Laplace operator on finite graphs and a network diffusion model for the progression of the Alzheimer disease

Nella tesi viene descritto il Network Diffusion Model, ovvero il modello di A. Ray, A. Kuceyeski, M. Weiner inerente i meccanismi di progressione della demenza senile. In tale modello si approssima l'encefalo sano con una rete cerebrale (ovvero un grafo pesato), si identifica un generale fattore di malattia e se ne analizza la propagazione che avviene secondo meccanismi analoghi a quelli di un'infezione da prioni. La progressione del fattore di malattia e le conseguenze macroscopiche di tale processo(tra cui principalmente l'atrofia corticale) vengono, poi, descritte mediante approccio matematico. I risultati teoretici vengono confrontati con quanto osservato sperimentalmente in pazienti affetti da demenza senile. Nella tesi, inoltre, si fornisce una panoramica sui recenti studi inerenti i processi neurodegenerativi e si costruisce il contesto matematico di riferimento del modello preso in esame. Si presenta una panoramica sui grafi finiti, si introduce l'operatore di Laplace sui grafi e si forniscono stime dall'alto e dal basso per gli autovalori. Al fine di costruire una cornice matematica completa si analizza la relazione tra caso discreto e continuo: viene descritto l'operatore di Laplace-Beltrami sulle varietà riemanniane compatte e vengono fornite stime dall'alto per gli autovalori dell'operatore di Laplace-Beltrami associato a tali varietà a partire dalle stime dall'alto per gli autovalori del laplaciano sui grafi finiti.

IMEX finite volume methods for the shallow water equations

Die Flachwassergleichungen (SWE) sind ein hyperbolisches System von Bilanzgleichungen, die adäquate Approximationen an groß-skalige Strömungen der Ozeane, Flüsse und der Atmosphäre liefern. Dabei werden Masse und Impuls erhalten. Wir unterscheiden zwei charakteristische Geschwindigkeiten: die Advektionsgeschwindigkeit, d.h. die Geschwindigkeit des Massentransports, und die Geschwindigkeit von Schwerewellen, d.h. die Geschwindigkeit der Oberflächenwellen, die Energie und Impuls tragen. Die Froude-Zahl ist eine Kennzahl und ist durch das Verhältnis der Referenzadvektionsgeschwindigkeit zu der Referenzgeschwindigkeit der Schwerewellen gegeben. Für die oben genannten Anwendungen ist sie typischerweise sehr klein, z.B. 0.01. Zeit-explizite Finite-Volume-Verfahren werden am öftersten zur numerischen Berechnung hyperbolischer Bilanzgleichungen benutzt. Daher muss die CFL-Stabilitätsbedingung eingehalten werden und das Zeitinkrement ist ungefähr proportional zu der Froude-Zahl. Deswegen entsteht bei kleinen Froude-Zahlen, etwa kleiner als 0.2, ein hoher Rechenaufwand. Ferner sind die numerischen Lösungen dissipativ. Es ist allgemein bekannt, dass die Lösungen der SWE gegen die Lösungen der Seegleichungen/ Froude-Zahl Null SWE für Froude-Zahl gegen Null konvergieren, falls adäquate Bedingungen erfüllt sind. In diesem Grenzwertprozess ändern die Gleichungen ihren Typ von hyperbolisch zu hyperbolisch.-elliptisch. Ferner kann bei kleinen Froude-Zahlen die Konvergenzordnung sinken oder das numerische Verfahren zusammenbrechen. Insbesondere wurde bei zeit-expliziten Verfahren falsches asymptotisches Verhalten (bzgl. der Froude-Zahl) beobachtet, das diese Effekte verursachen könnte.Ozeanographische und atmosphärische Strömungen sind typischerweise kleine Störungen eines unterliegenden Equilibriumzustandes. Wir möchten, dass numerische Verfahren für Bilanzgleichungen gewisse Equilibriumzustände exakt erhalten, sonst können künstliche Strömungen vom Verfahren erzeugt werden. Daher ist die Quelltermapproximation essentiell. Numerische Verfahren die Equilibriumzustände erhalten heißen ausbalanciert.rnrnIn der vorliegenden Arbeit spalten wir die SWE in einen steifen, linearen und einen nicht-steifen Teil, um die starke Einschränkung der Zeitschritte durch die CFL-Bedingung zu umgehen. Der steife Teil wird implizit und der nicht-steife explizit approximiert. Dazu verwenden wir IMEX (implicit-explicit) Runge-Kutta und IMEX Mehrschritt-Zeitdiskretisierungen. Die Raumdiskretisierung erfolgt mittels der Finite-Volumen-Methode. Der steife Teil wird mit Hilfe von finiter Differenzen oder au eine acht mehrdimensional Art und Weise approximniert. Zur mehrdimensionalen Approximation verwenden wir approximative Evolutionsoperatoren, die alle unendlich viele Informationsausbreitungsrichtungen berücksichtigen. Die expliziten Terme werden mit gewöhnlichen numerischen Flüssen approximiert. Daher erhalten wir eine Stabilitätsbedingung analog zu einer rein advektiven Strömung, d.h. das Zeitinkrement vergrößert um den Faktor Kehrwert der Froude-Zahl. Die in dieser Arbeit hergeleiteten Verfahren sind asymptotisch erhaltend und ausbalanciert. Die asymptotischer Erhaltung stellt sicher, dass numerische Lösung das "korrekte" asymptotische Verhalten bezüglich kleiner Froude-Zahlen besitzt. Wir präsentieren Verfahren erster und zweiter Ordnung. Numerische Resultate bestätigen die Konvergenzordnung, so wie Stabilität, Ausbalanciertheit und die asymptotische Erhaltung. Insbesondere beobachten wir bei machen Verfahren, dass die Konvergenzordnung fast unabhängig von der Froude-Zahl ist.

