Rigorous results in Spin Glasses and Monomer-Dimer systems

In this work I reported recent results in the field of Statistical Mechanics of Equilibrium, and in particular in Spin Glass models and Monomer Dimer models . We start giving the mathematical background and the general formalism for Spin (Disordered) Models with some of their applications to physical and mathematical problems. Next we move on general aspects of the theory of spin glasses, in particular to the Sherrington-Kirkpatrick model which is of fundamental interest for the work. In Chapter 3, we introduce the Multi-species Sherrington-Kirkpatrick model (MSK), we prove the existence of the thermodynamical limit and the Guerra's Bound for the quenched pressure together with a detailed analysis of the annealed and the replica symmetric regime. The result is a multidimensional generalization of the Parisi's theory. Finally we brie y illustrate the strategy of the Panchenko's proof of the lower bound. In Chapter 4 we discuss the Aizenmann-Contucci and the Ghirlanda-Guerra identities for a wide class of Spin Glass models. As an example of application, we discuss the role of these identities in the proof of the lower bound. In Chapter 5 we introduce the basic mathematical formalism of Monomer Dimer models. We introduce a Gaussian representation of the partition function that will be fundamental in the rest of the work. In Chapter 6, we introduce an interacting Monomer-Dimer model. Its exact solution is derived and a detailed study of its analytical properties and related physical quantities is performed. In Chapter 7, we introduce a quenched randomness in the Monomer Dimer model and show that, under suitable conditions the pressure is a self averaging quantity. The main result is that, if we consider randomness only in the monomer activity, the model is exactly solvable.

New analytical LC-mass spectrometry methodologies for the quali-quantitative determination of natural substances and drugs in complex matrices

This thesis reports an integrated analytical and physicochemical approach for the study of natural substances and new drugs based on mass spectrometry techniques combined with liquid chromatography. In particular, Chapter 1 concerns the study of Berberine a natural substance with pharmacological activity for the treatment of hepatobiliary and intestinal diseases. The first part focused on the relationships between physicochemical properties, pharmacokinetics and metabolism of Berberine and its metabolites. For this purpose a sensitive HPLC-ES-MS/MS method have been developed, validated and used to determine these compounds during their physicochemical properties studies and plasma levels of berberine and its metabolites including berberrubine(M1), demethylenberberine(M3), and jatrorrhizine(M4) in humans. Data show that M1, could have an efficient intestinal absorption by passive diffusion due to a keto-enol tautomerism confirmed by NMR studies and its higher plasma concentration. In the second part of Chapter 1, a comparison between M1 and BBR in vivo biodistribution in rat has been studied. In Chapter 2 a new HPLC-ES-MS/MS method for the simultaneous determination and quantification of glucosinolates, as glucoraphanin, glucoerucin and sinigrin, and isothiocyanates, as sulforaphane and erucin, has developed and validated. This method has been used for the analysis of functional foods enriched with vegetable extracts. Chapter 3 focused on a physicochemical study of the interaction between the bile acid sequestrants used in the treatment of hypercholesterolemia including colesevelam and cholestyramine with obeticolic acid (OCA), potent agonist of nuclear receptor farnesoid X (FXR). In particular, a new experimental model for the determination of equilibrium binding isotherm was developed. Chapter 4 focused on methodological aspects of new hard ionization coupled with liquid chromatography (Direct-EI-UHPLC-MS) not yet commercially available and potentially useful for qualitative analysis and for “transparent” molecules to soft ionization techniques. This method was applied to the analysis of several steroid derivatives.

