Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Climatological analysis of temperature and salinity fields in the Mediterranean sea

A climatological field is a mean gridded field that represents the monthly or seasonal trend of an ocean parameter. This instrument allows to understand the physical conditions and physical processes of the ocean water and their impact on the world climate. To construct a climatological field, it is necessary to perform a climatological analysis on an historical dataset. In this dissertation, we have constructed the temperature and salinity fields on the Mediterranean Sea using the SeaDataNet 2 dataset. The dataset contains about 140000 CTD, bottles, XBT and MBT profiles, covering the period from 1900 to 2013. The temperature and salinity climatological fields are produced by the DIVA software using a Variational Inverse Method and a Finite Element numerical technique to interpolate data on a regular grid. Our results are also compared with a previous version of climatological fields and the goodness of our climatologies is assessed, according to the goodness criteria suggested by Murphy (1993). Finally the temperature and salinity seasonal cycle for the Mediterranean Sea is described.

Hunting for warped extra dimensions via loop-induced processes

This thesis is on loop-induced processes in theories with warped extra dimensions where the fermions and gauge bosons are allowed to propagate in the bulk, while the Higgs sector is localized on or near the infra-red brane. These so-called Randall-Sundrum (RS) models have the potential to simultaneously explain the hierarchy problem and address the question of what causes the large hierarchies in the fermion sector of the Standard Model (SM). The Kaluza-Klein (KK) excitations of the bulk fields can significantly affect the loop-level processes considered in this thesis and, hence, could indirectly indicate the existence of warped extra dimensions. The analytical part of this thesis deals with the detailed calculation of three loop-induced processes in the RS models in question: the Higgs production process via gluon fusion, the Higgs decay into two photons, and the flavor-changing neutral current b → sγ. A comprehensive, five-dimensional (5D) analysis will show that the amplitudes of the Higgs processes can be expressed in terms of integrals over 5D propagators with the Higgs-boson profile along the extra dimension, which can be used for arbitrary models with a compact extra dimension. To this end, both the boson and fermion propagators in a warped 5D background are derived. It will be shown that the seemingly contradictory results for the gluon fusion amplitude in the literature can be traced back to two distinguishable, not smoothly-connected incarnations of the RS model. The investigation of the b → sγ transition is performed in the KK decomposed theory. It will be argued that summing up the entire KK tower leads to a finite result, which can be well approximated by a closed, analytical expression.rnIn the phenomenological part of this thesis, the analytic results of all relevant Higgs couplings in the RS models in question are compared with current and in particular future sensitivities of the Large Hadron Collider (LHC) and the planned International Linear Collider. The latest LHC Higgs data is then used to exclude significant portions of the parameter space of each RS scenario. The analysis will demonstrate that especially the loop-induced Higgs couplings are sensitive to KK particles of the custodial RS model with masses in the multi tera-electronvolt range. Finally, the effect of the RS model on three flavor observables associated with the b → sγ transition are examined. In particular, we study the branching ratio of the inclusive decay B → X_s γ

The role of paved surfaces in the Urban Heat Island phenomenon: Assessment of fundamental thermal parameters and finite element analysis for UHI mitigation

Nowadays the environmental issues and the climatic change play fundamental roles in the design of urban spaces. Our cities are growing in size, many times only following immediate needs without a long-term vision. Consequently, the sustainable development has become not only an ethical but also a strategic need: we can no longer afford an uncontrolled urban expansion. One serious effect of the territory industrialisation process is the increase of urban air and surfaces temperatures compared to the outlying rural surroundings. This difference in temperature is what constitutes an urban heat island (UHI). The purpose of this study is to provide a clarification on the role of urban surfacing materials in the thermal dynamics of an urban space, resulting in useful indications and advices in mitigating UHI. With this aim, 4 coloured concrete bricks were tested, measuring their emissivity and building up their heat release curves using infrared thermography. Two emissivity evaluation procedures were carried out and subsequently put in comparison. Samples performances were assessed, and the influence of the colour on the thermal behaviour was investigated. In addition, some external pavements were analysed. Albedo and emissivity parameters were evaluated in order to understand their thermal behaviour in different conditions. Surfaces temperatures were recorded in a one-day measurements campaign. ENVI-met software was used to simulate how the tested materials would behave in two typical urban scenarios: a urban canyon and a urban heat basin. Improvements they can carry to the urban microclimate were investigated. Emissivities obtained for the bricks ranged between 0.92 and 0.97, suggesting a limited influence of the colour on this parameter. Nonetheless, white concrete brick showed the best thermal performance, whilst the black one the worst; red and yellow ones performed pretty identical intermediate trends. De facto, colours affected the overall thermal behaviour. Emissivity parameter was measured in the outdoor work, getting (as expected) high values for the asphalts. Albedo measurements, conducted with a sunshine pyranometer, proved the improving effect given by the yellow paint in terms of solar reflection, and the bad influence of haze on the measurement accuracy. ENVI-met simulations gave a demonstration on the effectiveness in thermal improving of some tested materials. In particular, results showed good performances for white bricks and granite in the heat basin scenario, and painted concrete and macadam in the urban canyon scenario. These materials can be considered valuable solutions in UHI mitigation.