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.

The finite lambda calculus

In questa tesi si descrive il lambda calcolo finito, un'istanza del lambda calcolo con tipi finiti. Si studia la metateoria e la complessità della riduzione.

The contribution of the Finite Volume Point Dilution Method to the determination of solute mass flux in an alluvial aquifer.

Groundwater represents one of the most important resources of the world and it is essential to prevent its pollution and to consider remediation intervention in case of contamination. According to the scientific community the characterization and the management of the contaminated sites have to be performed in terms of contaminant fluxes and considering their spatial and temporal evolution. One of the most suitable approach to determine the spatial distribution of pollutant and to quantify contaminant fluxes in groundwater is using control panels. The determination of contaminant mass flux, requires measurement of contaminant concentration in the moving phase (water) and velocity/flux of the groundwater. In this Master Thesis a new solute flux mass measurement approach, based on an integrated control panel type methodology combined with the Finite Volume Point Dilution Method (FVPDM), for the monitoring of transient groundwater fluxes, is proposed. Moreover a new adsorption passive sampler, which allow to capture the variation of solute concentration with time, is designed. The present work contributes to the development of this approach on three key points. First, the ability of the FVPDM to monitor transient groundwater fluxes was verified during a step drawdown test at the experimental site of Hermalle Sous Argentau (Belgium). The results showed that this method can be used, with optimal results, to follow transient groundwater fluxes. Moreover, it resulted that performing FVPDM, in several piezometers, during a pumping test allows to determine the different flow rates and flow regimes that can occurs in the various parts of an aquifer. The second field test aiming to determine the representativity of a control panel for measuring mass flus in groundwater underlined that wrong evaluations of Darcy fluxes and discharge surfaces can determine an incorrect estimation of mass fluxes and that this technique has to be used with precaution. Thus, a detailed geological and hydrogeological characterization must be conducted, before applying this technique. Finally, the third outcome of this work concerned laboratory experiments. The test conducted on several type of adsorption material (Oasis HLB cartridge, TDS-ORGANOSORB 10 and TDS-ORGANOSORB 10-AA), in order to determine the optimum medium to dimension the passive sampler, highlighted the necessity to find a material with a reversible adsorption tendency to completely satisfy the request of the new passive sampling technique.

Dynamic characterisation of four nine-story large-panel R.C. buildings in Bishkek (Kyrgyzstan): A comparison between experimental ambient vibration analysis and numerical finite element modeling

With the outlook of improving seismic vulnerability assessment for the city of Bishkek (Kyrgyzstan), the global dynamic behaviour of four nine-storey r.c. large-panel buildings in elastic regime is studied. The four buildings were built during the Soviet era within a serial production system. Since they all belong to the same series, they have very similar geometries both in plan and in height. Firstly, ambient vibration measurements are performed in the four buildings. The data analysis composed of discrete Fourier transform, modal analysis (frequency domain decomposition) and deconvolution interferometry, yields the modal characteristics and an estimate of the linear impulse response function for the structures of the four buildings. Then, finite element models are set up for all four buildings and the results of the numerical modal analysis are compared with the experimental ones. The numerical models are finally calibrated considering the first three global modes and their results match the experimental ones with an error of less then 20%.

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.

Stochastic dynamics on infinite and finite transport capacity networks: an operatorial approach

Nella tesi viene studiata la dinamica stocastica di particelle non interagenti su network con capacita di trasporto finita. L'argomento viene affrontato introducendo un formalismo operatoriale per il sistema. Dopo averne verificato la consistenza su modelli risolvibili analiticamente, tale formalismo viene impiegato per dimostrare l'emergere di una forza entropica agente sulle particelle, dovuta alle limitazioni dinamiche del network. Inoltre viene proposta una spiegazione qualitativa dell'effetto di attrazione reciproca tra nodi vuoti nel caso di processi sincroni.

