Julien Tailleur
Centre national de la recherche scientifique
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Publication
Featured researches published by Julien Tailleur.
Annual Review of Condensed Matter Physics | 2015
M. E. Cates; Julien Tailleur
Self-propelled particles include both self-phoretic synthetic colloids and various microorganisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: The steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density for either biochemical or steric reasons. This creates positive feedback, which can lead to motility-induced phase separation (MIPS) between dense and dilute fluid phases. At leading order in gradients, a mapping relates variable-speed, self-propelled particles to passive particles with attractions. This deep link to equilibrium phase separation is confirmed by simulations but generally breaks down at higher order in gradients: New effects, with no equilibrium counterpart, then emerge. We give a selective overview of the fast-developing field of MIPS, focusing on theory and...
Physical Review Letters | 2015
Alexandre Solon; Joakim Stenhammar; Raphael Wittkowski; Mehran Kardar; Yariv Kafri; M. E. Cates; Julien Tailleur
We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.
Nature Physics | 2015
Alexandre Solon; Y. Fily; A. Baskaran; M. E. Cates; Yariv Kafri; Mehran Kardar; Julien Tailleur
The pressure that a fluid of self-propelled particles exerts on its container is shown to depend on microscopic interactions between fluid and container, suggesting that there is no equation of state for mechanical pressure in generic active systems.
Physical Review Letters | 2016
Étienne Fodor; Cesare Nardini; Michael Cates; Julien Tailleur; Paolo Visco; Frédéric van Wijland
Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective fluctuation-dissipation theorem akin to that of thermal equilibrium systems. Last, we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a viscoelastic bath but driven out of equilibrium by nonconservative forces, hence providing energetic insight into the departure of active systems from equilibrium.
Journal of Statistical Physics | 2011
Cristian Giardinà; Jorge Kurchan; Vivien Lecomte; Julien Tailleur
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that are responsible for intermittency in a turbulent liquid, the active regions that allow a supercooled liquid to flow…. Simulating them in an efficient, accelerated way, is in fact quite simple.In this paper we review a computational technique to study such rare events in both stochastic and Hamiltonian systems. The method is based on the evolution of a family of copies of the system which are replicated or killed in such a way as to favor the realization of the atypical trajectories. We illustrate this with various examples.
Journal of Statistical Mechanics: Theory and Experiment | 2007
Vivien Lecomte; Julien Tailleur
We present an algorithm to evaluate large deviation functions associated to history-dependent observables. Instead of relying on a time discretization procedure to approximate the dynamics, we provide a direct continuous-time algorithm valuable for systems with multiple timescales, thus extending the work of Giardina, Kurchan and Peliti (2006 Phys. Rev. Lett. 96 120603). The procedure is supplemented with a thermodynamic-integration scheme which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition—revealed in our context through the appearance of a non-analyticity in the large deviation functions.
Nature Physics | 2007
Julien Tailleur; Jorge Kurchan
In nonlinear dynamical systems, atypical trajectories often play an important role. For instance, resonances and separatrices determine the fate of planetary systems, and localized objects such as solitons and breathers provide mechanisms of energy transport in systems such as Bose–Einstein condensates and biological molecules. Unfortunately, most of the numerical methods to locate these ‘rare’ trajectories are confined to low-dimensional or toy models, whereas the realms of statistical physics, chemical reactions or astronomy are still hard to reach. Here we implement an efficient method that enables us to work in higher dimensions by selecting trajectories with unusual chaoticity. As an example, we study the Fermi–Pasta–Ulam nonlinear chain in equilibrium and show that the algorithm rapidly singles out the soliton solutions when searching for trajectories with low levels of chaoticity, and chaotic breathers in the opposite situation. We expect the scheme to have natural applications in celestial mechanics and turbulence, where it can readily be combined with existing numerical methods.
European Physical Journal-special Topics | 2015
Alexandre Solon; M. E. Cates; Julien Tailleur
Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed v along a body-axis u that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along u becomes v(ρ) < v. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed v that is an explicit function or functional of the density ρ. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.
Physical Review Letters | 2015
Alexandre Solon; Hugues Chaté; Julien Tailleur
We show that the flocking transition in the Vicsek model is best understood as a liquid-gas transition, rather than an order-disorder one. The full phase separation observed in flocking models with Z(2) rotational symmetry is, however, replaced by a microphase separation leading to a smectic arrangement of traveling ordered bands. Remarkably, continuous deterministic descriptions do not account for this difference, which is only recovered at the fluctuating hydrodynamics level. Scalar and vectorial order parameters indeed produce different types of number fluctuations, which we show to be essential in selecting the inhomogeneous patterns. This highlights an unexpected role of fluctuations in the selection of flock shapes.
Journal of Statistical Physics | 2006
Julien Tailleur; Sorin Tănase-Nicola; Jorge Kurchan
Hamilton’s equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories in an elementary way. From a more practical point of view, the formalism provides new tools to study the reaction paths in systems with separated time scales. A ‘reduced current’ which contains the relevant part of the phase space probability current is introduced, together with strategies for its computation.