Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

Gravitational Lensing as a Tool on Galactic and Cosmological Scales

This work considers the reconstruction of strong gravitational lenses from their observed effects on the light distribution of background sources. After reviewing the formalism of gravitational lensing and the most common and relevant lens models, new analytical results on the elliptical power law lens are presented, including new expressions for the deflection, potential, shear and magnification, which naturally lead to a fast numerical scheme for practical calculation. The main part of the thesis investigates lens reconstruction with extended sources by means of the forward reconstruction method, in which the lenses and sources are given by parametric models. The numerical realities of the problem make it necessary to find targeted optimisations for the forward method, in order to make it feasible for general applications to modern, high resolution images. The result of these optimisations is presented in the \textsc{Lensed} algorithm. Subsequently, a number of tests for general forward reconstruction methods are created to decouple the influence of sourced from lens reconstructions, in order to objectively demonstrate the constraining power of the reconstruction. The final chapters on lens reconstruction contain two sample applications of the forward method. One is the analysis of images from a strong lensing survey. Such surveys today contain $\sim 100$ strong lenses, and much larger sample sizes are expected in the future, making it necessary to quickly and reliably analyse catalogues of lenses with a fixed model. The second application deals with the opposite situation of a single observation that is to be confronted with different lens models, where the forward method allows for natural model-building. This is demonstrated using an example reconstruction of the ``Cosmic Horseshoe''. An appendix presents an independent work on the use of weak gravitational lensing to investigate theories of modified gravity which exhibit screening in the non-linear regime of structure formation.

Linear and nonlinear thermal instability of Newtonian and non-Newtonian fluid saturated porous media

The present work aims to investigate the influence of different aspects, such as non-standard steady solutions, complex fluid rheologies and non-standard porous-channel geometries, on the stability of a Darcy-Bénard system. In order to do so, both linear and nonlinear stability theories are considered. A linear analysis focuses on studying the dynamics of the single disturbance wave present in the system, while its nonlinear counterpart takes into consideration the interactions among the single modes. The scope of the stability analysis is to obtain information regarding the transition from an equilibrium solution to another one, and also information regarding the transition nature and the emergent solution after the transition. The disturbance governing equations are solved analytically, whenever possible, and numerical by considering different approaches. Among other important results, it is found that a cylinder cross-section does not affect the thermal instability threshold, but just the linear pattern selection for dilatant and pseudoplastic fluid saturated porous media. A new rheological model is proposed as a solution for singular issues involving the power-law model. Also, a generalised class of one parameter basic solutions is proposed as an alternative description of the isoflux Darcy--Bénard problem. Its stability is investigated.

New indicators of star cluster dynamical evolution

This thesis presents a study of globular clusters (GCs), based on analysis of Monte Carlo simulations of globular clusters (GCs) with the aim to define new empirical parameters measurable from observations and able to trace the different phases of their dynamical evolution history. During their long term dynamical evolution, due to mass segregation and and dynamical friction, massive stars transfer kinetic energy to lower-mass objects, causing them to sink toward the cluster center. This continuous transfer of kinetic energy from the core to the outskirts triggers the runaway contraction of the core, known as "core collapse" (CC), followed by episodes of expansion and contraction called gravothermal oscillations. Clearly, such an internal dynamical evolution corresponds to significant variations also of the structure of the system. Determining the dynamical age of a cluster can be challenging as it depends on various internal and external properties. The traditional classification of GCs as CC or post-CC systems relies on detecting a steep power-law cusp in the central density profile, which may not always be reliable due to post-CC oscillations or other processes. In this thesis, based on the normalized cumulative radial distribution (nCRD) within a fraction of the half-mass radius is analyzed, and three diagnostics (A5, P5, and S2.5) are defined. These diagnostics show sensitivity to dynamical evolution and can distinguish pre-CC clusters from post-CC clusters.The analysis performed using multiple simulations with different initial conditions, including varying binary fractions and the presence of dark remnants showed the time variations of the diagnostics follow distinct patterns depending on the binary fraction and the retention or ejection of black holes. This analysis is extended to a larger set of simulations matching the observed properties of Galactic GCs, and the parameters show a potential to distinguish the dynamical stages of the observed clusters as well.

