Research Overview
My research focuses on developing accurate mathematical models to describe the dynamics of particles moving in fluids. These particles may be rigid, deformable, or elastic, and they interact with their environment in complex ways. I also investigate their controllability properties to determine whether such systems can be maneuvered as desired. Optimal control and optimization techniques play a key role in my work to design efficient and reliable control strategies.
Mathematical Modeling, Numerical Analysis and Simulations
I develop mathematical models of varying complexity, from reduced-order formulations to richly detailed physical representations. These models are used to simulate the behavior of microswimmers evolving in confined environments with complex geometries, such as those found in biological tissues. The goal is to accurately capture the emerging dynamics, both in isolation and during interaction with boundaries or obstacles. We have designed highly detailed digital twins of bio-inspired microswimmers composed of a rigid magnetic head and a passive elastic flagellum, as well as simplified models that help isolate key locomotion mechanisms. See for instance: [2], [5], [8], [15],[18] and [19].
Control
My work in control theory focuses on low-Reynolds-number systems where traditional actuation is replaced by non-local or indirect inputs, such as body deformation or external field. I develop theoretical results to determine, a priori, whether a given microswimmer system is maneuverable or not, depending on its physical structure and actuation constraints. See more details for instance: [1], [3], [6],[7], [9], [13] and [17].
Here for instance one of the challenge is to control an elastic-magneto swimmer close to a wall
Optimization
I use optimal control, shape optimization, and machine learning techniques to design and improve the performance of active systems. These problems often involve physical and geometric constraints modeled by partial differential equations (PDEs), and require the development of advanced numerical optimization algorithms. See for instance: [4], [10], [11], [13] and [16].