials for self-healing in corrosion protection

The corrosion of metallic materials is a crucial issue on an economical and ecological scale. Corrosion protection becomes then necessarily needed. The main focus of the thesis is to develop stimuli-responsive nanocontainers for self-healing in corrosion protection. A nanocontainer is efficient if distinct payloads can be selectively released via different stimuli because unwanted and unspecific release can be avoided. For anti-corrosion, the wanted nanocontainer is the one able to release its self-healing agents or corrosion inhibitors upon change of pH- or/and redox-potential due to the variation of these two signals at the corroded sites. Conducting polymers such as polyaniline (PANI) were chosen for building the shell of capsules due to their important characteristics of being both pH- and redox responsive.

On the experimental behaviour of a silty sand and its modelling through Generalized Plasticity.

La tesi contiene uno studio sperimentale sul comportamento di una sabbia limosa del sottosuolo della laguna veneta e propone un'interpretazione dei risultati sperimentali ottenuti alla luce dei presupposti teorici di un approccio costitutivo avanzato noto come "Plasticità Generalizzata". Il programma sperimentale è consistito nella realizzazione di prove edometriche e prove triassiali su campioni di sabbia provenienti dal sito di Treporti, situato in prossimità della bocca di Lido. La risposta sperimentale, in termini di modulo volumetrico, è stata messa a confronto con i risultati di alcuni studi di letteratura, con particolare riferimento a quelli condotti da Jefferies & Been (2000). La disponibilità di prove di compressione edometrica realizzate nella cella K0 e la conseguente possibilità di valutare il coefficiente di spinta a riposo ha permesso di interpretare le prove in termini di tensione media efficace p' e di verificare l'applicabilità al caso in esame degli approcci di letteratura disponibili, spesso sviluppati a partire da prove di compressione isotropa effettuate in cella triassiale. Il comportamento tenso-deformativo osservato è stato successivamente simulato con un modello costitutivo per sabbie sviluppato nell'ambito della Plasticità Generalizzata. In particolare sono state utilizzate tre diverse formulazioni, che costituiscono un avanzamento dell'iniziale modello costitutivo proposto da Pastor, Zienkiewicz e Chan (1990), basate sull'uso di un parametro di stato del materiale definito rispetto alle condizioni di Stato Critico. Dal confronto tra previsioni del modello e risposta sperimentale è stato possibile individuare la formulazione che meglio simula il comportamento meccanico osservato sia in compressione edometrica sia in prove di taglio ed è stato proposto un set di parametri costitutivi ritenuti rappresentativi del terreno studiato.

Evidence of a Generalized Defect of Acinar Cell Function in Shwachman-Diamond Syndrome

: Because the acinar cells of the exocrine pancreas in patients with Shwachman-Diamond syndrome (SDS) are severely depleted, we hypothesized that a similar deficiency may be present in acinar cells of the parotid gland.

Generalized expansion of nociceptive reflex receptive fields in chronic pain patients

Widespread central hypersensitivity is present in chronic pain and contributes to pain and disability. According to animal studies, expansion of receptive fields of spinal cord neurons is involved in central hypersensitivity. We recently developed a method to quantify nociceptive receptive fields in humans using spinal withdrawal reflexes. Here we hypothesized that patients with chronic pelvic pain display enlarged reflex receptive fields. Secondary endpoints were subjective pain thresholds and nociceptive withdrawal reflex thresholds after single and repeated (temporal summation) electrical stimulation. 20 patients and 25 pain-free subjects were tested. Electrical stimuli were applied to 10 sites on the foot sole for evoking reflexes in the tibialis anterior muscle. The reflex receptive field was defined as the area of the foot (fraction of the foot sole) from which a muscle contraction was evoked. For the secondary endpoints, the stimuli were applied to the cutaneous innervation area of the sural nerve. Medians (25-75 percentiles) of fraction of the foot sole in patients and controls were 0.48 (0.38-0.54) and 0.33 (0.27-0.39), respectively (P=0.008). Pain and reflex thresholds after sural nerve stimulation were significantly lower in patients than in controls (P<0.001 for all measurements). This study provides for the first time evidence for widespread expansion of reflex receptive fields in chronic pain patients. It thereby identifies a mechanism involved in central hypersensitivity in human chronic pain. Reverting the expansion of nociceptive receptive fields and exploring the prognostic meaning of this phenomenon may become future targets of clinical research.