Prediction of dental implant torque with a fast and automatic finite element analysis: a pilot study

Despite its importance, implant removal torque can be assessed at present only after implantation. This paper presents a new technique to help clinicians preoperatively evaluate implant stability.

Teeth restored using fiber-reinforced posts: in vitro fracture tests and finite element analysis

In dentistry the restoration of decayed teeth is challenging and makes great demands on both the dentist and the materials. Hence, fiber-reinforced posts have been introduced. The effects of different variables on the ultimate load on teeth restored using fiber-reinforced posts is controversial, maybe because the results are mostly based on non-standardized in vitro tests and, therefore, give inhomogeneous results. This study combines the advantages of in vitro tests and finite element analysis (FEA) to clarify the effects of ferrule height, post length and cementation technique used for restoration. Sixty-four single rooted premolars were decoronated (ferrule height 1 or 2 mm), endodontically treated and restored using fiber posts (length 2 or 7 mm), composite fillings and metal crowns (resin bonded or cemented). After thermocycling and chewing simulation the samples were loaded until fracture, recording first damage events. Using UNIANOVA to analyze recorded fracture loads, ferrule height and cementation technique were found to be significant, i.e. increased ferrule height and resin bonding of the crown resulted in higher fracture loads. Post length had no significant effect. All conventionally cemented crowns with a 1-mm ferrule height failed during artificial ageing, in contrast to resin-bonded crowns (75% survival rate). FEA confirmed these results and provided information about stress and force distribution within the restoration. Based on the findings of in vitro tests and computations we concluded that crowns, especially those with a small ferrule height, should be resin bonded. Finally, centrally positioned fiber-reinforced posts did not contribute to load transfer as long as the bond between the tooth and composite core was intact.

Influence of Smoothing on Voxel-Based Mesh Accuracy in Micro-Finite Element

The interest in automatic volume meshing for finite element analysis (FEA) has grown more since the appearance of microfocus CT (μCT), due to its high resolution, which allows for the assessment of mechanical behaviour at a high precision. Nevertheless, the basic meshing approach of generating one hexahedron per voxel produces jagged edges. To prevent this effect, smoothing algorithms have been introduced to enhance the topology of the mesh. However, whether smoothing also improves the accuracy of voxel-based meshes in clinical applications is still under question. There is a trade-off between smoothing and quality of elements in the mesh. Distorted elements may be produced by excessive smoothing and reduce accuracy of the mesh. In the present work, influence of smoothing on the accuracy of voxel-based meshes in micro-FE was assessed. An accurate 3D model of a trabecular structure with known apparent mechanical properties was used as a reference model. Virtual CT scans of this reference model (with resolutions of 16, 32 and 64 μm) were then created and used to build voxel-based meshes of the microarchitecture. Effects of smoothing on the apparent mechanical properties of the voxel-based meshes as compared to the reference model were evaluated. Apparent Young’s moduli of the smooth voxel-based mesh were significantly closer to those of the reference model for the 16 and 32 μm resolutions. Improvements were not significant for the 64 μm, due to loss of trabecular connectivity in the model. This study shows that smoothing offers a real benefit to voxel-based meshes used in micro-FE. It might also broaden voxel-based meshing to other biomechanical domains where it was not used previously due to lack of accuracy. As an example, this work will be used in the framework of the European project ContraCancrum, which aims at providing a patient-specific simulation of tumour development in brain and lungs for oncologists. For this type of clinical application, such a fast, automatic, and accurate generation of the mesh is of great benefit.

Mesh-based vs. Image-based Statistical Appearance Model of the Human Femur: a Preliminary Comparison Study for the Creation of Finite Element Meshes

Statistical models have been recently introduced in computational orthopaedics to investigate the bone mechanical properties across several populations. A fundamental aspect for the construction of statistical models concerns the establishment of accurate anatomical correspondences among the objects of the training dataset. Various methods have been proposed to solve this problem such as mesh morphing or image registration algorithms. The objective of this study is to compare a mesh-based and an image-based statistical appearance model approaches for the creation of nite element(FE) meshes. A computer tomography (CT) dataset of 157 human left femurs was used for the comparison. For each approach, 30 finite element meshes were generated with the models. The quality of the obtained FE meshes was evaluated in terms of volume, size and shape of the elements. Results showed that the quality of the meshes obtained with the image-based approach was higher than the quality of the mesh-based approach. Future studies are required to evaluate the impact of this finding on the final mechanical simulations.