A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Reproduction of Mediterranean zooxanthellate and azooxanthellate scleractinian corals along environmental gradients

Despite extensive studies focus mainly on sexual reproductive characteristics in tropical scleractinian species, there is limited knowledge on temperate regions. The Mediterranean is a biodiversity hotspot under intense pressure from anthropogenic impacts. Climatic models further predict that the Mediterranean basin will be one of the most impacted regions by the ongoing warming trend. This makes it a potential model of more global patterns to occur in the world’s marine biota, and a natural focus of interest for research on climate. The present research contributed to increase data on reproductive modes and sexuality of temperate scleractinian corals, highlighting their developmental plasticity, showing different forms of propagation and different responses to environmental change. For the first time, sexuality and reproductive mode in Caryophyllia inornata were determined. An unusual embryogenesis without a clear seasonal pattern was observed, suggesting the possibility of an asexual origin. Sexual reproduction of Astroides calycularis was governed by annual changes in seawater temperature, as observed for other Mediterranean dendrophylliids. Defining the reproductive biology of these species is the starting point for studying their potential response to variations of environmental parameters, on a global climate change context. The results on the influence of temperature on reproductive output of the zooxanthellate (symbiosis with unicellular algae) Balanophyllia europaea and the non-zooxanthellate Leptopsammia pruvoti suggest that the latter may be quite tolerant to temperature increase, since the zooxanthellate species resulted less efficient at warm temperatures. A possible explanation could be related to their different trophic system. In B. europaea thermal tolerance is primarily governed by the symbiotic algae, making it more sensitive to temperature changes. On the contrary, the absence of symbionts in L. pruvoti might make it more resistant to temperature. In a progressively warming Mediterranean, the efficiency on scleractinian reproduction could be influenced in different ways, reflecting their extraordinary adaptability.

Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.