Ultrasensitive chemiluminescence bioassays based on microfluidics in miniaturized analytical devices

The activity carried out during my PhD was principally addressed to the development of portable microfluidic analytical devices based on biospecific molecular recognition reactions and CL detection. In particular, the development of biosensors required the study of different materials and procedures for their construction, with particular attention to the development of suitable immobilization procedures, fluidic systems and the selection of the suitable detectors. Different methods were exploited, such as gene probe hybridization assay or immunoassay, based on different platform (functionalized glass slide or nitrocellulose membrane) trying to improve the simplicity of the assay procedure. Different CL detectors were also employed and compared with each other in the search for the best compromise between portability and sensitivity. The work was therefore aimed at miniaturization and simplification of analytical devices and the study involved all aspects of the system, from the analytical methodology to the type of detector, in order to combine high sensitivity with easiness-of-use and rapidity. The latest development involving the use of smartphone as chemiluminescent detector paves the way for a new generation of analytical devices in the clinical diagnostic field thanks to the ideal combination of sensibility a simplicity of the CL with the day-by-day increase in the performance of the new generation smartphone camera. Moreover, the connectivity and data processing offered by smartphones can be exploited to perform analysis directly at home with simple procedures. The system could eventually be used to monitor patient health and directly notify the physician of the analysis results allowing a decrease in costs and an increase in the healthcare availability and accessibility.

Development of new analytical procedures aimet at the characterization of artistic samples

In this thesis, new advances in the development of spectroscopic based methods for the characterization of heritage materials have been achieved. As concern FTIR spectroscopy new approaches aimed at exploiting near and far IR region for the characterization of inorganic or organic materials have been tested. Paint cross-section have been analysed by FTIR spectroscopy in the NIR range and an “ad hoc” chemometric approach has been developed for the elaboration of hyperspectral maps. Moreover, a new method for the characterization of calcite based on the use of grinding curves has been set up both in MIR and in FAR region. Indeed, calcite is a material widely applied in cultural heritage, and this spectroscopic approach is an efficient and rapid tool to distinguish between different calcite samples. Different enhanced vibrational techniques for the characterisation of dyed fibres have been tested. First a SEIRA (Surface Enhanced Infra-Red Absorption) protocol has been optimised allowing the analysis of colorant micro-extracts thanks to the enhancement produced by the addition of gold nanoparticles. These preliminary studies permitted to identify a new enhanced FTIR method, named ATR/RAIRS, which allowed to reach lower detection limits. Regarding Raman microscopy, the research followed two lines, which have in common the aim of avoiding the use of colloidal solutions. AgI based supports obtained after deposition on a gold-coated glass slides have been developed and tested spotting colorant solutions. A SERS spectrum can be obtained thanks to the photoreduction, which the laser may induce on the silver salt. Moreover, these supports can be used for the TLC separation of a mixture of colorants and the analyses by means of both Raman/SERS and ATR-RAIRS can be successfully reached. Finally, a photoreduction method for the “on fiber” analysis of colorant without the need of any extraction have been optimised.

The effect of elastic modulus and equilibrium vapor adsorption on capillary forces

Die Kapillarkraft entsteht durch die Bildung eines Meniskus zwischen zwei Festkörpen. In dieser Doktorarbeit wurden die Auswirkungen von elastischer Verformung und Flϋssigkeitadsorption auf die Kapillarkraft sowohl theoretisch als auch experimentell untersucht. Unter Verwendung eines Rasterkraftmikroskops wurde die Kapillarkraft zwischen eines Siliziumoxid Kolloids von 2 µm Radius und eine weiche Oberfläche wie n.a. Polydimethylsiloxan oder Polyisopren, unter normalen Umgebungsbedingungen sowie in variierende Ethanoldampfdrϋcken gemessen. Diese Ergebnisse wurden mit den Kapillarkräften verglichen, die auf einem harten Substrat (Silizium-Wafer) unter denselben Bedingungen gemessen wurden. Wir beobachteten eine monotone Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck (P) fϋr P/Psat > 0,2, wobei Psat der Sättigungsdampfdruck ist.rnUm die experimentellen Ergebnisse zu erklären, wurde ein zuvor entwickeltes analytisches Modell (Soft Matter 2010, 6, 3930) erweitert, um die Ethanoladsorption zu berϋcksichtigen. Dieses neue analytische Modell zeigte zwei verschiedene Abhängigkeiten der Kapillarkraft von P/Psat auf harten und weichen Oberflächen. Fϋr die harte Oberfläche des Siliziumwafers wird die Abhängigkeit der Kapillarkraft vom Dampfdruck vom Verhältnis der Dicke der adsorbierten Ethanolschicht zum Meniskusradius bestimmt. Auf weichen Polymeroberflächen hingegen hängt die Kapillarkraft von der Oberflächenverformung und des Laplace-Drucks innerhalb des Meniskus ab. Eine Abnahme der Kapillarkraft mit zunehmendem Ethanoldampfdruck hat demnach eine Abnahme des Laplace-Drucks mit zunehmendem Meniskusradius zur folge. rnDie analytischen Berechnungen, fϋr die eine Hertzsche Kontakt-deformation angenommen wurde, wurden mit Finit Element Methode Simulationen verglichen, welche die reale Deformation des elastischen Substrats in der Nähe des Meniskuses explizit berϋcksichtigen. Diese zusätzliche nach oben gerichtete oberflächenverformung im Bereich des Meniskus fϋhrt zu einer weiteren Erhöhung der Kapillarkraft, insbesondere fϋr weiche Oberflächen mit Elastizitätsmodulen < 100 MPa.rn

