A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.

Self-organising coordination systems

Many research fields are pushing the engineering of large-scale, mobile, and open systems towards the adoption of techniques inspired by self-organisation: pervasive computing, but also distributed artificial intelligence, multi-agent systems, social networks, peer-topeer and grid architectures exploit adaptive techniques to make global system properties emerge in spite of the unpredictability of interactions and behaviour. Such a trend is visible also in coordination models and languages, whenever a coordination infrastructure needs to cope with managing interactions in highly dynamic and unpredictable environments. As a consequence, self-organisation can be regarded as a feasible metaphor to define a radically new conceptual coordination framework. The resulting framework defines a novel coordination paradigm, called self-organising coordination, based on the idea of spreading coordination media over the network, and charge them with services to manage interactions based on local criteria, resulting in the emergence of desired and fruitful global coordination properties of the system. Features like topology, locality, time-reactiveness, and stochastic behaviour play a key role in both the definition of such a conceptual framework and the consequent development of self-organising coordination services. According to this framework, the thesis presents several self-organising coordination techniques developed during the PhD course, mainly concerning data distribution in tuplespace-based coordination systems. Some of these techniques have been also implemented in ReSpecT, a coordination language for tuple spaces, based on logic tuples and reactions to events occurring in a tuple space. In addition, the key role played by simulation and formal verification has been investigated, leading to analysing how automatic verification techniques like probabilistic model checking can be exploited in order to formally prove the emergence of desired behaviours when dealing with coordination approaches based on self-organisation. To this end, a concrete case study is presented and discussed.

Analytical challenges in the fields of Nanobioscience and Nanobiotecnology: integrated methods for separation and characterization

Nano(bio)science and nano(bio)technology play a growing and tremendous interest both on academic and industrial aspects. They are undergoing rapid developments on many fronts such as genomics, proteomics, system biology, and medical applications. However, the lack of characterization tools for nano(bio)systems is currently considered as a major limiting factor to the final establishment of nano(bio)technologies. Flow Field-Flow Fractionation (FlFFF) is a separation technique that is definitely emerging in the bioanalytical field, and the number of applications on nano(bio)analytes such as high molar-mass proteins and protein complexes, sub-cellular units, viruses, and functionalized nanoparticles is constantly increasing. This can be ascribed to the intrinsic advantages of FlFFF for the separation of nano(bio)analytes. FlFFF is ideally suited to separate particles over a broad size range (1 nm-1 μm) according to their hydrodynamic radius (rh). The fractionation is carried out in an empty channel by a flow stream of a mobile phase of any composition. For these reasons, fractionation is developed without surface interaction of the analyte with packing or gel media, and there is no stationary phase able to induce mechanical or shear stress on nanosized analytes, which are for these reasons kept in their native state. Characterization of nano(bio)analytes is made possible after fractionation by interfacing the FlFFF system with detection techniques for morphological, optical or mass characterization. For instance, FlFFF coupling with multi-angle light scattering (MALS) detection allows for absolute molecular weight and size determination, and mass spectrometry has made FlFFF enter the field of proteomics. Potentialities of FlFFF couplings with multi-detection systems are discussed in the first section of this dissertation. The second and the third sections are dedicated to new methods that have been developed for the analysis and characterization of different samples of interest in the fields of diagnostics, pharmaceutics, and nanomedicine. The second section focuses on biological samples such as protein complexes and protein aggregates. In particular it focuses on FlFFF methods developed to give new insights into: a) chemical composition and morphological features of blood serum lipoprotein classes, b) time-dependent aggregation pattern of the amyloid protein Aβ1-42, and c) aggregation state of antibody therapeutics in their formulation buffers. The third section is dedicated to the analysis and characterization of structured nanoparticles designed for nanomedicine applications. The discussed results indicate that FlFFF with on-line MALS and fluorescence detection (FD) may become the unparallel methodology for the analysis and characterization of new, structured, fluorescent nanomaterials.