Recycling the city: a sustainable planning framework to reduce, reuse and recycle urban residual spaces

Cities are key locations where Sustainability needs to be addressed at all levels, as land is a finite resource. However, not all urban spaces are exploited at best, and land developers often evaluate unused, misused, or poorly-designed urban portions as impracticable constraints. Further, public authorities lose the challenge to enable and turn these urban spaces into valuable opportunities where Sustainable Urban Development may flourish. Arguing that these spatial elements are at the centre of SUD, the paper elaborates a prototype in the form of a conceptual strategic planning framework, committed to an effective recycling of the city spaces using a flexible and multidisciplinary approach. Firstly, the research focuses upon a broad review of Sustainability literature, highlighting established principles and guidelines, building a sound theoretical base for the new concept. Hence, it investigates origins, identifies and congruently suggests a definition, characterisation and classification for urban “R-Spaces”. Secondly, formal, informal and temporary fitting functions are analysed and inserted into a portfolio meant to enhance adaptability and enlarge the choices for the on-site interventions. Thirdly, the study outlines ideal quality requirements for a sustainable planning process. Then, findings are condensed in the proposal, which is articulated in the individuation of tools, actors, plans, processes and strategies. Afterwards, the prototype is tested upon case studies: Solar Community (Casalecchio di Reno, Bologna) and Hyllie Sustainable City Project, the latter developed via an international workshop (ACSI-Camp, Malmö, Sweden). Besides, the qualitative results suggest, inter alia, the need to right-size spatial interventions, separate structural and operative actors, involve synergies’ multipliers and intermediaries (e.g. entrepreneurial HUBs, innovation agencies, cluster organisations…), maintain stakeholders’ diversity and create a circular process open for new participants. Finally, the paper speculates upon a transfer of the Swedish case study to Italy, and then indicates desirable future researches to favour the prototype implementation.

Finite element modeling of flow/compression-induced deformation of alginate scaffolds for bone tissue engineering

Trauma or degenerative diseases such as osteonecrosis may determine bone loss whose recover is promised by a "tissue engineering“ approach. This strategy involves the use of stem cells, grown onboard of adequate biocompatible/bioreabsorbable hosting templates (usually defined as scaffolds) and cultured in specific dynamic environments afforded by differentiation-inducing actuators (usually defined as bioreactors) to produce implantable tissue constructs. The purpose of this thesis is to evaluate, by finite element modeling of flow/compression-induced deformation, alginate scaffolds intended for bone tissue engineering. This work was conducted at the Biomechanics Laboratory of the Institute of Biomedical and Neural Engineering of the Reykjavik University of Iceland. In this respect, Comsol Multiphysics 5.1 simulations were carried out to approximate the loads over alginate 3D matrices under perfusion, compression and perfusion+compression, when varyingalginate pore size and flow/compression regimen. The results of the simulations show that the shear forces in the matrix of the scaffold increase coherently with the increase in flow and load, and decrease with the increase of the pore size. Flow and load rates suggested for proper osteogenic cell differentiation are reported.

