Spatial mechanisms for modelling the human ankle passive motion

Knowledge on how ligaments and articular surfaces guide passive motion at the human ankle joint complex is fundamental for the design of relevant surgical treatments. The dissertation presents a possible improvement of this knowledge by a new kinematic model of the tibiotalar articulation. In this dissertation two one-DOF spatial equivalent mechanisms are presented for the simulation of the passive motion of the human ankle joint: the 5-5 fully parallel mechanism and the fully parallel spherical wrist mechanism. These mechanisms are based on the main anatomical structures of the ankle joint, namely the talus/calcaneus and the tibio/fibula bones at their interface, and the TiCaL and CaFiL ligaments. In order to show the accuracy of the models and the efficiency of the proposed procedure, these mechanisms are synthesized from experimental data and the results are compared with those obtained both during experimental sessions and with data published in the literature. Experimental results proved the efficiency of the proposed new mechanisms to simulate the ankle passive motion and, at the same time, the potentiality of the mechanism to replicate the ankle’s main anatomical structures quite well. The new mechanisms represent a powerful tool for both pre-operation planning and new prosthesis design.

Modelling spillover effects in spatial stochastic frontier analysis

In the last two decades, authors have begun to expand classical stochastic frontier (SF) models in order to include also some spatial components. Indeed, firms tend to concentrate in clusters, taking advantage of positive agglomeration externalities due to cooperation, shared ideas and emulation, resulting in increased productivity levels. Until now scholars have introduced spatial dependence into SF models following two different paths: evaluating global and local spatial spillover effects related to the frontier or considering spatial cross-sectional correlation in the inefficiency and/or in the error term. In this thesis, we extend the current literature on spatial SF models introducing two novel specifications for panel data. First, besides considering productivity and input spillovers, we introduce the possibility to evaluate the specific spatial effects arising from each inefficiency determinant through their spatial lags aiming to capture also knowledge spillovers. Second, we develop a very comprehensive spatial SF model that includes both frontier and error-based spillovers in order to consider four different sources of spatial dependence (i.e. productivity and input spillovers related to the frontier function and behavioural and environmental correlation associated with the two error terms). Finally, we test the finite sample properties of the two proposed spatial SF models through simulations, and we provide two empirical applications to the Italian accommodation and agricultural sectors. From a practical perspective, policymakers, based on results from these models, can rely on precise, detailed and distinct insights on the spillover effects affecting the productive performance of neighbouring spatial units obtaining interesting and relevant suggestions for policy decisions.

The assessment of change in rural landscape and the analysis of the driving forces. Proposal of a spatial model for the rural built environment

The presented study carried out an analysis on rural landscape changes. In particular the study focuses on the understanding of driving forces acting on the rural built environment using a statistical spatial model implemented through GIS techniques. It is well known that the study of landscape changes is essential for a conscious decision making in land planning. From a bibliography review results a general lack of studies dealing with the modeling of rural built environment and hence a theoretical modelling approach for such purpose is needed. The advancement in technology and modernity in building construction and agriculture have gradually changed the rural built environment. In addition, the phenomenon of urbanization of a determined the construction of new volumes that occurred beside abandoned or derelict rural buildings. Consequently there are two types of transformation dynamics affecting mainly the rural built environment that can be observed: the conversion of rural buildings and the increasing of building numbers. It is the specific aim of the presented study to propose a methodology for the development of a spatial model that allows the identification of driving forces that acted on the behaviours of the building allocation. In fact one of the most concerning dynamic nowadays is related to an irrational expansion of buildings sprawl across landscape. The proposed methodology is composed by some conceptual steps that cover different aspects related to the development of a spatial model: the selection of a response variable that better describe the phenomenon under study, the identification of possible driving forces, the sampling methodology concerning the collection of data, the most suitable algorithm to be adopted in relation to statistical theory and method used, the calibration process and evaluation of the model. A different combination of factors in various parts of the territory generated favourable or less favourable conditions for the building allocation and the existence of buildings represents the evidence of such optimum. Conversely the absence of buildings expresses a combination of agents which is not suitable for building allocation. Presence or absence of buildings can be adopted as indicators of such driving conditions, since they represent the expression of the action of driving forces in the land suitability sorting process. The existence of correlation between site selection and hypothetical driving forces, evaluated by means of modeling techniques, provides an evidence of which driving forces are involved in the allocation dynamic and an insight on their level of influence into the process. GIS software by means of spatial analysis tools allows to associate the concept of presence and absence with point futures generating a point process. Presence or absence of buildings at some site locations represent the expression of these driving factors interaction. In case of presences, points represent locations of real existing buildings, conversely absences represent locations were buildings are not existent and so they are generated by a stochastic mechanism. Possible driving forces are selected and the existence of a causal relationship with building allocations is assessed through a spatial model. The adoption of empirical statistical models provides a mechanism for the explanatory variable analysis and for the identification of key driving variables behind the site selection process for new building allocation. The model developed by following the methodology is applied to a case study to test the validity of the methodology. In particular the study area for the testing of the methodology is represented by the New District of Imola characterized by a prevailing agricultural production vocation and were transformation dynamic intensively occurred. The development of the model involved the identification of predictive variables (related to geomorphologic, socio-economic, structural and infrastructural systems of landscape) capable of representing the driving forces responsible for landscape changes.. The calibration of the model is carried out referring to spatial data regarding the periurban and rural area of the study area within the 1975-2005 time period by means of Generalised linear model. The resulting output from the model fit is continuous grid surface where cells assume values ranged from 0 to 1 of probability of building occurrences along the rural and periurban area of the study area. Hence the response variable assesses the changes in the rural built environment occurred in such time interval and is correlated to the selected explanatory variables by means of a generalized linear model using logistic regression. Comparing the probability map obtained from the model to the actual rural building distribution in 2005, the interpretation capability of the model can be evaluated. The proposed model can be also applied to the interpretation of trends which occurred in other study areas, and also referring to different time intervals, depending on the availability of data. The use of suitable data in terms of time, information, and spatial resolution and the costs related to data acquisition, pre-processing, and survey are among the most critical aspects of model implementation. Future in-depth studies can focus on using the proposed model to predict short/medium-range future scenarios for the rural built environment distribution in the study area. In order to predict future scenarios it is necessary to assume that the driving forces do not change and that their levels of influence within the model are not far from those assessed for the time interval used for the calibration.