Semantic coordination through programmable Tuple spaces

Two of the main features of today complex software systems like pervasive computing systems and Internet-based applications are distribution and openness. Distribution revolves around three orthogonal dimensions: (i) distribution of control|systems are characterised by several independent computational entities and devices, each representing an autonomous and proactive locus of control; (ii) spatial distribution|entities and devices are physically distributed and connected in a global (such as the Internet) or local network; and (iii) temporal distribution|interacting system components come and go over time, and are not required to be available for interaction at the same time. Openness deals with the heterogeneity and dynamism of system components: complex computational systems are open to the integration of diverse components, heterogeneous in terms of architecture and technology, and are dynamic since they allow components to be updated, added, or removed while the system is running. The engineering of open and distributed computational systems mandates for the adoption of a software infrastructure whose underlying model and technology could provide the required level of uncoupling among system components. This is the main motivation behind current research trends in the area of coordination middleware to exploit tuple-based coordination models in the engineering of complex software systems, since they intrinsically provide coordinated components with communication uncoupling and further details in the references therein. An additional daunting challenge for tuple-based models comes from knowledge-intensive application scenarios, namely, scenarios where most of the activities are based on knowledge in some form|and where knowledge becomes the prominent means by which systems get coordinated. Handling knowledge in tuple-based systems induces problems in terms of syntax - e.g., two tuples containing the same data may not match due to differences in the tuple structure - and (mostly) of semantics|e.g., two tuples representing the same information may not match based on a dierent syntax adopted. Till now, the problem has been faced by exploiting tuple-based coordination within a middleware for knowledge intensive environments: e.g., experiments with tuple-based coordination within a Semantic Web middleware (surveys analogous approaches). However, they appear to be designed to tackle the design of coordination for specic application contexts like Semantic Web and Semantic Web Services, and they result in a rather involved extension of the tuple space model. The main goal of this thesis was to conceive a more general approach to semantic coordination. In particular, it was developed the model and technology of semantic tuple centres. It is adopted the tuple centre model as main coordination abstraction to manage system interactions. A tuple centre can be seen as a programmable tuple space, i.e. an extension of a Linda tuple space, where the behaviour of the tuple space can be programmed so as to react to interaction events. By encapsulating coordination laws within coordination media, tuple centres promote coordination uncoupling among coordinated components. Then, the tuple centre model was semantically enriched: a main design choice in this work was to try not to completely redesign the existing syntactic tuple space model, but rather provide a smooth extension that { although supporting semantic reasoning { keep the simplicity of tuple and tuple matching as easier as possible. By encapsulating the semantic representation of the domain of discourse within coordination media, semantic tuple centres promote semantic uncoupling among coordinated components. The main contributions of the thesis are: (i) the design of the semantic tuple centre model; (ii) the implementation and evaluation of the model based on an existent coordination infrastructure; (iii) a view of the application scenarios in which semantic tuple centres seem to be suitable as coordination media.

Anaerobic oxidation of ethanol over spinel mixed oxides: the first step in the steam-iron process for H2 production

The future hydrogen demand is expected to increase, both in existing industries (including upgrading of fossil fuels or ammonia production) and in new technologies, like fuel cells. Nowadays, hydrogen is obtained predominantly by steam reforming of methane, but it is well known that hydrocarbon based routes result in environmental problems and besides the market is dependent on the availability of this finite resource which is suffering of rapid depletion. Therefore, alternative processes using renewable sources like wind, solar energy and biomass, are now being considered for the production of hydrogen. One of those alternative methods is the so-called “steam-iron process” which consists in the reduction of a metal-oxide by hydrogen-containing feedstock, like ethanol for instance, and then the reduced material is reoxidized with water to produce “clean” hydrogen (water splitting). This kind of thermochemical cycles have been studied before but currently some important facts like the development of more active catalysts, the flexibility of the feedstock (including renewable bio-alcohols) and the fact that the purification of hydrogen could be avoided, have significantly increased the interest for this research topic. With the aim of increasing the understanding of the reactions that govern the steam-iron route to produce hydrogen, it is necessary to go into the molecular level. Spectroscopic methods are an important tool to extract information that could help in the development of more efficient materials and processes. In this research, ethanol was chosen as a reducing fuel and the main goal was to study its interaction with different catalysts having similar structure (spinels), to make a correlation with the composition and the mechanism of the anaerobic oxidation of the ethanol which is the first step of the steam-iron cycle. To accomplish this, diffuse reflectance spectroscopy (DRIFTS) was used to study the surface composition of the catalysts during the adsorption of ethanol and its transformation during the temperature program. Furthermore, mass spectrometry was used to monitor the desorbed products. The set of studied materials include Cu, Co and Ni ferrites which were also characterized by means of X-ray diffraction, surface area measurements, Raman spectroscopy, and temperature programmed reduction.

