arXiv subjects

Christophe Eloy

Publications and source records attributed to Christophe Eloy.

At least 19 recordsLinked to original sources

arXiv2026

Soft Mobility Theory

Predicting how a deformable body moves and deforms in a viscous flow underlies problems ranging from microorganism locomotion to soft microrobotics, yet existing frameworks are either problem-specific or ill-suited to inverse design. We propose the soft mobility theory: applying the principle of virtual power and the Lorentz reciprocal theorem to a hyperelastic body in a background Stokes flow yields a configuration-dependent ordinary differential equation for the generalized coordinates of the body. This soft mobility equation extends classical rigid-body mobility theory in that the mobility, elastic, body-force, and flow-coupling tensors all depend explicitly on the instantaneous deformation. We specialize the framework to assemblies of hydrodynamically interacting spheres connected by elastic springs, using the Rotne-Prager-Yamakawa approximation to compute the mobility, and validate it on canonical problems spanning rigid and flexible bodies in quiescent and shear flows. An open-source JAX implementation makes entire simulations end-to-end differentiable. This allows efficient gradient-based inverse design: as proofs of concept, we recover the asymptotic optimum of a three-sphere swimmer and design a soft gyrotactic "surfer" that exploits passive deformation to ascend faster than its rigid counterpart in a Taylor-Green flow.

physics.flu-dyn↗

arXiv2026

Steer'n Roll: A Stereoscopic Flow-Sensing Strategy for Planktonic Prey Detection and Capture

Planktonic organisms such as copepods sense swimming prey and sinking food particles through the hydrodynamic disturbances they generate. However, because these flow fields are often highly symmetric, they provide little directional information, making accurate localization of the source challenging. Here, we introduce the steer'n roll sensing and response strategy. This strategy combines stereoscopic flow sensing and a roll motion. Stereoscopic sensing allows plankton to disambiguate flow signals by integrating two spatially separated flow measurements, while a roll about the swimming axis enhances exploration of the three-dimensional space. We show that steer'n roll is efficient, achieving a 100% success rate, versatile across signal type, and robust to flow sensing noise, orientational diffusion, and turbulence. Together, these findings identify a biologically plausible mechanism for prey detection and capture via flow sensing, and offer testable insights into the sensory-motor strategies of planktonic organisms.

physics.bio-ph↗

arXiv2025

A critical assessment of reinforcement learning methods for microswimmer navigation in complex flows

Navigating in a fluid flow while being carried by it, using only information accessible from on-board sensors, is a problem commonly faced by small planktonic organisms. It is also directly relevant to autonomous robots deployed in the oceans. In the last ten years, the fluid mechanics community has widely adopted reinforcement learning, often in the form of its simplest implementations, to address this challenge. But it is unclear how good are the strategies learned by these algorithms. In this paper, we perform a quantitative assessment of reinforcement learning methods applied to navigation in partially observable flows. We first introduce a well-posed problem of directional navigation for which a quasi-optimal policy is known analytically. We then report on the poor performance and robustness of commonly used algorithms (Q-Learning, Advantage Actor Critic) in flows regularly encountered in the literature: Taylor-Green vortices, Arnold-Beltrami-Childress flow, and two-dimensional turbulence. We show that they are vastly surpassed by PPO (Proximal Policy Optimization), a more advanced algorithm that has established dominance across a wide range of benchmarks in the reinforcement learning community. In particular, our custom implementation of PPO matches the theoretical quasi-optimal performance in turbulent flow and does so in a robust manner. Reaching this result required the use of several additional techniques, such as vectorized environments and generalized advantage estimation, as well as hyperparameter optimization. This study demonstrates the importance of algorithm selection, implementation details, and fine-tuning for discovering truly smart autonomous navigation strategies in complex flows.

