Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Recycling the city: a sustainable planning framework to reduce, reuse and recycle urban residual spaces

Cities are key locations where Sustainability needs to be addressed at all levels, as land is a finite resource. However, not all urban spaces are exploited at best, and land developers often evaluate unused, misused, or poorly-designed urban portions as impracticable constraints. Further, public authorities lose the challenge to enable and turn these urban spaces into valuable opportunities where Sustainable Urban Development may flourish. Arguing that these spatial elements are at the centre of SUD, the paper elaborates a prototype in the form of a conceptual strategic planning framework, committed to an effective recycling of the city spaces using a flexible and multidisciplinary approach. Firstly, the research focuses upon a broad review of Sustainability literature, highlighting established principles and guidelines, building a sound theoretical base for the new concept. Hence, it investigates origins, identifies and congruently suggests a definition, characterisation and classification for urban “R-Spaces”. Secondly, formal, informal and temporary fitting functions are analysed and inserted into a portfolio meant to enhance adaptability and enlarge the choices for the on-site interventions. Thirdly, the study outlines ideal quality requirements for a sustainable planning process. Then, findings are condensed in the proposal, which is articulated in the individuation of tools, actors, plans, processes and strategies. Afterwards, the prototype is tested upon case studies: Solar Community (Casalecchio di Reno, Bologna) and Hyllie Sustainable City Project, the latter developed via an international workshop (ACSI-Camp, Malmö, Sweden). Besides, the qualitative results suggest, inter alia, the need to right-size spatial interventions, separate structural and operative actors, involve synergies’ multipliers and intermediaries (e.g. entrepreneurial HUBs, innovation agencies, cluster organisations…), maintain stakeholders’ diversity and create a circular process open for new participants. Finally, the paper speculates upon a transfer of the Swedish case study to Italy, and then indicates desirable future researches to favour the prototype implementation.