Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling

Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises.

HAWAIIAN SUGAR CANE RAT CONTROL METHODS AND PROBLEMS

The problem of rats in our Hawaiian sugar cane fields has been with us for a long time. Early records tell of heavy damage at various times on all the islands where sugar cane is grown. Many methods were tried to control these rats. Trapping was once used as a control measure, a bounty was used for a time, gangs of dogs were trained to catch the rats as the cane was harvested. Many kinds of baits and poisons were used. All of these methods were of some value as long as labor was cheap. Our present day problem started when the labor costs started up and the sugar industry shifted to long cropping. Until World War II cane was an annual crop. After the war it was shifted to a two year crop, three years in some places. Depending on variety, location, and soil we raise 90 to 130 tons of sugar cane per acre, which produces 7 to 15 tons of sugar per acre for a two year crop. This sugar brings about $135 dollars per ton. This tonnage of cane is a thick tangle of vegetation. The cane grows erect for almost a year, as it continues to grow it bends over at the base. This allows the stalk to rest on the ground or on other stalks of cane as it continues to grow. These stalks form a tangled mat of stalks and dead leaves that may be two feet thick at the time of harvest. At the same time the leafy growing portion of the stalk will be sticking up out of the mat of cane ten feet in the air. Some of these individual stalks may be 30 feet long and still growing at the time of harvest. All this makes it very hard to get through a cane field as it is one long, prolonged stumble over and through the cane. It is in this mat of cane that our three species of rats live. Two species are familiar to most people in the pest control field. Rattus norvegicus and Rattus rattus. In the latter species we include both the black rat and the alexandrine rats, their habits seem to be the same in Hawaii. Our third rat is the Polynesian rat, Rattus exlans, locally called the Hawaiian rat. This is a small rat, the average length head to tip of tail is nine inches and the average body weight is 65 grams. It has dark brownish fur like the alexandrine rats, and a grey belly. It is found in Indonesia, on most of the islands of Oceania and in New Zealand. All three rats live in our cane fields and the brushy and forested portions of our islands. The norway and alexandrine rats are found in and around the villages and farms, the Polynesian rat is only found in the fields and waste areas. The actual amount of damage done by rats is small, but destruction they cause is large. The rats gnaw through the rind of the cane stalk and eat the soft juicy and sweet tissues inside. They will hollow out one to several nodes per stalk attacked. The effect to the cane stalk is like ringing a tree. After this attack the stalk above the chewed portion usually dies, and sometimes the lower portion too. If the rat does not eat through the stalk the cane stalk could go on living and producing sugar at a reduced rate. Generally an injured stalk does not last long. Disease and souring organisms get in the injury and kill the stalk. And if this isn't enough, some insects are attracted to the injured stalk and will sometimes bore in and kill it. An injured stalk of cane doesn't have much of a chance. A rat may only gnaw out six inches of a 30 foot stalk and the whole stalk will die. If the rat only destroyed what he ate we could ignore them but they cause the death of too much cane. This dead, dying, and souring cane cause several direct and indirect tosses. First we lose the sugar that the cane would have produced. We harvest all of our cane mechanically so we haul the dead and souring cane to the mill where we have to grind it with our good cane and the bad cane reduces the purity of the sugar juices we squeeze from the cane. Rats reduce our income and run up our overhead.

Assessing Pathogenicity for Novel Mutation/Sequence Variants: The Value of Healthy Older Individuals

Improvement in DNA technology is increasingly revealing unexpected/unknown mutations in healthy persons and generating anxiety due to their still unknown health consequences. We report a 44-year-old healthy father of a 10-year-old daughter with bilateral coloboma and hearing loss, but without muscle weakness, in whom a whole-genome CGH revealed a deletion of exons 38-44 in the dystrophin gene. This mutation was inherited from her asymptomatic father, who was further clinically and molecularly evaluated for prognosis and genetic counseling (GC). This deletion was never identified by us in 982 Duchenne/Becker patients. To assess whether the present case represents a rare case of non-penetrance, and aiming to obtain more information for prognosis and GC, we suggested that healthy older relatives submit their DNA for analysis, to which several complied. Mutation analysis revealed that his mother, brother, and 56-year-old maternal uncle also carry the 38-44 deletion, suggesting it an unlikely cause of muscle weakness. Genome sequencing will disclose mutations and variants whose health impact are still unknown, raising important problems in interpreting results, defining prognosis, and discussing GC. We suggest that, in addition to family history, keeping the DNA of older relatives could be very informative, in particular for those interested in having their genome sequenced.

