arXiv subjects

Benoît Mahault

Publications and source records attributed to Benoît Mahault.

28 records · Page 2Linked to original sources

arXiv2022

Optimal navigation of microswimmers in complex and noisy environments

We design new navigation strategies for travel time optimization of microscopic self-propelled particles in complex and noisy environments. In contrast to strategies relying on the results of optimal control theory, these protocols allow for semi-autonomous navigation as they do not require control over the microswimmer motion via external feedback loops. Although the strategies we propose rely on simple principles, they show arrival time statistics strikingly similar to those obtained from stochastic optimal control theory, as well as performances that are robust to environmental changes and strong fluctuations. These features, as well as their applicability to more general optimization problems, make these strategies promising candidates for the realization of optimized semi-autonomous navigation.

cond-mat.stat-mech↗

arXiv2021

Small Obstacle in a Large Polar Flock

We show that arbitrarily large polar flocks are susceptible to the presence of a single small obstacle. In a wide region of parameter space, the obstacle triggers counter-propagating dense bands leading to reversals of the flow. In very large systems, these bands interact yielding a never-ending chaotic dynamics that constitutes a new disordered phase of the system. While most of these results were obtained using simulations of aligning self-propelled particles, we find similar phenomena at the continuous level, not when considering the basic Toner-Tu hydrodynamic theory, but in simulations of truncations of the relevant Boltzmann equation.

cond-mat.soft↗

arXiv2021

A topological fluctuation theorem

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

cond-mat.stat-mech↗

arXiv2021

Long-Range Nematic Order in Two-Dimensional Active Matter

Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond $\ell_{\rm r}$, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below $\ell_{\rm r}$, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of $π$-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.

cond-mat.soft↗

arXiv2021

Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder

We show that spatial quenched disorder affects polar active matter in ways more complex and far-reaching than believed heretofore. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.

cond-mat.stat-mech↗

arXiv2020

Magnetic microswimmers exhibit Bose-Einstein-like condensation

We study an active matter system comprised of magnetic microswimmers confined in a microfluidic channel and show that it exhibits a new type of self-organized behavior. Combining analytical techniques and Brownian dynamics simulations, we demonstrate how the interplay of non-equilibrium activity, external driving, and magnetic interactions leads to the condensation of swimmers at the center of the channel via a non-equilibrium phase transition that is formally akin to Bose-Einstein condensation. We find that the effective dynamics of the microswimmers can be mapped onto a diffusivity-edge problem, and use the mapping to build a generalized thermodynamic framework, which is verified by a parameter-free comparison with our simulations. Our work reveals how driven active matter has the potential to generate exotic classical non-equilibrium phases of matter with traits that are analogous to those observed in quantum systems.

cond-mat.stat-mech↗

arXiv2020

Bose-Einstein-like Condensation due to Diffusivity Edge under Periodic Confinement

A generic class of scalar active matter, characterized at the mean field level by the diffusivity vanishing above some threshold density, was recently introduced [Golestanian R 2019 Phys. Rev. E 100 010601(R)]. In the presence of harmonic confinement, such 'diffusivity edge' was shown to lead to condensation in the ground state, with the associated transition exhibiting formal similarities with Bose-Einstein condensation (BEC). In this work, the effect of a diffusivity edge is addressed in a periodic potential in arbitrary dimensions, where the system exhibits coexistence between many condensates. Using a generalized thermodynamic description of the system, it is found that the overall phenomenology of BEC holds even for finite energy barriers separating each neighbouring pair of condensates. Shallow potentials are shown to quantitatively affect the transition, and introduce non-universality in the values of the scaling exponents.

cond-mat.stat-mech↗

arXiv2019

Quantitative Assessment of the Toner and Tu Theory of Polar Flocks

We present a quantitative assessment of the Toner and Tu theory describing the universal scaling of fluctuations in polar phases of dry active matter. Using large scale simulations of the Vicsek model in two and three dimensions, we find the overall phenomenology and generic algebraic scaling predicted by Toner and Tu, but our data on density correlations reveal some qualitative discrepancies. The values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995. In particular, we identify a large crossover scale beyond which flocks are only weakly anisotropic. We discuss the meaning and consequences of these results.

cond-mat.stat-mech↗

arXiv2019

Dry, aligning, dilute, active matter: A synthetic and self-contained overview

These notes are based on lectures given during the Summer School `Active Matter and Nonequilibrium Statistical Physics', held in Les Houches in September 2018. Dry, aligning, dilute, active matter (DADAM), with its many adjectives, refers to a corner of the multidimensional, fast-growing field of active matter studies. This corner, however, has both historical and theoretical importance for the entire field. These lectures notes first describe this particular status of DADAM. We then provide an overview of our current knowledge of DADAM in a synthetic and coherent manner. This constitutes the bulk of these notes. For convenience, we first describe the phenomenology of simple active particle models representing the basic DADAM classes, limiting ourselves to two spatial dimensions, where most work has been performed. Then we discuss the continuous hydrodynamic theories derived from these models using the Boltzmann-Ginzburg-Landau approach. We show in particular that they are largely faithful to the microscopic level, albeit qualitatively. In the conclusion, we come back to the nodal situation of DADAM within active matter studies and provide perspectives on how one can expand DADAM knowledge into various directions, approaching more realistic and more complex situations in a controlled way.

cond-mat.stat-mech↗

arXiv2018

Deriving hydrodynamic equations from dry active matter models in three dimensions

We derive hydrodynamic equations from Vicsek-style dry active matter models in three dimensions (3D), building on our experience on the 2D case using the Boltzmann-Ginzburg-Landau approach. The hydrodynamic equations are obtained from a Boltzmann equation expressed in terms of an expansion in spherical harmonics. All their transport coefficients are given with explicit dependences on particle-level parameters. The linear stability analysis of their spatially-homogeneous solutions is presented. While the equations derived for the polar case (original Vicsek model with ferromagnetic alignment) and their solutions do not differ much from their 2D counterparts, the active nematics case exhibits remarkable differences: we find a true discontinuous transition to order with a bistability region, and cholesteric solutions whose stability we discuss.

cond-mat.soft↗