Circulation dynamics and its influence on European and Mediterranean January-April climate over the past half millennium: results and insights from instrumental data, documentary evidence and coupled climate models

We use long instrumental temperature series together with available field reconstructions of sea-level pressure (SLP) and three-dimensional climate model simulations to analyze relations between temperature anomalies and atmospheric circulation patterns over much of Europe and the Mediterranean for the late winter/early spring (January–April, JFMA) season. A Canonical Correlation Analysis (CCA) investigates interannual to interdecadal covariability between a new gridded SLP field reconstruction and seven long instrumental temperature series covering the past 250 years. We then present and discuss prominent atmospheric circulation patterns related to anomalous warm and cold JFMA conditions within different European areas spanning the period 1760–2007. Next, using a data assimilation technique, we link gridded SLP data with a climate model (EC-Bilt-Clio) for a better dynamical understanding of the relationship between large scale circulation and European climate. We thus present an alternative approach to reconstruct climate for the pre-instrumental period based on the assimilated model simulations. Furthermore, we present an independent method to extend the dynamic circulation analysis for anomalously cold European JFMA conditions back to the sixteenth century. To this end, we use documentary records that are spatially representative for the long instrumental records and derive, through modern analogs, large-scale SLP, surface temperature and precipitation fields. The skill of the analog method is tested in the virtual world of two three-dimensional climate simulations (ECHO-G and HadCM3). This endeavor offers new possibilities to both constrain climate model into a reconstruction mode (through the assimilation approach) and to better asses documentary data in a quantitative way.

The importance of ship log data: reconstructing North Atlantic, European and Mediterranean sea level pressure fields back to 1750

Local to regional climate anomalies are to a large extent determined by the state of the atmospheric circulation. The knowledge of large-scale sea level pressure (SLP) variations in former times is therefore crucial when addressing past climate changes across Europe and the Mediterranean. However, currently available SLP reconstructions lack data from the ocean, particularly in the pre-1850 period. Here we present a new statistically-derived 5° × 5° resolved gridded seasonal SLP dataset covering the eastern North Atlantic, Europe and the Mediterranean area (40°W–50°E; 20°N–70°N) back to 1750 using terrestrial instrumental pressure series and marine wind information from ship logbooks. For the period 1750–1850, the new SLP reconstruction provides a more accurate representation of the strength of the winter westerlies as well as the location and variability of the Azores High than currently available multiproxy pressure field reconstructions. These findings strongly support the potential of ship logbooks as an important source to determine past circulation variations especially for the pre-1850 period. This new dataset can be further used for dynamical studies relating large-scale atmospheric circulation to temperature and precipitation variability over the Mediterranean and Eurasia, for the comparison with outputs from GCMs as well as for detection and attribution studies.

Men's Modesty, Religion, and the State: Spaces of Collision

This article examines religious practices in the United States, which govern modesty and other dress norms for men. I focus both on the spaces within which they most collide with regulatory regimes of the state and the legal implications of these norms, particularly for observant Muslim men. Undergirding the research are those ‘‘gender equality’’ claims made by many religious adherents, that men are required to maintain proper modesty norms just as are women. Also undergirding the research is the extensive anti-Islam bias in American culture today. The spaces within which men’s religiously proscribed dress and grooming norms are most at issue—indicated by First Amendment legal challenges to rights of religious practice—are primarily those state-controlled, total institutions Goffman describes, such as in the military and prisons. The implications of gendered modesty norms are important, as state control over religious expression in prisons, for example, is much more difficult to contest than in other spaces, although this depends entirely on who is doing the contesting and within which religious context. In American society today—and particularly within the context of growing Islamaphobia following the 9/11 attacks—the implications are greatest for those men practicing ‘‘prison Islam.’’

Tumor budding score based on 10 high-power fields is a promising basis for a standardized prognostic scoring system in stage II colorectal cancer