cs.LG↗

arXiv2024

Hydrodynamics of flow sensing in plankton

Planktonic organisms, despite their passive drift in the ocean, exhibit complex responses to fluid flow, including escape behaviors and larval settlement detection. But what flow signals can they perceive? This paper addresses this question by considering an organism covered with sensitive cilia and immersed in a background flow. The organism is modeled as a spherical particle in Stokes flow, with cilia assumed to measure the local shear at the particle surface. This study reveals that, while these organisms can always measure certain components of the flow strain, bottom-heaviness is necessary to measure the horizontal component of vorticity. These findings shed light on flow sensing by plankton, contributing to a better understanding of their behavior.

physics.flu-dyn↗

arXiv2024

Flow associated with Lighthill's elongated-body theory

The hydrodynamic forces acting on an undulating swimming fish consist of two components: a drag-based resistive force and a reactive force originating from the necessary acceleration of an added mass of water. Lighthill's elongated-body theory, based on potential flow, provides a framework for calculating this reactive force. By leveraging the high aspect ratio of most fish, the theory simplifies the problem into a series of independent two-dimensional slices of fluids along the fish's body, which exchange momentum with the body and neighbouring slices. Using momentum conservation arguments, Lighthill's theory predicts the total thrust generated by an undulating fish, based solely on the dimensions and kinematics of its caudal fin. However, the assumption of independent slices has led to the common misconception that the flow produced lacks a longitudinal component. In this paper, we revisit Lighthill's theory, offering a modern reinterpretation using essential singularities of potential flows. We then extend it to predict the full three-dimensional flow field induced by the fish's body motion. Our results compare favourably with numerical simulations of realistic fish geometries.

physics.flu-dyn↗

arXiv2024

Visual collective behaviors on spherical robots

The implementation of collective motion, traditionally, disregard the limited sensing capabilities of an individual, to instead assuming an omniscient perception of the environment. This study implements a visual flocking model in a ``robot-in-the-loop'' approach to reproduce these behaviors with a flock composed of 10 independent spherical robots. The model achieves robotic collective motion by only using panoramic visual information of each robot, such as retinal position, optical size and optic flow of the neighboring robots. We introduce a virtual anchor to confine the collective robotic movements so to avoid wall interactions. For the first time, a simple visual robot-in-the-loop approach succeed in reproducing several collective motion phases, in particular, swarming, and milling. Another milestone achieved with by this model is bridging the gap between simulation and physical experiments by demonstrating nearly identical behaviors in both environments with the same visual model. To conclude, we show that our minimal visual collective motion model is sufficient to recreate most collective behaviors on a robot-in-the-loop system that is scalable, behaves as numerical simulations predict and is easily comparable to traditional models.

cs.RO↗

arXiv2024

Modeling collective behaviors from optic flow and retinal cues

Animal collective behavior is often modeled with self-propelled particles, assuming each individual has ``omniscient'' knowledge of its neighbors. Yet, neighbors may be hidden from view and we do not know the effect of this information loss. To address this question, we propose a visual model of collective behavior where each particle moves according to bio-plausible visual cues, in particular the optic flow. This visual model successfully reproduces three classical collective behaviors: swarming, schooling, and milling. This model offers a potential solution for controlling artificial swarms visually.

physics.bio-ph↗

arXiv2022

Surfing on turbulence: a strategy for planktonic navigation

In marine plankton, many swimming species can perceive their environment with flow sensors. Can they use this flow information to travel faster in turbulence? To address this question, we consider plankters swimming at constant speed, whose goal is to move upwards. We propose a robust analytical behavior that allows plankters to choose a swimming direction according to the local flow gradients. We show numerically that such plankters can "surf" on turbulence and reach net vertical speeds up to twice their swimming speed. This new physics-based model suggests that planktonic organisms can exploit turbulence features for navigation.

physics.flu-dyn↗

arXiv2022

Searching for a source without gradients: how good is infotaxis and how to beat it

