Aristotle’s modal syllogistic and first-order modal logic

In Prior Analytics 1.1–22, Aristotle develops his proof system of non-modal and modal propositions. This system is given in the language of propositions, and Aristotle is concerned with establishing some properties and relations that the expressions of this language enjoy. However, modern scholarship has found some of his results inconsistent with positions defended elsewhere. The set of rules of inference of this system has also caused perplexity: there does not seem to be a single interpretation that validates all the rules which Aristotle is explicitly committed to using in his proofs. Some commentators have argued that these and other problems cannot be successfully addressed from the viewpoint of the traditional, ‘first-order’ interpretation of Aristotle’s syllogistic, whereby propositions are taken to involve quantification over individuals only. Accordingly, this interpretation not only is inadequate for formal analysis, but also stems from a misunderstanding of Aristotle’s ideas about quantification. On the contrary, in this study I purport to vindicate the adequacy and plausibility of the first-order interpretation. Together with some assumptions about the language of propositions and an appropriate regimentation, the first-order interpretation yields promising solutions to many of the problems raised by the modal syllogistic. Thus, I present a reconstruction of the language of propositions and a formal interpretation thereof which will prove respectful and responsive to most of the views endorsed by Aristotle in the ‘modal’ chapters of the Analytics.

Sviluppo e validazione di un modello di film fluido per simulazioni CFD di motori a combustione interna

A wall film model has been implemented in a customized version of KIVA code developed at University of Bologna. Under the hypothesis of `thin laminar ow' the model simulates the dynamics of a liquid wall film generated by impinging sprays. Particular care has been taken in numerical implementation of the model. The major phenomena taken into account in the present model are: wall film formation by impinging spray; body forces, such as gravity or acceleration of the wall; shear stress at the interface with the gas and no slip condition on the wall; momentum contribution and dynamic pressure generated by the tangential and normal component of the impinging drops; film evaporation by heat exchange with wall and surrounding gas. The model doesn't consider the effect of the wavy film motion and suppose that all the impinging droplets adhere to the film. The governing equations have been integrated in space by using a finite volume approach with a first order upwind differencing scheme and they have been integrated in time with a fully explicit method. The model is validated using two different test cases reproducing PFI gasoline and DI Diesel engine wall film conditions.

Higher-Order Concurrency: Expressiveness and Decidability Results

Higher-order process calculi are formalisms for concurrency in which processes can be passed around in communications. Higher-order (or process-passing) concurrency is often presented as an alternative paradigm to the first order (or name-passing) concurrency of the pi-calculus for the description of mobile systems. These calculi are inspired by, and formally close to, the lambda-calculus, whose basic computational step ---beta-reduction--- involves term instantiation. The theory of higher-order process calculi is more complex than that of first-order process calculi. This shows up in, for instance, the definition of behavioral equivalences. A long-standing approach to overcome this burden is to define encodings of higher-order processes into a first-order setting, so as to transfer the theory of the first-order paradigm to the higher-order one. While satisfactory in the case of calculi with basic (higher-order) primitives, this indirect approach falls short in the case of higher-order process calculi featuring constructs for phenomena such as, e.g., localities and dynamic system reconfiguration, which are frequent in modern distributed systems. Indeed, for higher-order process calculi involving little more than traditional process communication, encodings into some first-order language are difficult to handle or do not exist. We then observe that foundational studies for higher-order process calculi must be carried out directly on them and exploit their peculiarities. This dissertation contributes to such foundational studies for higher-order process calculi. We concentrate on two closely interwoven issues in process calculi: expressiveness and decidability. Surprisingly, these issues have been little explored in the higher-order setting. Our research is centered around a core calculus for higher-order concurrency in which only the operators strictly necessary to obtain higher-order communication are retained. We develop the basic theory of this core calculus and rely on it to study the expressive power of issues universally accepted as basic in process calculi, namely synchrony, forwarding, and polyadic communication.