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Investigating Smart Sampling as a population initialization method for Differential Evolution in continuous problems

Recently, researches have shown that the performance of metaheuristics can be affected by population initialization. Opposition-based Differential Evolution (ODE), Quasi-Oppositional Differential Evolution (QODE), and Uniform-Quasi-Opposition Differential Evolution (UQODE) are three state-of-the-art methods that improve the performance of the Differential Evolution algorithm based on population initialization and different search strategies. In a different approach to achieve similar results, this paper presents a technique to discover promising regions in a continuous search-space of an optimization problem. Using machine-learning techniques, the algorithm named Smart Sampling (SS) finds regions with high possibility of containing a global optimum. Next, a metaheuristic can be initialized inside each region to find that optimum. SS and DE were combined (originating the SSDE algorithm) to evaluate our approach, and experiments were conducted in the same set of benchmark functions used by ODE, QODE and UQODE authors. Results have shown that the total number of function evaluations required by DE to reach the global optimum can be significantly reduced and that the success rate improves if SS is employed first. Such results are also in consonance with results from the literature, stating the importance of an adequate starting population. Moreover, SS presents better efficacy to find initial populations of superior quality when compared to the other three algorithms that employ oppositional learning. Finally and most important, the SS performance in finding promising regions is independent of the employed metaheuristic with which SS is combined, making SS suitable to improve the performance of a large variety of optimization techniques. (C) 2012 Elsevier Inc. All rights reserved.

Use of different commercial Artemia sp. Enrichements in Octopus Vulgaris, paralarval rearing at initial planctonic phase: effects on growth, survival and fatty acid composition of the paralarvae

[EN] Octopus "paralarvae", are planktonic, swim actively and have high metabolic rates, requiring large quantities of live prey of adequate motility and nutritional quality ( Iglesias et al., 2000; Navarro and Villanueva, 2000, 2003). During the planktonic phase, they undergo strong morphological changes, after which the octopuses start settling to the bottom. The potential of Octopus vulgaris as candiadate for diversification of marine aquacultures are mainly due to its high food conversion rate and fast growth.( Iglesias et al 2006). Despite the research effort taken until now, paralarval rearing of O. vulgaris still suffers high mortalities which limited the industrial culture of this species. The main problems in the paralarval rearing stages are the high mortality rates and poor growth. These are attributed to the lack of standardized culture techniques and nutritional deficiencies in the diet of paralarvae, especially in n-3 highly unsaturated fatty acids (n-3 HUFA). The objective if this experience was to test different commercial live prey enrichment to improve nutritional quality of the artemia.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Sistema per l'estrazione e purificazione di sostanze antiossidanti naturali nelle acque di vegetazione delle olive