Magnetic fields around radio galaxies from Faraday rotation measure analysis

The purpose of this thesis is to investigate the strength and structure of the magnetized medium surrounding radio galaxies via observations of the Faraday effect. This study is based on an analysis of the polarization properties of radio galaxies selected to have a range of morphologies (elongated tails, or lobes with small axial ratios) and to be located in a variety of environments (from rich cluster core to small group). The targets include famous objects like M84 and M87. A key aspect of this work is the combination of accurate radio imaging with high-quality X-ray data for the gas surrounding the sources. Although the focus of this thesis is primarily observational, I developed analytical models and performed two- and three-dimensional numerical simulations of magnetic fields. The steps of the thesis are: (a) to analyze new and archival observations of Faraday rotation measure (RM) across radio galaxies and (b) to interpret these and existing RM images using sophisticated two and three-dimensional Monte Carlo simulations. The approach has been to select a few bright, very extended and highly polarized radio galaxies. This is essential to have high signal-to-noise in polarization over large enough areas to allow computation of spatial statistics such as the structure function (and hence the power spectrum) of rotation measure, which requires a large number of independent measurements. New and archival Very Large Array observations of the target sources have been analyzed in combination with high-quality X-ray data from the Chandra, XMM-Newton and ROSAT satellites. The work has been carried out by making use of: 1) Analytical predictions of the RM structure functions to quantify the RM statistics and to constrain the power spectra of the RM and magnetic field. 2) Two-dimensional Monte Carlo simulations to address the effect of an incomplete sampling of RM distribution and so to determine errors for the power spectra. 3) Methods to combine measurements of RM and depolarization in order to constrain the magnetic-field power spectrum on small scales. 4) Three-dimensional models of the group/cluster environments, including different magnetic field power spectra and gas density distributions. This thesis has shown that the magnetized medium surrounding radio galaxies appears more complicated than was apparent from earlier work. Three distinct types of magnetic-field structure are identified: an isotropic component with large-scale fluctuations, plausibly associated with the intergalactic medium not affected by the presence of a radio source; a well-ordered field draped around the front ends of the radio lobes and a field with small-scale fluctuations in rims of compressed gas surrounding the inner lobes, perhaps associated with a mixing layer.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

On moduli spaces of semistable sheaves on K3 surfaces

Ich untersuche die nicht bereits durch die Arbeit "Singular symplectic moduli spaces" von Kaledin, Lehn und Sorger (Invent. Math. 164 (2006), no. 3) abgedeckten Fälle von Modulräumen halbstabiler Garben auf projektiven K3-Flächen - die Fälle mit Mukai-Vektor (0,c,0) sowie die Modulräume zu nichtgenerischen amplen Divisoren - hinsichtlich der möglichen Konstruktion neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten. Ich stelle einen Zusammenhang zu den bereits untersuchten Modulräumen und Verallgemeinerungen derselben her und erweitere bekannte Ergebnisse auf alle offenen Fälle von Garben vom Rang 0 und viele Fälle von Garben von positivem Rang. Insbesondere kann in diesen Fällen die Existenz neuer Beispiele von kompakten irreduziblen symplektischen Mannigfaltigkeiten, die birational über Komponenten des Modulraums liegen, ausgeschlossen werden.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Experimental Analysis and Numerical Simulation of Quench in Superconducting HTS Tapes and Coils

The quench characteristics of second generation (2 G) YBCO Coated Conductor (CC) tapes are of fundamental importance for the design and safe operation of superconducting cables and magnets based on this material. Their ability to transport high current densities at high temperature, up to 77 K, and at very high fields, over 20 T, together with the increasing knowledge in their manufacturing, which is reducing their cost, are pushing the use of this innovative material in numerous system applications, from high field magnets for research to motors and generators as well as for cables. The aim of this Ph. D. thesis is the experimental analysis and numerical simulations of quench in superconducting HTS tapes and coils. A measurements facility for the characterization of superconducting tapes and coils was designed, assembled and tested. The facility consist of a cryostat, a cryocooler, a vacuum system, resistive and superconducting current leads and signal feedthrough. Moreover, the data acquisition system and the software for critical current and quench measurements were developed. A 2D model was developed using the finite element code COMSOL Multiphysics R . The problem of modeling the high aspect ratio of the tape is tackled by multiplying the tape thickness by a constant factor, compensating the heat and electrical balance equations by introducing a material anisotropy. The model was then validated both with the results of a 1D quench model based on a non-linear electric circuit coupled to a thermal model of the tape, to literature measurements and to critical current and quench measurements made in the cryogenic facility. Finally the model was extended to the study of coils and windings with the definition of the tape and stack homogenized properties. The procedure allows the definition of a multi-scale hierarchical model, able to simulate the windings with different degrees of detail.