Mixed Mode Fracture Behaviour of Piezoelectric Materials

Piezoelectrics present an interactive electromechanical behaviour that, especially in recent years, has generated much interest since it renders these materials adapt for use in a variety of electronic and industrial applications like sensors, actuators, transducers, smart structures. Both mechanical and electric loads are generally applied on these devices and can cause high concentrations of stress, particularly in proximity of defects or inhomogeneities, such as flaws, cavities or included particles. A thorough understanding of their fracture behaviour is crucial in order to improve their performances and avoid unexpected failures. Therefore, a considerable number of research works have addressed this topic in the last decades. Most of the theoretical studies on this subject find their analytical background in the complex variable formulation of plane anisotropic elasticity. This theoretical approach bases its main origins in the pioneering works of Muskelishvili and Lekhnitskii who obtained the solution of the elastic problem in terms of independent analytic functions of complex variables. In the present work, the expressions of stresses and elastic and electric displacements are obtained as functions of complex potentials through an analytical formulation which is the application to the piezoelectric static case of an approach introduced for orthotropic materials to solve elastodynamics problems. This method can be considered an alternative to other formalisms currently used, like the Stroh’s formalism. The equilibrium equations are reduced to a first order system involving a six-dimensional vector field. After that, a similarity transformation is induced to reach three independent Cauchy-Riemann systems, so justifying the introduction of the complex variable notation. Closed form expressions of near tip stress and displacement fields are therefore obtained. In the theoretical study of cracked piezoelectric bodies, the issue of assigning consistent electric boundary conditions on the crack faces is of central importance and has been addressed by many researchers. Three different boundary conditions are commonly accepted in literature: the permeable, the impermeable and the semipermeable (“exact”) crack model. This thesis takes into considerations all the three models, comparing the results obtained and analysing the effects of the boundary condition choice on the solution. The influence of load biaxiality and of the application of a remote electric field has been studied, pointing out that both can affect to a various extent the stress fields and the angle of initial crack extension, especially when non-singular terms are retained in the expressions of the electro-elastic solution. Furthermore, two different fracture criteria are applied to the piezoelectric case, and their outcomes are compared and discussed. The work is organized as follows: Chapter 1 briefly introduces the fundamental concepts of Fracture Mechanics. Chapter 2 describes plane elasticity formalisms for an anisotropic continuum (Eshelby-Read-Shockley and Stroh) and introduces for the simplified orthotropic case the alternative formalism we want to propose. Chapter 3 outlines the Linear Theory of Piezoelectricity, its basic relations and electro-elastic equations. Chapter 4 introduces the proposed method for obtaining the expressions of stresses and elastic and electric displacements, given as functions of complex potentials. The solution is obtained in close form and non-singular terms are retained as well. Chapter 5 presents several numerical applications aimed at estimating the effect of load biaxiality, electric field, considered permittivity of the crack. Through the application of fracture criteria the influence of the above listed conditions on the response of the system and in particular on the direction of crack branching is thoroughly discussed.

Numerical modeling of the Alto Tiberina low angle normal fault

The aim of this Thesis is to obtain a better understanding of the mechanical behavior of the active Alto Tiberina normal fault (ATF). Integrating geological, geodetic and seismological data, we perform 2D and 3D quasi-static and dynamic mechanical models to simulate the interseismic phase and rupture dynamic of the ATF. Effects of ATF locking depth, synthetic and antithetic fault activity, lithology and realistic fault geometries are taken in account. The 2D and 3D quasi-static model results suggest that the deformation pattern inferred by GPS data is consistent with a very compliant ATF zone (from 5 to 15 km) and Gubbio fault activity. The presence of the ATF compliant zone is a first order condition to redistribute the stress in the Umbria-Marche region; the stress bipartition between hanging wall (high values) and footwall (low values) inferred by the ATF zone activity could explain the microseismicity rates that are higher in the hanging wall respect to the footwall. The interseismic stress build-up is mainly located along the Gubbio fault zone and near ATF patches with higher dip (30°