Modelling coupled physical-biogeochemical processes in ice-covered oceans

The last decades have seen a large effort of the scientific community to study and understand the physics of sea ice. We currently have a wide - even though still not exhaustive - knowledge of the sea ice dynamics and thermodynamics and of their temporal and spatial variability. Sea ice biogeochemistry is instead largely unknown. Sea ice algae production may account for up to 25% of overall primary production in ice-covered waters of the Southern Ocean. However, the influence of physical factors, such as the location of ice formation, the role of snow cover and light availability on sea ice primary production is poorly understood. There are only sparse localized observations and little knowledge of the functioning of sea ice biogeochemistry at larger scales. Modelling becomes then an auxiliary tool to help qualifying and quantifying the role of sea ice biogeochemistry in the ocean dynamics. In this thesis, a novel approach is used for the modelling and coupling of sea ice biogeochemistry - and in particular its primary production - to sea ice physics. Previous attempts were based on the coupling of rather complex sea ice physical models to empirical or relatively simple biological or biogeochemical models. The focus is moved here to a more biologically-oriented point of view. A simple, however comprehensive, physical model of the sea ice thermodynamics (ESIM) was developed and coupled to a novel sea ice implementation (BFM-SI) of the Biogeochemical Flux Model (BFM). The BFM is a comprehensive model, largely used and validated in the open ocean environment and in regional seas. The physical model has been developed having in mind the biogeochemical properties of sea ice and the physical inputs required to model sea ice biogeochemistry. The central concept of the coupling is the modelling of the Biologically-Active-Layer (BAL), which is the time-varying fraction of sea ice that is continuously connected to the ocean via brines pockets and channels and it acts as rich habitat for many microorganisms. The physical model provides the key physical properties of the BAL (e.g., brines volume, temperature and salinity), and the BFM-SI simulates the physiological and ecological response of the biological community to the physical enviroment. The new biogeochemical model is also coupled to the pelagic BFM through the exchange of organic and inorganic matter at the boundaries between the two systems . This is done by computing the entrapment of matter and gases when sea ice grows and release to the ocean when sea ice melts to ensure mass conservation. The model was tested in different ice-covered regions of the world ocean to test the generality of the parameterizations. The focus was particularly on the regions of landfast ice, where primary production is generally large. The implementation of the BFM in sea ice and the coupling structure in General Circulation Models will add a new component to the latters (and in general to Earth System Models), which will be able to provide adequate estimate of the role and importance of sea ice biogeochemistry in the global carbon cycle.

New mechanisms for modelling the motion of the human ankle complex

The relevance of human joint models was shown in the literature. In particular, the great importance of models for the joint passive motion simulation (i.e. motion under virtually unloaded conditions) was outlined. They clarify the role played by the principal anatomical structures of the articulation, enhancing the comprehension of surgical treatments, and in particular the design of total ankle replacement and ligament reconstruction. Equivalent rigid link mechanisms proved to be an efficient tool for an accurate simulation of the joint passive motion. This thesis focuses on the ankle complex (i.e. the anatomical structure composed of the tibiotalar and the subtalar joints), which has a considerable role in human locomotion. The lack of interpreting models of this articulation and the poor results of total ankle replacement arthroplasty have strongly suggested devising new mathematical models capable of reproducing the restraining function of each structure of the joint and of replicating the relative motion of the bones which constitute the joint itself. In this contest, novel equivalent mechanisms are proposed for modelling the ankle passive motion. Their geometry is based on the joint’s anatomical structures. In particular, the role of the main ligaments of the articulation is investigated under passive conditions by means of nine 5-5 fully parallel mechanisms. Based on this investigation, a one-DOF spatial mechanism is developed for modelling the passive motion of the lower leg. The model considers many passive structures constituting the articulation, overcoming the limitations of previous models which took into account few anatomical elements of the ankle complex. All the models have been identified from experimental data by means of optimization procedure. Then, the simulated motions have been compared to the experimental one, in order to show the efficiency of the approach and thus to deduce the role of each anatomical structure in the ankle kinematic behavior.

