Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Dynamic development of hydrofractures

Natürliche hydraulische Bruchbildung ist in allen Bereichen der Erdkruste ein wichtiger und stark verbreiteter Prozess. Sie beeinflusst die effektive Permeabilität und Fluidtransport auf mehreren Größenordnungen, indem sie hydraulische Konnektivität bewirkt. Der Prozess der Bruchbildung ist sowohl sehr dynamisch als auch hoch komplex. Die Dynamik stammt von der starken Wechselwirkung tektonischer und hydraulischer Prozesse, während sich die Komplexität aus der potentiellen Abhängigkeit der poroelastischen Eigenschaften von Fluiddruck und Bruchbildung ergibt. Die Bildung hydraulischer Brüche besteht aus drei Phasen: 1) Nukleation, 2) zeitabhängiges quasi-statisches Wachstum so lange der Fluiddruck die Zugfestigkeit des Gesteins übersteigt, und 3) in heterogenen Gesteinen der Einfluss von Lagen unterschiedlicher mechanischer oder sedimentärer Eigenschaften auf die Bruchausbreitung. Auch die mechanische Heterogenität, die durch präexistierende Brüche und Gesteinsdeformation erzeugt wird, hat großen Einfluß auf den Wachstumsverlauf. Die Richtung der Bruchausbreitung wird entweder durch die Verbindung von Diskontinuitäten mit geringer Zugfestigkeit im Bereich vor der Bruchfront bestimmt, oder die Bruchausbreitung kann enden, wenn der Bruch auf Diskontinuitäten mit hoher Festigkeit trifft. Durch diese Wechselwirkungen entsteht ein Kluftnetzwerk mit komplexer Geometrie, das die lokale Deformationsgeschichte und die Dynamik der unterliegenden physikalischen Prozesse reflektiert. rnrnNatürliche hydraulische Bruchbildung hat wesentliche Implikationen für akademische und kommerzielle Fragestellungen in verschiedenen Feldern der Geowissenschaften. Seit den 50er Jahren wird hydraulisches Fracturing eingesetzt, um die Permeabilität von Gas und Öllagerstätten zu erhöhen. Geländebeobachtungen, Isotopenstudien, Laborexperimente und numerische Analysen bestätigen die entscheidende Rolle des Fluiddruckgefälles in Verbindung mit poroelastischen Effekten für den lokalen Spannungszustand und für die Bedingungen, unter denen sich hydraulische Brüche bilden und ausbreiten. Die meisten numerischen hydromechanischen Modelle nehmen für die Kopplung zwischen Fluid und propagierenden Brüchen vordefinierte Bruchgeometrien mit konstantem Fluiddruck an, um das Problem rechnerisch eingrenzen zu können. Da natürliche Gesteine kaum so einfach strukturiert sind, sind diese Modelle generell nicht sonderlich effektiv in der Analyse dieses komplexen Prozesses. Insbesondere unterschätzen sie die Rückkopplung von poroelastischen Effekten und gekoppelte Fluid-Festgestein Prozesse, d.h. die Entwicklung des Porendrucks in Abhängigkeit vom Gesteinsversagen und umgekehrt.rnrnIn dieser Arbeit wird ein zweidimensionales gekoppeltes poro-elasto-plastisches Computer-Model für die qualitative und zum Teil auch quantitativ Analyse der Rolle lokalisierter oder homogen verteilter Fluiddrücke auf die dynamische Ausbreitung von hydraulischen Brüchen und die zeitgleiche Evolution der effektiven Permeabilität entwickelt. Das Programm ist rechnerisch effizient, indem es die Fluiddynamik mittels einer Druckdiffusions-Gleichung nach Darcy ohne redundante Komponenten beschreibt. Es berücksichtigt auch die Biot-Kompressibilität poröser Gesteine, die implementiert wurde um die Kontrollparameter in der Mechanik hydraulischer Bruchbildung in verschiedenen geologischen Szenarien mit homogenen und heterogenen Sedimentären Abfolgen zu bestimmen. Als Resultat ergibt sich, dass der Fluiddruck-Gradient in geschlossenen Systemen lokal zu Störungen des homogenen Spannungsfeldes führen. Abhängig von den Randbedingungen können sich diese Störungen eine Neuausrichtung der Bruchausbreitung zur Folge haben kann. Durch den Effekt auf den lokalen Spannungszustand können hohe Druckgradienten auch schichtparallele Bruchbildung oder Schlupf in nicht-entwässerten heterogenen Medien erzeugen. Ein Beispiel von besonderer Bedeutung ist die Evolution von Akkretionskeilen, wo die große Dynamik der tektonischen Aktivität zusammen mit extremen Porendrücken lokal starke Störungen des Spannungsfeldes erzeugt, die eine hoch-komplexe strukturelle Entwicklung inklusive vertikaler und horizontaler hydraulischer Bruch-Netzwerke bewirkt. Die Transport-Eigenschaften der Gesteine werden stark durch die Dynamik in der Entwicklung lokaler Permeabilitäten durch Dehnungsbrüche und Störungen bestimmt. Möglicherweise besteht ein enger Zusammenhang zwischen der Bildung von Grabenstrukturen und großmaßstäblicher Fluid-Migration. rnrnDie Konsistenz zwischen den Resultaten der Simulationen und vorhergehender experimenteller Untersuchungen deutet darauf hin, dass das beschriebene numerische Verfahren zur qualitativen Analyse hydraulischer Brüche gut geeignet ist. Das Schema hat auch Nachteile wenn es um die quantitative Analyse des Fluidflusses durch induzierte Bruchflächen in deformierten Gesteinen geht. Es empfiehlt sich zudem, das vorgestellte numerische Schema um die Kopplung mit thermo-chemischen Prozessen zu erweitern, um dynamische Probleme im Zusammenhang mit dem Wachstum von Kluftfüllungen in hydraulischen Brüchen zu untersuchen.

