We show that these discrete confocal coordinate systems may equivalently be constructed geometrically via polarity with respect to a sequence of classical confocal quadrics. In comparison to the first approach, this definition results in a broader class of nets capturing arbitrary reparametrizations also in the discrete case. We use these two properties to propose another discretization of confocal coordinates, while again employing the aforementioned discrete orthogonality constraint. Secondly, we show that classical confocal coordinates and their reparametrizations along coordinate lines are characterized by orthogonality and the factorization property. The coordinate functions of these discrete confocal coordinates are explicitly given in terms of gamma functions. The constructed solutions are discrete Koenigs nets and feature a novel discrete orthogonality constraint defined on pairs of dual discrete nets, as well as a corresponding discrete isothermicity condition. In this cumulative thesis we propose two approaches to the discretization of confocal coordinates, and study the closely related checkerboard incircular nets.įirst, we propose a discretization based on factorizable solutions to an integrable discretization of the Euler-Poisson-Darboux equation. She worked in Spain, the Politécnico de Torino and in Greece (there she was Marie Curie fellow at the Foundation for Research and Technology - Hellas) before she decided to spend time in Australia and India.Confocal quadrics constitute a special example of orthogonal coordinate systems. Serena has a Bachelor in Chemistry and a Master's in Forensic Chemistry from the University of Torino. The results show a qualitative agreement with ageing behavior known from experimental literature. The combined modeling and simulation framework is able to predict calendaric and cyclic ageing up to the end of life of the battery cells. The electrochemistry is coupled to a multi-scale heat and mass transport model based on a pseudo-3D approach.Ī time-upscaling methodology is developed that allows to simulate large time spans (thousands of operating hours).
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