"Modelling, Identification, Control, and Design with respect to Shapes and Geometries"

该研究和培训计划的主题及其长期目标是研究物理和技术系统的建模、设计、控制和识别中形状和几何的数学和理论方面。 基本思想来自系统论、最优化和控制论，但建模、优化或控制变量不再是一组参数或函数，而是几何对象的形状或结构。这一研究领域具有重要的应用潜力和对许多不同领域的挑战和紧迫问题的响应：机械部件的优化设计(汽车和航空航天工业)、传感器和执行器的位置、材料科学中自由边界位置的控制、噪声的主动控制、图像处理、自由和移动边界问题、医疗器械设计、薄结构的设计和控制、通过飞机机翼形状的微小变化控制阻力、优化游泳等。 该计划专注于三个内在利益的相互交织的项目，这些项目被选得足够远，为该计划提供了一个广泛的平台，但通过常见的数学工具和方法非常紧密地联系在一起： P1。考兰特度规、速度生成的微分同胚、演化方程和几何变分原理； P2.药物释放动力学和药物洗脱支架的设计； P3.流体中拉格朗日相干结构的网格适应和识别与图像分割。

The theme of this research and training program and its long-term objectives are the study of the mathematical and theoretical aspects of shapes and geometries in the modeling, design, control, and identification of physical and technological systems. Fundamental ideas come from systems theory, optimization, and control theory, but the modeling, optimization, or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. This area of research has an important potential for applications and for responding to challenging and pressing issues in many different areas: optimal design of mechanical parts (automotive and aerospace 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 medical devices, design and control of thin structures, control of the drag by small changes in the shape of the wing of an aircraft, optimal swimming, etc... The program concentrates on three intertwined projects of intrinsic interest that have been chosen sufficiently distant to provide a broad platform for the program but are very closely connected by common mathematical tools and methodologies: P1. Courant metrics, velocity generated diffeomorphisms, evolution equations, and geometrical variational principles; P2. Design of drug release dynamics and drug eluting stents; P3. Grid adaptation and identification of Lagrangian Coherent Structures in fluids versus image segmentation.