Incompressible limit and well-posedness of PDE models of tissue growth

Both compressible and incompressible porous medium models are used in the literature to describe the mechanical aspects of living tissues. Using a stiff pressure law, it is possible to build a link between these two different representations. In the incompressible limit, compressible models generate free boundary problems where saturation holds in the moving domain. Our work aims at investigating the stiff pressure limit of reaction-advection-porous medium equations motivated by tumor development. Our first study concerns the analysis and numerical simulation of a model including the effect of nutrients. A coupled system of equations describes the cell density and the nutrient concentration and the derivation of the pressure equation in the stiff limit was an open problem for which the strong compactness of the pressure gradient is needed. To establish it, we use two new ideas: an L3-version of the celebrated Aronson-Bénilan estimate, and a sharp uniform L4-bound on the pressure gradient. We further investigate the sharpness of this bound through a finite difference upwind scheme, which we prove to be stable and asymptotic preserving. Our second study is centered around porous medium equations including convective effects. We are able to extend the techniques developed for the nutrient case, hence finding the complementarity relation on the limit pressure. Moreover, we provide an estimate of the convergence rate at the incompressible limit. Finally, we study a multi-species system. In particular, we account for phenotypic heterogeneity, including a structured variable into the problem. In this case, a cross-(degenerate)-diffusion system describes the evolution of the phenotypic distributions. Adapting methods recently developed in the context of two-species systems, we prove existence of weak solutions and we pass to the incompressible limit. Furthermore, we prove new regularity results on the total pressure, which is related to the total density by a power law of state.

The abuse of intellectual property rights and regulations in China: a law and economic analysis

From the institutional point of view, the legal system of IPR (intellectual property right, hereafter, IPR) is one of incentive institutions of innovation and it plays very important role in the development of economy. According to the law, the owner of the IPR enjoy a kind of exclusive right to use his IP(intellectual property, hereafter, IP), in other words, he enjoys a kind of legal monopoly position in the market. How to well protect the IPR and at the same time to regulate the abuse of IPR is very interested topic in this knowledge-orientated market and it is the basic research question in this dissertation. In this paper, by way of comparing study and by way of law and economic analyses, and based on the Austrian Economics School’s theories, the writer claims that there is no any contradiction between the IPR and competition law. However, in this new economy (high-technology industries), there is really probability of the owner of IPR to abuse his dominant position. And with the characteristics of the new economy, such as, the high rates of innovation, “instant scalability”, network externality and lock-in effects, the IPR “will vest the dominant undertakings with the power not just to monopolize the market but to shift such power from one market to another, to create strong barriers to enter and, in so doing, granting the perpetuation of such dominance for quite a long time.”1 Therefore, in order to keep the order of market, to vitalize the competition and innovation, and to benefit the customer, in EU and US, it is common ways to apply the competition law to regulate the IPR abuse. In Austrian Economic School perspective, especially the Schumpeterian theories, the innovation/competition/monopoly and entrepreneurship are inter-correlated, therefore, we should apply the dynamic antitrust model based on the AES theories to analysis the relationship between the IPR and competition law. China is still a developing country with relative not so high ability of innovation. Therefore, at present, to protect the IPR and to make good use of the incentive mechanism of IPR legal system is the first important task for Chinese government to do. However, according to the investigation reports,2 based on their IPR advantage and capital advantage, some multinational companies really obtained the dominant or monopoly market position in some aspects of some industries, and there are some IPR abuses conducted by such multinational companies. And then, the Chinese government should be paying close attention to regulate any IPR abuse. However, how to effectively regulate the IPR abuse by way of competition law in Chinese situation, from the law and economic theories’ perspective, from the legislation perspective, and from the judicial practice perspective, there is a long way for China to go!

Algorithmic business and EU law on fair trading

This thesis studies how commercial practice is developing with artificial intelligence (AI) technologies and discusses some normative concepts in EU consumer law. The author analyses the phenomenon of 'algorithmic business', which defines the increasing use of data-driven AI in marketing organisations for the optimisation of a range of consumer-related tasks. The phenomenon is orienting business-consumer relations towards some general trends that influence power and behaviors of consumers. These developments are not taking place in a legal vacuum, but against the background of a normative system aimed at maintaining fairness and balance in market transactions. The author assesses current developments in commercial practices in the context of EU consumer law, which is specifically aimed at regulating commercial practices. The analysis is critical by design and without neglecting concrete practices tries to look at the big picture. The thesis consists of nine chapters divided in three thematic parts. The first part discusses the deployment of AI in marketing organisations, a brief history, the technical foundations, and their modes of integration in business organisations. In the second part, a selected number of socio-technical developments in commercial practice are analysed. The following are addressed: the monitoring and analysis of consumers’ behaviour based on data; the personalisation of commercial offers and customer experience; the use of information on consumers’ psychology and emotions, the mediation through marketing conversational applications. The third part assesses these developments in the context of EU consumer law and of the broader policy debate concerning consumer protection in the algorithmic society. In particular, two normative concepts underlying the EU fairness standard are analysed: manipulation, as a substantive regulatory standard that limits commercial behaviours in order to protect consumers’ informed and free choices and vulnerability, as a concept of social policy that portrays people who are more exposed to marketing practices.