Three Essays in Spatial Economics

This work contributes to the field of spatial economics by embracing three distinct modelling approaches, belonging to different strands of the theoretical literature. In the first chapter I present a theoretical model in which the changes in urban system’s degree of functional specialisation are linked to (i) firms’ organisational choices and firms’ location decisions. The interplay between firms’ internal communication/managing costs (between headquarters and production plants) and the cost of communicating with distant business services providers leads the transition process from an “integrated” urban system where each city hosts every different functions to a “functionally specialised” urban system where each city is either a primary business center (hosting advanced business services providers, a secondary business center or a pure manufacturing city and all this city-types coexist in equilibrium.The second chapter investigates the impact of free trade on welfare in a two-country world modelled as an international Hotelling duopoly with quadratic transport costs and asymmetric countries, where a negative environmental externality is associated with the consumption of the good produced in the smaller country. Countries’ relative sizes as well as the intensity of negative environmental externality affect potential welfare gains of trade liberalisation. The third chapter focuses on the paradox, by which, contrary to theoretical predictions, empirical evidence shows that a decrease in international transport costs causes an increase in foreign direct investments (FDIs). Here we propose an explanation to this apparent puzzle by exploiting an approach which delivers a continuum of Bertrand- Nash equilibria ranging above marginal cost pricing. In our setting, two Bertrand firms, supplying a homogeneous good with a convex cost function, enter the market of a foreign country. We show that allowing for a softer price competition may indeed more than offset the standard effect generated by a decrease in trade costs, thereby restoring FDI incentives.

Methods for Clearance Influence Analysis in Planar and Spatial Mechanisms

This doctoral dissertation presents a new method to asses the influence of clearancein the kinematic pairs on the configuration of planar and spatial mechanisms. The subject has been widely investigated in both past and present scientific literature, and is approached in different ways: a static/kinetostatic way, which looks for the clearance take-up due to the external loads on the mechanism; a probabilistic way, which expresses clearance-due displacements using probability density functions; a dynamic way, which evaluates dynamic effects like the actual forces in the pairs caused by impacts, or the consequent vibrations. This dissertation presents a new method to approach the problem of clearance. The problem is studied from a purely kinematic perspective. With reference to a given mechanism configuration, the pose (position and orientation) error of the mechanism link of interest is expressed as a vector function of the degrees of freedom introduced in each pair by clearance: the presence of clearance in a kinematic pair, in facts, causes the actual pair to have more degrees of freedom than the theoretical clearance-free one. The clearance-due degrees of freedom are bounded by the pair geometry. A proper modelling of clearance-affected pairs allows expressing such bounding through analytical functions. It is then possible to study the problem as a maximization problem, where a continuous function (the pose error of the link of interest) subject to some constraints (the analytical functions bounding clearance- due degrees of freedom) has to be maximize. Revolute, prismatic, cylindrical, and spherical clearance-affected pairs have been analytically modelled; with reference to mechanisms involving such pairs, the solution to the maximization problem has been obtained in a closed form.

Statistical Analysis and Modelling Aspects of Thermally Driven Turbulence

The present work aims to provide a deeper understanding of thermally driven turbulence and to address some modelling aspects related to the physics of the flow. For this purpose, two idealized systems are investigated by Direct Numerical Simulation: the rotating and non-rotating Rayleigh-Bénard convection. The preliminary study of the flow topologies shows how the coherent structures organise into different patterns depending on the rotation rate. From a statistical perspective, the analysis of the turbulent kinetic energy and temperature variance budgets allows to identify the flow regions where the production, the transport, and the dissipation of turbulent fluctuations occur. To provide a multi-scale description of the flows, a theoretical framework based on the Kolmogorov and Yaglom equations is applied for the first time to the Rayleigh-Bénard convection. The analysis shows how the spatial inhomogeneity modulates the dynamics at different scales and wall-distances. Inside the core of the flow, the space of scales can be divided into an inhomogeneity-dominated range at large scales, an inertial-like range at intermediate scales and a dissipative range at small scales. This classic scenario breaks close to the walls, where the inhomogeneous mechanisms and the viscous/diffusive processes are important at every scale and entail more complex dynamics. The same theoretical framework is extended to the filtered velocity and temperature fields of non-rotating Rayleigh-Bénard convection. The analysis of the filtered Kolmogorov and Yaglom equations reveals the influence of the residual scales on the filtered dynamics both in physical and scale space, highlighting the effect of the relative position between the filter length and the crossover that separates the inhomogeneity-dominated range from the quasi-homogeneous range. The assessment of the filtered and residual physics results to be instrumental for the correct use of the existing Large-Eddy Simulation models and for the development of new ones.