Predictability in Social Science, The statistical mechanics approach.

The subject of this work concerns the study of the immigration phenomenon, with emphasis on the aspects related to the integration of an immigrant population in a hosting one. Aim of this work is to show the forecasting ability of a recent finding where the behavior of integration quantifiers was analyzed and investigated with a mathematical model of statistical physics origins (a generalization of the monomer dimer model). After providing a detailed literature review of the model, we show that not only such a model is able to identify the social mechanism that drives a particular integration process, but it also provides correct forecast. The research reported here proves that the proposed model of integration and its forecast framework are simple and effective tools to reduce uncertainties about how integration phenomena emerge and how they are likely to develop in response to increased migration levels in the future.

Limiting theorems in statistical mechanics. The mean-field case.

The Curie-Weiss model is defined by ah Hamiltonian according to spins interact. For some particular values of the parameters, the sum of the spins normalized with square-root normalization converges or not toward Gaussian distribution. In the thesis we investigate some correlations between the behaviour of the sum and the central limit for interacting random variables.

In-situ detection of defect formation in organic flexible electronics by Kelvin Probe Force Microscopy

Organic semiconductor technology has attracted considerable research interest in view of its great promise for large area, lightweight, and flexible electronics applications. Owing to their advantages in processing and unique physical properties, organic semiconductors can bring exciting new opportunities for broad-impact applications requiring large area coverage, mechanical flexibility, low-temperature processing, and low cost. In order to achieve highly flexible device architecture it is crucial to understand on a microscopic scale how mechanical deformation affects the electrical performance of organic thin film devices. Towards this aim, I established in this thesis the experimental technique of Kelvin Probe Force Microscopy (KPFM) as a tool to investigate the morphology and the surface potential of organic semiconducting thin films under mechanical strain. KPFM has been employed to investigate the strain response of two different Organic Thin Film Transistor with active layer made by 6,13-bis(triisopropylsilylethynyl)-pentacene (TIPS-Pentacene), and Poly(3-hexylthiophene-2,5-diyl) (P3HT). The results show that this technique allows to investigate on a microscopic scale failure of flexible TFT with this kind of materials during bending. I find that the abrupt reduction of TIPS-pentacene device performance at critical bending radii is related to the formation of nano-cracks in the microcrystal morphology, easily identified due to the abrupt variation in surface potential caused by local increase in resistance. Numerical simulation of the bending mechanics of the transistor structure further identifies the mechanical strain exerted on the TIPS-pentacene micro-crystals as the fundamental origin of fracture. Instead for P3HT based transistors no significant reduction in electrical performance is observed during bending. This finding is attributed to the amorphous nature of the polymer giving rise to an elastic response without the occurrence of crack formation.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.

FRAX® assessment of osteoporotic fracture probability in Switzerland

A Swiss-specific FRAX model was developed. Patient profiles at increased probability of fracture beyond currently accepted reimbursement thresholds for bone mineral density (BMD) measurement by dual X-ray absorptiometry (DXA), and osteoporosis treatment were identified.

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.

Surgical hip dislocation for osteochondral transplantation as a salvage procedure for a femoral head impaction fracture

Obturator anterior hip dislocation is very rare. Poor results are described in patients with additional large transchondral fractures and treatment of these injuries remains challenging. Appropriate treatment recommendations are missing in the literature. This case report introduces surgical hip dislocation for osteochondral autograft transplantation with graft harvest from the nonweightbearing area of the head-neck junction as a salvage procedure in a large femoral head defect. We report the treatment and outcome of a 48-year-old man who sustained an anterior dislocation of the left hip after a motorcycle accident. After initial closed reduction in the emergency room, imaging analysis revealed a large osteochondral defect of the femoral head within the weightbearing area (10 × 20 mm, depth: 5 mm). The hip was exposed with a surgical hip dislocation using a trochanteric osteotomy. An osteochondral autograft was harvested from a nonweightbearing area of the femoral head and transferred into the defect. The patient was prospectively examined clinically and radiologically. Two years postoperatively, the patient was free of pain and complaints. The function of the injured hip was comparable to that of the contralateral, healthy hip and showed satisfying radiologic results. Surgical hip dislocation with a trochanteric flip osteotomy is a simple, one-step technique that allows full inspection of the hip to treat osteochondral femoral defects by osteochondral transplantation. The presented technique, used as a salvage procedure in a large femoral head defect, yielded good clinical and satisfying radiologic outcomes at the midterm.

Fracture hospitalizations between years 2000 and 2007 in Switzerland: a trend analysis

In Switzerland, the total number and incidence of hospitalizations for major osteoporotic fractures increased between years 2000 and 2007, while hospitalizations due to hip fracture decreased. The cost impact of shorter hospital stays was offset by the increasing cost per day of hospitalization.

Influence of defective bone marrow osteogenesis on fracture repair in an experimental model of senile osteoporosis

http://www.ncbi.nlm.nih.gov/pubmed/20014309