Tumor budding is recognized by the World Health Organization as an additional prognostic factor in colorectal cancer but remains unreported in diagnostic work due to the absence of a standardized scoring method. This study aims to assess the most prognostic and reproducible scoring systems for tumor budding in colorectal cancer. Tumor budding on pancytokeratin-stained whole tissue sections from 105 well-characterized stage II patients was scored by 3 observers using 7 methods: Hase, Nakamura, Ueno, Wang (conventional and rapid method), densest high-power field, and 10 densest high-power fields. The predictive value for clinicopathologic features, the prognostic significance, and interobserver variability of each scoring method was analyzed. Pancytokeratin staining allowed accurate evaluation of tumor buds. Interobserver agreement for 3 observers was excellent for densest high-power field (intraclass correlation coefficient, 0.83) and 10 densest high-power fields (intraclass correlation coefficient, 0.91). Agreement was moderate to substantial for the conventional Wang method (κ = 0.46-0.62) and moderate for the rapid method (κ = 0.46-0.58). For Nakamura, moderate agreement (κ = 0.41-0.52) was reached, whereas concordance was fair to moderate for Ueno (κ = 0.39-0.56) and Hase (κ = 0.29-0.51). The Hase, Ueno, densest high-power field, and 10 densest high-power field methods identified a significant association of tumor budding with tumor border configuration. In multivariate analysis, only tumor budding as evaluated in densest high-power field and 10 densest high-power fields had significant prognostic effects on patient survival (P < .01), with high prognostic accuracy over the full 10-year follow-up. Scoring tumor buds in 10 densest high-power fields is a promising method to identify stage II patients at high risk for recurrence in daily diagnostics; it is highly reproducible, accounts for heterogeneity, and has a strong predictive value for adverse outcome.

The long-term mechanical integrity of non-reinforced PEEK-OPTIMA polymer for demanding spinal applications: experimental and finite-element analysis

Polyetheretherketone (PEEK) is a novel polymer with potential advantages for its use in demanding orthopaedic applications (e.g. intervertebral cages). However, the influence of a physiological environment on the mechanical stability of PEEK has not been reported. Furthermore, the suitability of the polymer for use in highly stressed spinal implants such as intervertebral cages has not been investigated. Therefore, a combined experimental and analytical study was performed to address these open questions. A quasi-static mechanical compression test was performed to compare the initial mechanical properties of PEEK-OPTIMA polymer in a dry, room-temperature and in an aqueous, 37 degrees C environment (n=10 per group). The creep behaviour of cylindrical PEEK polymer specimens (n=6) was measured in a simulated physiological environment at an applied stress level of 10 MPa for a loading duration of 2000 hours (12 weeks). To compare the biomechanical performance of different intervertebral cage types made from PEEK and titanium under complex loading conditions, a three-dimensional finite element model of a functional spinal unit was created. The elastic modulus of PEEK polymer specimens in a physiological environment was 1.8% lower than that of specimens tested at dry, room temperature conditions (P<0.001). The results from the creep test showed an average creep strain of less than 0.1% after 2000 hours of loading. The finite element analysis demonstrated high strain and stress concentrations at the bone/implant interface, emphasizing the importance of cage geometry for load distribution. The stress and strain maxima in the implants were well below the material strength limits of PEEK. In summary, the experimental results verified the mechanical stability of the PEEK-OPTIMA polymer in a simulated physiological environment, and over extended loading periods. Finite element analysis supported the use of PEEK-OPTIMA for load-bearing intervertebral implants.

Safety of Active Implantable Devices during MRI Examinations: A Finite Element Analysis of an Implantable Pump

The goal of this study was to propose a general numerical analysis methodology to evaluate the magnetic resonance imaging (MRI)-safety of active implants. Numerical models based on the finite element (FE) technique were used to estimate if the normal operation of an active device was altered during MRI imaging. An active implanted pump was chosen to illustrate the method. A set of controlled experiments were proposed and performed to validate the numerical model. The calculated induced voltages in the important electronic components of the device showed dependence with the MRI field strength. For the MRI radiofrequency fields, significant induced voltages of up to 20 V were calculated for a 0.3T field-strength MRI. For the 1.5 and 3.0T MRIs, the calculated voltages were insignificant. On the other hand, induced voltages up to 11 V were calculated in the critical electronic components for the 3.0T MRI due to the gradient fields. Values obtained in this work reflect to the worst case situation which is virtually impossible to achieve in normal scanning situations. Since the calculated voltages may be removed by appropriate protection circuits, no critical problems affecting the normal operation of the pump were identified. This study showed that the proposed methodology helps the identification of the possible incompatibilities between active implants and MR imaging, and can be used to aid the design of critical electronic systems to ensure MRI-safety