Infotaxis is a popular search algorithm designed to track a source of odor in a turbulent environment using information provided by odor detections. To exemplify its capabilities, the source-tracking task was framed as a partially observable Markov decision process consisting in finding, as fast as possible, a stationary target hidden in a 2D grid using stochastic partial observations of the target location. Here we provide an extended review of infotaxis, together with a toolkit for devising better strategies. We first characterize the performance of infotaxis in domains from 1D to 4D. Our results show that, while being suboptimal, infotaxis is reliable (the probability of not reaching the source approaches zero), efficient (the mean search time scales as expected for the optimal strategy), and safe (the tail of the distribution of search times decays faster than any power law, though subexponentially). We then present three possible ways of beating infotaxis, all inspired by methods used in artificial intelligence: tree search, heuristic approximation of the value function, and deep reinforcement learning. The latter is able to find, without any prior human knowledge, the (near) optimal strategy. Altogether, our results provide evidence that the margin of improvement of infotaxis toward the optimal strategy gets smaller as the dimensionality increases.

physics.bio-ph↗

arXiv2021

How memory architecture affects learning in a simple POMDP: the two-hypothesis testing problem

Reinforcement learning is generally difficult for partially observable Markov decision processes (POMDPs), which occurs when the agent's observation is partial or noisy. To seek good performance in POMDPs, one strategy is to endow the agent with a finite memory, whose update is governed by the policy. However, policy optimization is non-convex in that case and can lead to poor training performance for random initialization. The performance can be empirically improved by constraining the memory architecture, then sacrificing optimality to facilitate training. Here we study this trade-off in a two-hypothesis testing problem, akin to the two-arm bandit problem. We compare two extreme cases: (i) the random access memory where any transitions between $M$ memory states are allowed and (ii) a fixed memory where the agent can access its last $m$ actions and rewards. For (i), the probability $q$ to play the worst arm is known to be exponentially small in $M$ for the optimal policy. Our main result is to show that similar performance can be reached for (ii) as well, despite the simplicity of the memory architecture: using a conjecture on Gray-ordered binary necklaces, we find policies for which $q$ is exponentially small in $2^m$, i.e. $q\simα^{2^m}$ with $α< 1$. In addition, we observe empirically that training from random initialization leads to very poor results for (i), and significantly better results for (ii) thanks to the constraints on the memory architecture.

cs.LG↗

arXiv2021

Seismic response of cylinder assemblies in axial flow

Earthquakes are a great challenge for the safety of nuclear reactors. To address this challenge, we need to better understand how the reactor core responds to seismic forcing. The reactor core is made of fuel assemblies, which are themselves composed of flexible fuel rods immersed in a strong axial flow. This gives rise to strongly-coupled fluid-structure interactions whose accurate modelling generally requires high computational costs. In this paper, we introduce a new model able to capture the mechanical response of the reactor core subjected to seismic forcing with low computational costs. This model is based on potential flow theory for the fluid part and Euler-Bernoulli beam theory for the structural part allowing us to predict the response to seismic forcing in presence of axial flow.. The linear equations are solved in the Fourier space to decrease computational time. For validation purposes, we first use the proposed model to compute the response of a single cylinder in axial flow. We then implement a multiple cylinder geometry made of 4 fuel assemblies, each made of 8x8 cylinders, corresponding to an experimental facility available at CEA. The comparison between numerical results and experiments show good agreement. The model can correctly predict the added mass. It can also qualitatively capture the coupling between assemblies and the effect of confinement. This shows that a potential flow approach can give insight into the complex fluid-structure interactions within a nuclear reactor and, in particular, be used to predict the response to seismic forcing at low computational cost.

