## PhD Thesis - Calibration and control (inverse problems) for generic footprint models

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University of Nice Sophia Antipolis, France
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auroux$unice.fr Job Description: Dieudonné Laboratory (Mathematics), University of Nice Sophia Antipolis, France Marie Curie ITN Project: A Synergic Training Network on Energy beam Processing (STEEP) Early Stage Researcher (ESR): PhD fellowship, 2 positions available 1. Mathematical modelling of generic footprints in energy beams 2. Calibration and control (inverse problems) for generic footprint models Approx. 30,000 EURO per annum (net income) Applications are invited for the above post to work with Professor Didier Auroux, within a European funded project in the area of energy beam processing to underpin work at the University of Nice Sophia Antipolis, France. The successful candidates will register for a 3 year PhD in the Mathematics laboratory (J. A. Dieudonné), University of Nice Sophia Antipolis, France, within the Marie Curie Initial Training Network (ITN): A Synergetic Training Network on Energy beam Processing: from Modelling to Industrial Applications – STEEP (coordinated by the University of Nottingham). Project 1: Mathematical modelling of generic footprints in energy beams. Based on the previous expertise developed at the University of Nottingham, this project aims to develop generic mathematical models for energy beam footprints. The idea is to parameterize the surface, possibly with PDE models depending on the etching rate function. These models should be dynamic and account for overlapping. Numerical implementation will be carefully studied. This project will be carried out in collaboration with the University of Nottingham. Project 2: Calibration and control (inverse problems) for generic footprints models. Using a variational approach, a cost function measuring the difference between the predicted (modelled) footprints and experimental data (or desired footprints) will be minimized (using the adjoint model), providing the optimal etching rate function. The secondary objectives are to study model calibration and prediction of the evolution of beam footprints, and possibly feedback control problems. This project will be carried out in collaboration with the University of Nottingham. This is an exciting opportunity to contribute to the development of a unified STEEP modelling platform of the footprints as result of energy beams (waterjet, laser, ion beam) – workpiece interactions. These projects will involve: numerical modelling techniques; on hand experience on abrasive waterjet/pulsed laser/focussed ion beam machining; understanding the physics of material removal by abrasive, thermal and momentum transfer methods; surface and materials analysis techniques; liaison with industry and professional associations in UK and EU. The PhD candidates will benefit from the Hi-Tech facilities (abrasive waterjet, pulsed laser, focussed ion beam) and expertise which Manufacturing division at Nottingham University possess at world-leading level. The overall aim of STEEP – Initial Training Network is to establish a transnational research training platform for the formation and career development of young researchers on energy beam processing methods that represent a scientific field of critical importance for further advancement of European of high value-added manufacturing industry. Hence, the selected candidates will be able to develop multidisciplinary knowledge such as analytical skills related to energy beam processes, modelling and software development making them highly employable to knowledge-intensive companies/institutes. It is planned that each Early Stage Researcher will have in total 3 months placement (1month/year) at industrial/research /academic institutions related to topics of their studies within UK and EU. Each yearly placement will be scoped to address the stage of the development of the PhD projects (1st year: theoretical studies; 2nd year: proof of concept; 3rd year: demonstrations). Candidates must therefore be able to move between countries as necessary for approx. 3 months for the entire duration of the project. Candidates should be in the first 4 years (full-time equivalent) of their research careers and not been awarded a doctorate degree, starting at the date of obtaining the degree which would formally entitle them to embark on a doctorate. Preference will be given to candidates with experience in applied mathematics, physics and engineering backgrounds. As part of our commitment to promoting diversity we encourage applications from women. To comply with the Marie Curie Actions rule for mobility, applicants must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months in the 3 years prior to their recruitment (short stays such as holidays are not taken into account). This full-time post is available from June 2013 and will be offered on a fixed-term contract for a period of 36 months. Applications and informal enquiries should be addressed to Prof Didier Auroux, email: auroux$unice.fr. For information about the Mathematics lab of the University of Nice Sophia Antipolis, see: http://math.unice.fr and http://www.unice.fr.

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