Analysis and control of shapes and systems

点击翻译按钮获取中文摘要

The theme of this program is the study of the theoretical and numerical aspects of shapes and geometries in the modeling, design, and control of physical and technological systems.  This area of research is very broad, rich and fascinating with an extremely important potential for applications in many different areas: optimal design of mechanical parts for the automotive industry, positioning of sensors and actuators, control of the position of the free boundary in material sciences, active control of noise, image processing, free and moving boundary problems, design of biomedical devices, design and control of thin structures, control of the drag by small changes in the shape of the wing of an aircraft, etc... There is a definite need for theory and directions to understand the modelling issues encountered, the challenges arising from new phenomenological studies, and to interpret the overwhelming number of computational results.   The program concentrates on the following five intertwined projects: 1) the mathematical analysis and optimization of shapes and geometries, 2) the development of appropriate intrinsic methods for the differential calculus and functional analysis on submanifolds of the Euclidean space, 3) the intrinsic modelling and analysis of thin and asymptotic mechanical shells, beams, and curved rods, piezoelectric shells, and thin fluid shells (e.g. oceans), 4) image processing, cracked sets, brain imaging, 5) modelling, design, and control of endoprotheses, (N+1)-D image reconstruction from N-D sections,   Some of this work has had an impact on the Canadian Space Program for the design of thermal diffusers and radiators to condition the thermal environment of satellites and on the positioning of sensors and actuators for satellites of the third generation.  The fundamental results of the research are also used on current projects on the design of medical devices (stents in interventional cardiology).