Knots and links in lens spaces

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.

Palaeo wind system reconstruction of the last glacial period over Europe, using high resolution proxy data and model-data-comparison

The atmosphere is a global influence on the movement of heat and humidity between the continents, and thus significantly affects climate variability. Information about atmospheric circulation are of major importance for the understanding of different climatic conditions. Dust deposits from maar lakes and dry maars from the Eifel Volcanic Field (Germany) are therefore used as proxy data for the reconstruction of past aeolian dynamics.rnrnIn this thesis past two sediment cores from the Eifel region are examined: the core SM3 from Lake Schalkenmehren and the core DE3 from the Dehner dry maar. Both cores contain the tephra of the Laacher See eruption, which is dated to 12,900 before present. Taken together the cores cover the last 60,000 years: SM3 the Holocene and DE3 the marine isotope stages MIS-3 and MIS-2, respectively. The frequencies of glacial dust storm events and their paleo wind direction are detected by high resolution grain size and provenance analysis of the lake sediments. Therefore two different methods are applied: geochemical measurements of the sediment using µXRF-scanning and the particle analysis method RADIUS (rapid particle analysis of digital images by ultra-high-resolution scanning of thin sections).rnIt is shown that single dust layers in the lake sediment are characterized by an increased content of aeolian transported carbonate particles. The limestone-bearing Eifel-North-South zone is the most likely source for the carbonate rich aeolian dust in the lake sediments of the Dehner dry maar. The dry maar is located on the western side of the Eifel-North-South zone. Thus, carbonate rich aeolian sediment is most likely to be transported towards the Dehner dry maar within easterly winds. A methodology is developed which limits the detection to the aeolian transported carbonate particles in the sediment, the RADIUS-carbonate module.rnrnIn summary, during the marine isotope stage MIS-3 the storm frequency and the east wind frequency are both increased in comparison to MIS-2. These results leads to the suggestion that atmospheric circulation was affected by more turbulent conditions during MIS-3 in comparison to the more stable atmospheric circulation during the full glacial conditions of MIS-2.rnThe results of the investigations of the dust records are finally evaluated in relation a study of atmospheric general circulation models for a comprehensive interpretation. Here, AGCM experiments (ECHAM3 and ECHAM4) with different prescribed SST patterns are used to develop a synoptic interpretation of long-persisting east wind conditions and of east wind storm events, which are suggested to lead to an enhanced accumulation of sediment being transported by easterly winds to the proxy site of the Dehner dry maar.rnrnThe basic observations made on the proxy record are also illustrated in the 10 m-wind vectors in the different model experiments under glacial conditions with different prescribed sea surface temperature patterns. Furthermore, the analysis of long-persisting east wind conditions in the AGCM data shows a stronger seasonality under glacial conditions: all the different experiments are characterized by an increase of the relative importance of the LEWIC during spring and summer. The different glacial experiments consistently show a shift from a long-lasting high over the Baltic Sea towards the NW, directly above the Scandinavian Ice Sheet, together with contemporary enhanced westerly circulation over the North Atlantic.rnrnThis thesis is a comprehensive analysis of atmospheric circulation patterns during the last glacial period. It has been possible to reconstruct important elements of the glacial paleo climate in Central Europe. While the proxy data from sediment cores lead to a binary signal of the wind direction changes (east versus west wind), a synoptic interpretation using atmospheric circulation models is successful. This shows a possible distribution of high and low pressure areas and thus the direction and strength of wind fields which have the capacity to transport dust. In conclusion, the combination of numerical models, to enhance understanding of processes in the climate system, with proxy data from the environmental record is the key to a comprehensive approach to paleo climatic reconstruction.rn

Computer aided design and finite element modeling to predict bulk mechanical properties of bone scaffolds using triply periodic minimal surfaces (progettazione assistita al calcolatore ed analisi con il metodo degli elementi finiti per predire il comportamento meccanico di scaffolds ossei creati con l'uso di superfici minime periodiche in tre direzioni)