The olive oil extraction industry is responsible for the production of high quantities of vegetation waters, represented by the constitutive water of the olive fruit and by the water used during the process. This by-product represent an environmental problem in the olive’s cultivation areas because of its high content of organic matter, with high value of BOD5 and COD. For that reason the disposal of the vegetation water is very difficult and needs a previous depollution. The organic matter of vegetation water mainly consists of polysaccharides, sugars, proteins, organic acids, oil and polyphenols. This last compounds are the principal responsible for the pollution problems, due to their antimicrobial activity, but, at the same time they are well known for their antioxidant properties. The most concentrate phenolic compounds in waters and also in virgin olive oils are secoiridoids like oleuropein, demethyloleuropein and ligstroside derivatives (the dialdehydic form of elenolic acid linked to 3,4-DHPEA, or p-HPEA (3,4-DHPEA-EDA or p-HPEA-EDA) and an isomer of the oleuropein aglycon (3,4-DHPEA-EA). The management of the olive oil vegetation water has been extensively investigated and several different valorisation methods have been proposed, such as the direct use as fertilizer or the transformation by physico-chemical or biological treatments. During the last years researchers focused their interest on the recovery of the phenolic fraction from this waste looking for its exploitation as a natural antioxidant source. At the present only few contributes have been aimed to the utilization for a large scale phenols recovery and further investigations are required for the evaluation of feasibility and costs of the proposed processes. The present PhD thesis reports a preliminary description of a new industrial scale process for the recovery of the phenolic fraction from olive oil vegetation water treated with enzymes, by direct membrane filtration (microfiltration/ultrafiltration with a cut-off of 250 KDa, ultrafiltration with a cut-off of 7 KDa/10 KDa and nanofiltration/reverse osmosis), partial purification by the use of a purification system based on SPE analysis and by a liquid-liquid extraction system (LLE) with contemporary reduction of the pollution related problems. The phenolic fractions of all the samples obtained were qualitatively and quantitatively by HPLC analysis. The work efficiency in terms of flows and in terms of phenolic recovery gave good results. The final phenolic recovery is about 60% respect the initial content in the vegetation waters. The final concentrate has shown a high content of phenols that allow to hypothesize a possible use as zootechnic nutritional supplements. The purification of the final concentrate have garanteed an high purity level of the phenolic extract especially in SPE analysis by the use of XAD-16 (73% of the total phenolic content of the concentrate). This purity level could permit a future food industry employment such as food additive, or, thanks to the strong antioxidant activity, it would be also use in pharmaceutical or cosmetic industry. The vegetation water depollutant activity has brought good results, as a matter of fact the final reverse osmosis permeate has a low pollutant rate in terms of COD and BOD5 values (2% of the initial vegetation water), that could determinate a recycling use in the virgin olive oil mechanical extraction system producing a water saving and reducing thus the oil industry disposal costs .

Modelli non lineari statici e dinamici su dati microeconomici: analisi delle condizioni finanziarie delle famiglie italiane

The thesis studies the economic and financial conditions of Italian households, by using microeconomic data of the Survey on Household Income and Wealth (SHIW) over the period 1998-2006. It develops along two lines of enquiry. First it studies the determinants of households holdings of assets and liabilities and estimates their correlation degree. After a review of the literature, it estimates two non-linear multivariate models on the interactions between assets and liabilities with repeated cross-sections. Second, it analyses households financial difficulties. It defines a quantitative measure of financial distress and tests, by means of non-linear dynamic probit models, whether the probability of experiencing financial difficulties is persistent over time. Chapter 1 provides a critical review of the theoretical and empirical literature on the estimation of assets and liabilities holdings, on their interactions and on households net wealth. The review stresses the fact that a large part of the literature explain households debt holdings as a function, among others, of net wealth, an assumption that runs into possible endogeneity problems. Chapter 2 defines two non-linear multivariate models to study the interactions between assets and liabilities held by Italian households. Estimation refers to a pooling of cross-sections of SHIW. The first model is a bivariate tobit that estimates factors affecting assets and liabilities and their degree of correlation with results coherent with theoretical expectations. To tackle the presence of non normality and heteroskedasticity in the error term, generating non consistent tobit estimators, semi-parametric estimates are provided that confirm the results of the tobit model. The second model is a quadrivariate probit on three different assets (safe, risky and real) and total liabilities; the results show the expected patterns of interdependence suggested by theoretical considerations. Chapter 3 reviews the methodologies for estimating non-linear dynamic panel data models, drawing attention to the problems to be dealt with to obtain consistent estimators. Specific attention is given to the initial condition problem raised by the inclusion of the lagged dependent variable in the set of explanatory variables. The advantage of using dynamic panel data models lies in the fact that they allow to simultaneously account for true state dependence, via the lagged variable, and unobserved heterogeneity via individual effects specification. Chapter 4 applies the models reviewed in Chapter 3 to analyse financial difficulties of Italian households, by using information on net wealth as provided in the panel component of the SHIW. The aim is to test whether households persistently experience financial difficulties over time. A thorough discussion is provided of the alternative approaches proposed by the literature (subjective/qualitative indicators versus quantitative indexes) to identify households in financial distress. Households in financial difficulties are identified as those holding amounts of net wealth lower than the value corresponding to the first quartile of net wealth distribution. Estimation is conducted via four different methods: the pooled probit model, the random effects probit model with exogenous initial conditions, the Heckman model and the recently developed Wooldridge model. Results obtained from all estimators accept the null hypothesis of true state dependence and show that, according with the literature, less sophisticated models, namely the pooled and exogenous models, over-estimate such persistence.