Original analytical methods for the determination of psychoactive compounds in complex matrices

This thesis work aims to develop original analytical methods for the determination of drugs with a potential for abuse, for the analysis of substances used in the pharmacological treatment of drug addiction in biological samples and for the monitoring of potentially toxic compounds added to street drugs. In fact reliable analytical techniques can play an important role in this setting. They can be employed to reveal drug intake, allowing the identification of drug users and to assess drug blood levels, assisting physicians in the management of the treatment. Pharmacological therapy needs to be carefully monitored indeed in order to optimize the dose scheduling according to the specific needs of the patient and to discourage improper use of the medication. In particular, different methods have been developed for the detection of gamma-hydroxybutiric acid (GHB), prescribed for the treatment of alcohol addiction, of glucocorticoids, one of the most abused pharmaceutical class to enhance sport performance and of adulterants, pharmacologically active compounds added to illicit drugs for recreational purposes. All the presented methods are based on capillary electrophoresis (CE) and high performance liquid chromatography (HPLC) coupled to various detectors (diode array detector, mass spectrometer). Biological samples pre-treatment was carried out using different extraction techniques, liquid-liquid extraction (LLE) and solid phase extraction (SPE). Different matrices have been considered: human plasma, dried blood spots, human urine, simulated street drugs. These developed analytical methods are individually described and discussed in this thesis work.

