Parameter estimation in a growth model for a biological population

The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.

Physical model of PD behavior and relevant damage growth from micro-cavities in polyethylene-based material under AC voltage

In the framework of developing defect-based life models, in which breakdown is explicitly associated with partial discharge (PD)-induced damage growth from a defect, ageing tests and PD measurements were carried out in the lab on polyethylene (PE) layered specimens containing artificial cavities. PD activity was monitored continuously during aging. A quasi-deterministic series of stages can be observed in the behavior of the main PD parameters (i.e. discharge repetition rate and amplitude). Phase-resolved PD patterns at various ageing stages were reproduced by numerical simulation which is based on a physical discharge model devoid of adaptive parameters. The evolution of the simulation parameters provides insight into the physical-chemical changes taking place at the dielectric/cavity interface during the aging process. PD activity shows similar time behavior under constant cavity gas volume and constant cavity gas pressure conditions, suggesting that the variation of PD parameters may not be attributed to the variation of the gas pressure. Brownish PD byproducts, consisting of oxygen containing moieties, and degradation pits were found at the dielectric/cavity interface. It is speculated that the change of PD activity is related to the composition of the cavity gas, as well as to the properties of dielectric/cavity interface.