Formulations and Algorithms for Routing Problems

Combinatorial Optimization is a branch of optimization that deals with the problems where the set of feasible solutions is discrete. Routing problem is a well studied branch of Combinatorial Optimization that concerns the process of deciding the best way of visiting the nodes (customers) in a network. Routing problems appear in many real world applications including: Transportation, Telephone or Electronic data Networks. During the years, many solution procedures have been introduced for the solution of different Routing problems. Some of them are based on exact approaches to solve the problems to optimality and some others are based on heuristic or metaheuristic search to find optimal or near optimal solutions. There is also a less studied method, which combines both heuristic and exact approaches to face different problems including those in the Combinatorial Optimization area. The aim of this dissertation is to develop some solution procedures based on the combination of heuristic and Integer Linear Programming (ILP) techniques for some important problems in Routing Optimization. In this approach, given an initial feasible solution to be possibly improved, the method follows a destruct-and-repair paradigm, where the given solution is randomly destroyed (i.e., customers are removed in a random way) and repaired by solving an ILP model, in an attempt to find a new improved solution.

Oceanic crust and island arc formation in Central Asia during late Neoproterozoic times - evidence from petrological and geochemical studies

Die vorliegende Arbeit behandelt die Entwicklung des 570 Ma alten, neoproterozoischen Agardagh - Tes-Chem Ophioliths (ATCO) in Zentralasien. Dieser Ophiolith liegt südwestlich des Baikalsees (50.5° N, 95° E) und wurde im frühen Stadium der Akkretion des Zentralasiatischen Mobilgürtels auf den nordwestlichen Rand des Tuvinisch-Mongolischen Mikrokontinentes aufgeschoben. Bei dem Zentralasiatische Mobilgürtel handelt es sich um einen riesigen Akkretions-Subduktionskomplex, der heute das größte zusammenhängende Orogen der Erde darstellt. Im Rahmen dieser Arbeit wurden eine Reihe plutonischer und vulkanischer Gesteine, sowie verschiedene Mantelgesteine des ATCO mittels mikroanalytischer und geochemischer Verfahren untersucht (Elektronenstrahlmikrosonde, Ionenstrahlmikrosonde, Spurenelement- und Isotopengeochemie). Die Auswertung dieser Daten ermöglichte die Entwicklung eines geodynamisch-petrologischen Modells zur Entstehung des ATCO. Die vulkanischen Gesteine lassen sich aufgrund ihrer Spurenelement- und Isotopenzusammensetzung in inselbogenbezogene und back-arc Becken bezogene Gesteine (IA-Gesteine und BAB-Gesteine) unterscheiden. Darüber hinaus gibt es eine weitere, nicht eindeutig zuzuordnende Gruppe, die hauptsächlich mafische Gänge umfasst. Der grösste Teil der untersuchen Vulkanite gehört zur Gruppe der IA-Gesteine. Es handelt sich um Al-reiche Basalte und basaltische Andesite, welche aus einem evolvierten Stammmagma mit Mg# 0.60, Cr ~ 180 µg/g und Ni ~ 95 µg/g hauptsächlich durch Klinopyroxenfraktionierung entstanden sind. Das Stammmagma selbst entstand durch Fraktionierung von ca. 12 % Olivin und geringen Anteilen von Cr-Spinell aus einer primären, aus dem Mantel abgeleiteten Schmelze. Die IA-Gesteine haben hohe Konzentrationen an inkompatiblen Spurenelementen (leichte-(L)- Seltenerdelement-(SEE)-Konzentrationen etwa 100-fach chondritisch, chondrit-normierte (La/Yb)c von 14.6 - 5.1), negative Nb-Anomalien (Nb/La = 0.37 - 0.62) und niedrige Zr/Nb Verhältnisse (7 - 14) relativ zu den BAB-Gesteinen. Initiale eNd Werte liegen bei etwa +5.5, initiale Bleiisotopenverhältnisse sind: 206Pb/204Pb = 17.39 - 18.45, 207Pb/204Pb = 15.49 - 15.61, 208Pb/204Pb = 37.06 - 38.05. Die Anreicherung lithophiler inkompatibler Spurenelemente (LILE) in dieser Gruppe ist signifikant (Ba/La = 11 - 130) und zeigt den Einfluss subduzierter Komponenten an. Die BAB-Gesteine repräsentieren Schmelzen, die sehr wahrscheinlich aus der gleichen Mantelquelle wie die IA-Gesteine stammen, aber durch höhere Aufschmelzgrade (8 - 15 %) und ohne den Einfluss subduzierter Komponenten entstanden sind. Sie haben niedrigere Konzentrationen an inkompatiblen Spurenelementen, flache SEE-Muster ((La/Yb)c = 0.6 - 2.4) und höhere initiale eNd Werte zwischen +7.8 und +8.5. Nb Anomalien existieren nicht und Zr/Nb Verhältnisse sind hoch (21 - 48). Um die geochemische Entwicklung der vulkanischen Gesteine des ATCO zu erklären, sind mindestens drei Komponenten erforderlich: (1) eine angereicherte, ozeaninselbasalt-ähnliche Komponente mit hoher Nb Konzentration über ~ 30 µg/g, einem niedrigen Zr/Nb Verhältnis (ca. 6.5), einem niedrigen initialen eNd Wert (um 0), aber mit radiogenen 206Pb/204Pb-, 207Pb/204Pb- und 208Pb/204Pb-Verhältnissen; (2) eine N-MORB ähnliche back-arc Becken Komponente mit flachem SEE-Muster und einem hohen initialen eNd Wert von mindestens +8.5, und (3) eine Inselbogen-Komponente aus einer verarmten Mantelquelle, welche durch die abtauchende Platte geochemisch modifiziert wurde. Die geochemische Entstehung der ATCO Vulkanite lässt sich dann am besten durch eine Kombination aus Quellenkontamination, fraktionierte Kristallisation und Magmenmischung erklären. Geodynamisch gesehen entstand der ATCO sehr wahrscheinlich in einem intraozeanischen Inselbogen - back-arc System. Bei den untersuchten Plutoniten handelt es sich um ultramafische Kumulate (Wehrlite und Pyroxenite) sowie um gabbroische Plutonite (Olivin-Gabbros bis Diorite). Die geochemischen Charakteristika der mafischen Plutonite sind deutlich unterschiedlich zu denen der vulkanischen Gesteine, weshalb sie sehr wahrscheinlich ein späteres Entwicklungsstadium des ATCO repräsentieren. Die Spurenelement-Konzentrationen in den Klinopyroxenen der ultramafischen Kumulate sind extrem niedrig, mit etwa 0.1- bis 1-fach chondritischen SEE-Konzentrationen und mit deutlich LSEE-verarmten Mustern ((La/Yb)c = 0.27 - 0.52). Berechnete Gleichgewichtsschmelzen der ultramafischen Kumulate zeigen grosse Ähnlichkeit zu primären boninitischen Schmelzen. Die primären Magmen waren daher boninitischer Zusammensetzung und entstanden in dem durch vorausgegangene Schmelzprozesse stark verarmten Mantelkeil über einer Subduktionszone. Niedrige Spurenelement-Konzentrationen zeigen einen geringen Einfluss der abtauchenden Platte an. Die Spurenelement-Konzentrationen der Gabbros sind ebenfalls niedrig, mit etwa 0.5 - 10-fach chondritischen SEE-Konzentrationen und mit variablen SEE-Mustern ((La/Yb)c = 0.25 - 2.6). Analog zu den Vulkaniten der IA-Gruppe haben alle Gabbros eine negative Nb-Anomalie mit Nb/La = 0.01 - 0.31. Die initialen eNd Werte der Gabbros variieren zwischen +4.8 und +7.1, mit einem Mittelwert von +5.9, und sind damit identisch mit denen der IA-Vulkanite. Bei den untersuchten Mantelgesteinen handelt es sich um teilweise serpentinisierte Dunite und Harzburgite, die alle durch hohe Mg/Si- und niedrige Al/Si-Verhältnisse gekennzeichnet sind. Dies zeigt einen refraktären Charakter an und steht in guter Übereinstimmung mit den hohen Cr-Zahlen (Cr#) der Spinelle (bis zu Cr# = 0.83), auf deren Basis der Aufschmelzgrad der residuellen Mantelgesteine berechnet wurde. Dieser beträgt etwa 25 %. Die geochemische Zusammensetzung und die petrologischen Daten der Ultramafite und Gabbros lassen sich am besten erklären, wenn man für die Entstehung dieser Gesteine einen zweistufigen Prozess annimmt. In einer ersten Stufe entstanden die ultramafischen Kumulate unter hohem Druck in einer Magmenkammer an der Krustenbasis, hauptsächlich durch Klinopyroxen-Fraktionierung. Bei dieser Magmenkammer handelte es sich um ein offenes System, dem von unten laufend neue Schmelze zugeführt wurde, und aus dem im oberen Bereich evolviertere Schmelzen geringerer Dichte entwichen. Diese evolvierten Schmelzen stiegen in flachere krustale Bereiche auf und bildeten dort meist isolierte Intrusionskörper. Diese Intrusionskörper erstarrten ohne Magmen-Nachschub, weshalb petrographisch sehr unterschiedliche Gesteine entstehen konnten. Eine geochemische Modifikation der abkühlenden Schmelzen erfolgte allerdings durch die Assimilation von Nebengestein. Da innerhalb der Gabbros keine signifikante Variation der initalen eNd Werte existiert, handelte es sich bei dem assimilierten Material hauptsächlich um vulkanische Gesteine des ATCO und nicht um ältere, möglicherweise kontinentale Kruste.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Ein inverses Problem für die degeneriert parabolische Richardsgleichung