Local dynamics and bending mechanics of mesostructured materials

Die vorliegende Arbeit behandelt die Anwendung der Rasterkraftmikroskopie auf die Untersuchung mesostrukturierter Materialien. Mesostrukturierte Materialien setzen sich aus einzelnen mesoskopen Bausteinen zusammen. Diese Untereinheiten bestimmen im Wesentlichen ihr charakteristisches Verhalten auf äußere mechanische oder elektrische Reize, weshalb diesen Materialien eine besondere Rolle in der Natur sowie im täglichen Leben zukommt. Ein genaues Verständnis der Selbstorganisation dieser Materialien und der Wechselwirkung der einzelnen Bausteine untereinander ist daher von essentieller Bedeutung zur Entwicklung neuer Synthesestrategien sowie zur Optimierung ihrer Materialeigenschaften. Die Charakterisierung dieser mesostrukturierten Materialien erfolgt üblicherweise mittels makroskopischer Analysemethoden wie der dielektrischen Breitbandspektroskopie, Thermogravimetrie sowie in Biegungsexperimenten. In dieser Arbeit wird gezeigt, wie sich diese Analysemethoden mit der Rasterkraftmikroskopie verbinden lassen, um mesostrukturierte Materialien zu untersuchen. Die Rasterkraftmikroskopie bietet die Möglichkeit, die Oberfläche eines Materials abzubilden und zusätzlich dazu seine quantitativen Eigenschaften, wie die mechanische Biegefestigkeit oder die dielektrische Relaxation, zu bestimmen. Die Übertragung makroskopischer Analyseverfahren auf den Nano- bzw. Mikrometermaßstab mittels der Rasterkraftmikroskopie erlaubt die Charakterisierung von räumlich sehr begrenzten Proben bzw. von Proben, die nur in einer sehr kleinen Menge (&lt;10 mg) vorliegen. Darüberhinaus umfasst das Auflösungsvermögen eines Rasterkraftmikroskops, welche durch die Größe seines Federbalkens (50 µm) sowie seines Spitzenradius (5 nm) definiert ist, genau den Längenskalenbereich, der einzelne Atome mit der makroskopischen Welt verbindet, nämlich die Mesoskala. In dieser Arbeit werden Polymerfilme, kolloidale Nanofasern sowie Biomineralien ausführlicher untersucht.rnIm ersten Projekt werden mittels Rasterkraftmikroskopie dielektrische Spektren von mischbaren Polymerfilmen aufgenommen und mit ihrer lokalen Oberflächenstruktur korreliert. Im zweiten Projekt wird die Rasterkraftmikroskopie eingesetzt, um Biegeexperimente an kolloidalen Nanofasern durchzuführen und so ihre Brucheigenschaften genauer zu untersuchen. Im letzten Projekt findet diese Methode Anwendung bei der Charakterisierung der Biegeeigenschaften von Biomineralien. Des Weiteren erfolgt eine Analyse der organischen Zusammensetzung dieser Biomineralien. Alle diese Projekte demonstrieren die vielseitige Einsetzbarkeit der Rasterkraftmikroskopie zur Charakterisierung mesostrukturierter Materialien. Die Korrelation ihrer mechanischen und dielektrischen Eigenschaften mit ihrer topographischen Beschaffenheit erlaubt ein tieferes Verständnis der mesoskopischen Materialien und ihres Verhaltens auf die Einwirkung äußerer Stimuli.rn

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.

Numerical and semi-analytical models of sliding masses: application to the 1783 Scilla tsunamigenic landslide

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the Terremoto delle Calabrie seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighboring Marina Grande beach. The main goal of this work is the application of semi-analtycal and numerical models to simulate this event. The first one is a MATLAB code expressly created for this work that solves the equations of motion for sliding particles on a two-dimensional surface through a fourth-order Runge-Kutta method. The second one is a code developed by the Tsunami Research Team of the Department of Physics and Astronomy (DIFA) of the Bologna University that describes a slide as a chain of blocks able to interact while sliding down over a slope and adopts a Lagrangian point of view. A wide description of landslide phenomena and in particular of landslides induced by earthquakes and with tsunamigenic potential is proposed in the first part of the work. Subsequently, the physical and mathematical background is presented; in particular, a detailed study on derivatives discratization is provided. Later on, a description of the dynamics of a point-mass sliding on a surface is proposed together with several applications of numerical and analytical models over ideal topographies. In the last part, the dynamics of points sliding on a surface and interacting with each other is proposed. Similarly, different application on an ideal topography are shown. Finally, the applications on the 1783 Scilla event are shown and discussed.

Analytical model for the prediction of wrinkling of rear pressure bulkheads

In Airbus GmbH (Hamburg) has been developed a new design of Rear Pressure Bulkhead (RPB) for the A320-family. The new model has been formed with vacuum forming technology. During this process the wrinkling phenomenon occurs. In this thesis is described an analytical model for prediction of wrinkling based on the energetic method of Timoshenko. Large deflection theory has been used for analyze two cases of study: a simply supported circular thin plate stamped by a spherical punch and a simply supported circular thin plate formed with vacuum forming technique. If the edges are free to displace radially, thin plates will develop radial wrinkles near the edge at a central deflection approximately equal to four plate thicknesses w0/ℎ≈4 if they’re stamped by a spherical punch and w0/ℎ≈3 if they’re formed with vacuum forming technique. Initially, there are four symmetrical wrinkles, but the number increases if the central deflection is increased. By using experimental results, the “Snaptrhough” phenomenon is described.

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.