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18-19 sept. 2024 Sophia-Antipolis (France)
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AbstractsList of Abstracts
-------------------------------------------------------------------------------- François Alouges
Mathematical models for flagellar activation
Flagellar beating is the way sperm cells propel themselves. It has been observed in the 60’s by Machin that, contrarily to bacteria,
an active mechanism along the flagellum is mandatory to achieve observed deformations of the flagellum of spermacetis cells. This active structure is now recognized to be micro-motors composed of dynein structures between the filaments that compose the tail of the sperm cell. However the exact way this structure works still remains obscure. We will present generalizations and mathematical studies on models proposed in a series of papers by Jülicher, Prost and coauthors.
This is a joint work with I. Anello, A. DeSimone, A. Lefebvre-Lepot and J. Levillain.
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Jérémie Bec
Impact of confinement and fluid flow on collective motions in a discrete active system
This talk explores the self-organization of active particles on a two-dimensional single-occupancy lattice, focusing on the effects of boundary confinement and external fluid flow. We examine the transition from disordered phases to orientationally ordered patterns and their impact on particle transport and flux. In confined environments without fluid flow, particles accumulate near walls, forming clogs or bands that limit self-propulsion yet still generate net flux along the channel. Introducing an external Poiseuille flow induces vorticity, shifts the phase transition to higher alignment sensitivities, and promotes particle clustering near the channel center, significantly enhancing flux. Finally, we discuss potential applications of this analysis for designing strategies to control particle behavior and optimize transport efficiency.
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Antoine Ferreira
Magnetically Controlled Microrobots for Endovascular Drug Delivery Therapies
Research activities on nanorobotics are an emerging interdisciplinary technological area raising new scientific challenges and promising revolutionary advancements in applications such as medicine, biology, and industrial manufacturing. Nanorobots would be able to perform at least one of the following actions: actuation, sensing, signalling, information processing, intelligence, swarm behaviour at the micro/nano scale. The development of micro/nanorobots presents difficult design, modeling, simulation and control challenges as such devices will operate in microenvironments whose physical properties differ from those encountered by conventional parts. Furthermore, nanorobotics is a field, which calls for collaborative efforts between physicists, chemists, biologists, computer scientists, engineers, and other specialists to work towards this common objective. To disseminate the current advances in micro/nanorobotics, we propose in this talk different magnetically controlled microrobotic platforms for drug delivery applications.
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Aline Lefbvre-Lepot
Numerical simulation of suspensions: taking close interactions into account
We address the problem of direct numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the singular effects due to short-range interactions (lubrication effects) as the particles approach each other. Taking these lubrication effects into account in numerical simulations is a difficult problem: capturing the singularity requires, for example, the use of very fine meshes in the gap between the particles.
We describe in this presentation two methods for taking account of the effects of lubrication in numerical simulations. The first is based on an asymptotic development of the solution in the gap between the particles. It provides accurate results using coarse meshes and without adding new assumptions or models. We then describe a second method, based on a ‘viscous’ contact model. From a numerical point of view, it boils down to solving a convex optimisation problem at each time step. It will be shown that dry contacts, with or without friction, can be treated within the same theoretical framework. Finally, the coupling problem between these different contact models will be discussed. --------------------------------------------------------------------------------
Pierre Lissy
Desensitizing control for the heat equation with respect to domain variations
In this talk, I will present some recent results obtained in collaboration with Sylvain Ervedoza and Yannick Privat on the desensitizing control of the heat equation posed on a bounded domain. The question is to find a control, distributed here on a subdomain, such that a certain functional depending on the solution of the heat equation (in our case, the energy of the solution localized on a subdomain of the heat equation) is locally insensitive to a certain perturbation of the equation. Here, the main originality of our work lies in the fact that the perturbation is the domain itself, in the sense that its boundary can be subject to small variations. I will present various definitions of the desensitization problem and give some positive and negative results, giving an interpretation in terms of robustness for controllability issues.
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Clément Moreau
Multi-scale analysis and reduced models for low-Reynolds swimmers
The topic of this presentation is a multi-timescale approach to derive reduced models of particles and swimmers in a viscous (low Reynolds-number) fluid. Over a long period of time, or from a distance, the trajectory of self-propelling bodies such as swimmers appears smooth, with their trajectories appearing almost ballistic. This long-time behaviour, however, masks more complex dynamics, such as the side-to-side snakelike motion exhibited by spermatozoa, or shape-changing microorganisms and microrobots. Many models of motion at microscopic scale, such as the celebrated Jeffery equations established in 1922, neglect, often without formal justification, these effects in favour of smoother long-term behaviours.
In this talk, I will present recent results based on multi-timescale analysis and evaluating the long-term effects of high-frequency oscillations on translational and angular motion for various classical swimming models of micro-scale swimmers, with the purpose of assessing the relevance of neglecting these oscillations, and derive simplified equivalent models. I will particularly focus on Jeffery equations and subsequent generalisations. When adding a fast-timescale term in the orientational dynamics, one can show that the averaged system still follows Jeffery trajectories, with effective parameters being explicitly calculable.
I will detail the multiscale method on this example, discuss its physical interpretation, and describe extensions to deformable particles and three-dimensional motion.
This work was conducted with M. Dalwadi (UCL), E. Gaffney (Oxford University), K. Ishimoto (Kyoto University), and B. Walker (University of Bath).
-------------------------------------------------------------------------------- The development of a navigated neurosurgical microrobot To address the challenges of accessing deep regions of the brain for diagnostic and therapeutic purposes, our team has pioneered a microrobot since 2017, enabling precise navigation along 3D curved trajectories. After years of development and refinement, in 2022, cadaveric testing commenced with several successful "ex-vivo" tests, facilitating progression to the "in-vivo" phase. The aim of this talk is to describe the developing process of this cutting-edge device and to report the results of the world’s first “in-vivo” neuronavigation with a self-propelled microrobot. ----------------------------------------------------------------------------------- Stabilization of the beam equation with piezoelectric actuators in presence of saturation and hysteresis This presentation deals with the general problem of saturated control of distributed parameter systems and more specifically with the stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing configuration. The model is composed by a PDE, describing the flexible deformations dynamics, interconnected with an ODE describing the electric charge dynamics. Firstly, we show that the derived linear model is well-posed and the origin is globally asymptotically stable when a voltage control law, containing the terms estimated in the self-sensing configuration, is applied. Secondly, we make the more realistic assumption of the presence of hysteresis in the electrical domain. Applying a passive control law, we show the well-posedness and the global asymptotic stability of the nonlinear closed-loop system. Joint work with Andrea Mattioni and Sophie Tarbouriech.
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