In der vorliegenden Arbeit werden zwei physikalischeFließexperimente an Vliesstoffen untersucht, die dazu dienensollen, unbekannte hydraulische Parameter des Materials, wiez. B. die Diffusivitäts- oder Leitfähigkeitsfunktion, ausMeßdaten zu identifizieren. Die physikalische undmathematische Modellierung dieser Experimente führt auf einCauchy-Dirichlet-Problem mit freiem Rand für die degeneriertparabolische Richardsgleichung in derSättigungsformulierung, das sogenannte direkte Problem. Ausder Kenntnis des freien Randes dieses Problems soll dernichtlineare Diffusivitätskoeffizient derDifferentialgleichung rekonstruiert werden. Für diesesinverse Problem stellen wir einOutput-Least-Squares-Funktional auf und verwenden zu dessenMinimierung iterative Regularisierungsverfahren wie dasLevenberg-Marquardt-Verfahren und die IRGN-Methode basierendauf einer Parametrisierung des Koeffizientenraumes durchquadratische B-Splines. Für das direkte Problem beweisen wirunter anderem Existenz und Eindeutigkeit der Lösung desCauchy-Dirichlet-Problems sowie die Existenz des freienRandes. Anschließend führen wir formal die Ableitung desfreien Randes nach dem Koeffizienten, die wir für dasnumerische Rekonstruktionsverfahren benötigen, auf einlinear degeneriert parabolisches Randwertproblem zurück.Wir erläutern die numerische Umsetzung und Implementierungunseres Rekonstruktionsverfahrens und stellen abschließendRekonstruktionsergebnisse bezüglich synthetischer Daten vor.