physics.flu-dyn↗

arXiv2021

Zonal flow in a resonant precessing cylinder

A cylinder undergoes precession when it rotates around its axis and this axis itself rotates around another direction. In a precessing cylinder full of fluid, a steady and axisymmetric component of the azimuthal flow is generally present. This component is called a zonal flow. Although zonal flows have been often observed in experiments and numerical simulations, their origin has eluded theoretical approaches so far. Here, we develop an asymptotic analysis to calculate the zonal flow forced in a resonant precessing cylinder, that is when the harmonic response is dominated by a single Kelvin mode. We find that the zonal flow originates from three different sources: (1) the nonlinear interaction of the inviscid Kelvin mode with its viscous correction; (2) the steady and axisymmetric response to the nonlinear interaction of the Kelvin mode with itself; and (3) the nonlinear interactions in the end boundary layers. In a precessing cylinder, two additional sources arise due to the equatorial Coriolis force and the forced shear flow. However, they cancel exactly. The study thus generalises to any Kelvin mode, forced by precession or any other mechanism. The present theoretical predictions of the zonal flow are confirmed by comparison with numerical simulations and experimental results. We also show numerically that the zonal flow is always retrograde in a resonant precessing cylinder (m=1) or when it results from resonant Kelvin modes of azimuthal wavenumbers m=2, 3, and presumably higher.

physics.flu-dyn↗

arXiv2021

Rebound and scattering of motile Chlamydomonas algae in confined chambers

Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.

physics.bio-ph↗

arXiv2018

Model of collective fish behavior with hydrodynamic interactions

Fish schooling is often modeled with self-propelled particles subject to phenomenological behavioral rules. Although fish are known to sense and exploit flow features, these models usually neglect hydrodynamics. Here, we propose a novel model that couples behavioral rules with far-field hydrodynamic interactions. We show that (1) a new "collective turning" phase emerges; (2) on average individuals swim faster thanks to the fluid; (3) the flow enhances behavioral noise. The results of this model suggest that hydrodynamic effects should be considered to fully understand the collective dynamics of fish.

physics.bio-ph↗

arXiv2015

Collective Motion with Anticipation: Flocking, Spinning, and Swarming

We investigate the collective dynamics of self-propelled particles able to probe and anticipate the orientation of their neighbors. We show that a simple anticipation strategy hinders the emergence of homogeneous flocking patterns. Yet, anticipation promotes two other forms of self-organization: collective spinning and swarming. In the spinning phase, all particles follow synchronous circular orbits, while in the swarming phase, the population condensates into a single compact swarm that cruises coherently without requiring any cohesive interactions. We quantitatively characterize and rationalize these phases of polar active matter and discuss potential applications to the design of swarming robots.

cond-mat.stat-mech↗

arXiv2013

Shape of optimal active flagella

Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molecular motors forcing the flagellum, only a portion of which ending up dissipated in the fluid. This optimisation approach allows us to derive a family of shapes depending on a single dimensionless number quantifying the relative importance of elastic to viscous effects: the Sperm number. The computed optimal shapes are found to agree with the waveforms observed on spermatozoon of marine organisms, thus suggesting that these eukaryotic flagella might have evolved to be mechanically optimal.

physics.bio-ph↗

arXiv2013

Drag Reduction, from Bending to Pruning

Most plants and benthic organisms have evolved efficient reconfiguration mechanisms to resist flow-induced loads. These mechanisms can be divided into bending, in which plants reduce their sail area through elastic deformation, and pruning, in which the loads are decreased through partial breakage of the structure. In this work, we show by using idealized models that these two mechanisms or, in fact, any combination of the two, are equally efficient to reduce the drag experienced by terrestrial and aquatic vegetation.

physics.bio-ph↗

arXiv2013

Flow-Induced Draping

Crumpled paper or drapery patterns are everyday examples of how elastic sheets can respond to external forcing. In this Letter, we study experimentally a novel sort of forcing. We consider a circular flexible plate clamped at its center and subject to a uniform flow normal to its initial surface. As the flow velocity is gradually increased, the plate exhibits a rich variety of bending deformations: from a cylindrical taco-like shape, to isometric developable cones with azimuthal periodicity two or three, to eventually a rolled-up period-three cone. We show that this sequence of flow-induced deformations can be qualitatively predicted by a linear analysis based on the balance between elastic energy and pressure force work.

cond-mat.soft↗