The aim of Tissue Engineering is to develop biological substitutes that will restore lost morphological and functional features of diseased or damaged portions of organs. Recently computer-aided technology has received considerable attention in the area of tissue engineering and the advance of additive manufacture (AM) techniques has significantly improved control over the pore network architecture of tissue engineering scaffolds. To regenerate tissues more efficiently, an ideal scaffold should have appropriate porosity and pore structure. More sophisticated porous configurations with higher architectures of the pore network and scaffolding structures that mimic the intricate architecture and complexity of native organs and tissues are then required. This study adopts a macro-structural shape design approach to the production of open porous materials (Titanium foams), which utilizes spatial periodicity as a simple way to generate the models. From among various pore architectures which have been studied, this work simulated pore structure by triply-periodic minimal surfaces (TPMS) for the construction of tissue engineering scaffolds. TPMS are shown to be a versatile source of biomorphic scaffold design. A set of tissue scaffolds using the TPMS-based unit cell libraries was designed. TPMS-based Titanium foams were meant to be printed three dimensional with the relative predicted geometry, microstructure and consequently mechanical properties. Trough a finite element analysis (FEA) the mechanical properties of the designed scaffolds were determined in compression and analyzed in terms of their porosity and assemblies of unit cells. The purpose of this work was to investigate the mechanical performance of TPMS models trying to understand the best compromise between mechanical and geometrical requirements of the scaffolds. The intention was to predict the structural modulus in open porous materials via structural design of interconnected three-dimensional lattices, hence optimising geometrical properties. With the aid of FEA results, it is expected that the effective mechanical properties for the TPMS-based scaffold units can be used to design optimized scaffolds for tissue engineering applications. Regardless of the influence of fabrication method, it is desirable to calculate scaffold properties so that the effect of these properties on tissue regeneration may be better understood.

Higher order Sobolev Spaces and polyharmonic boundary value problems in Carnot Groups

The main task of this work is to present a concise survey on the theory of certain function spaces in the contexts of Hörmander vector fields and Carnot Groups, and to discuss briefly an application to some polyharmonic boundary value problems on Carnot Groups of step 2.

Computer simulations of slowly relaxing systems in external fields

Eine der offenen Fragen der aktuellen Physik ist das Verständnis von Systemen im Nichtgleichgewicht. Im Gegensatz zu der Gleichgewichtsphysik ist in diesem Bereich aktuell kein Formalismus bekannt der ein systematisches Beschreiben der unterschiedlichen Systeme ermöglicht. Um das Verständnis über diese Systeme zu vergrößern werden in dieser Arbeit zwei unterschiedliche Systeme studiert, die unter einem externen Feld ein starkes nichtlineares Verhalten zeigen. Hierbei handelt es sich zum einen um das Verhalten von Teilchen unter dem Einfluss einer extern angelegten Kraft und zum anderen um das Verhalten eines Systems in der Nähe des kritischen Punktes unter Scherung. Das Modellsystem in dem ersten Teil der Arbeit ist eine binäre Yukawa Mischung, die bei tiefen Temperaturen einen Glassübergang zeigt. Dies führt zu einer stark ansteigenden Relaxationszeit des Systems, so dass man auch bei kleinen Kräften relativ schnell ein nichtlineares Verhalten beobachtet. In Abhängigkeit der angelegten konstanten Kraft können in dieser Arbeit drei Regime, mit stark unterschiedlichem Teilchenverhalten, identifiziert werden. In dem zweiten Teil der Arbeit wird das Ising-Modell unter Scherung betrachtet. In der Nähe des kritischen Punkts kommt es in diesem Modell zu einer Beeinflussung der Fluktuationen in dem System durch das angelegte Scherfeld. Dies hat zur Folge, dass das System stark anisotrop wird und man zwei unterschiedliche Korrelationslängen vorfindet, die mit unterschiedlichen Exponenten divergieren. Infolgedessen lässt sich der normale isotrope Formalismus des "finite-size scaling" nicht mehr auf dieses System anwenden. In dieser Arbeit wird gezeigt, wie dieser auf den anisotropen Fall zu verallgemeinern ist und wie damit die kritischen Punkte, sowie die dazu gehörenden kritischen Exponenten berechnet werden können.