Chemotactic particles as strong electrolytes: Debye-Hückel approximation and effective mobility law.

We consider a binary mixture of chemically active particles that produce or consume solute molecules and that interact with each other through the long-range concentration fields they generate. We analytically calculate the effective phoretic mobility of these particles when the mixture is submitted to a constant, external concentration gradient, at leading order in the overall concentration. Relying on an analogy with the modeling of strong electrolytes, we show that the effective phoretic mobility decays with the square root of the concentration: our result is, therefore, a nonequilibrium counterpart to the celebrated Kohlrausch and Debye-Hückel-Onsager conductivity laws for electrolytes, which are extended here to particles with long-range nonreciprocal interactions.

From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics.

Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the correlation between a generic observable and the density of particles at a given position and time. They have recently been shown to play a central role in single-file systems.

Enhanced diffusion of tracer particles in nonreciprocal mixtures.

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles.

Isotropic active colloids: explicit implicit descriptions of propulsion mechanisms.

Modeling the couplings between active particles often neglects the possible many-body effects that control the propulsion mechanism. Accounting for such effects requires the explicit modeling of the molecular details at the origin of activity. Here, we take advantage of a recent two-dimensional model of isotropic active particles whose propulsion originates from the interactions between solute particles in the bath.

On analytical theories for conductivity and self-diffusion in concentrated electrolytes.

Describing analytically the transport properties of electrolytes, such as their conductivity or the self-diffusion of the ions, has been a central challenge of chemical physics for almost a century. In recent years, this question has regained some interest in light of Stochastic Density Field Theory (SDFT) - an analytical framework that allows the approximate determination of density correlations in fluctuating systems. In spite of the success of this theory to describe dilute electrolytes, its extension to concentrated solutions raises a number of technical difficulties, and requires simplified descriptions of the short-range repulsion between the ions.

Absolute Negative Mobility of an Active Tracer in a Crowded Environment.

Absolute negative mobility (ANM) refers to the situation where the average velocity of a driven tracer is opposite to the direction of the driving force. This effect was evidenced in different models of nonequilibrium transport in complex environments, whose description remains effective. Here, we provide a microscopic theory for this phenomenon.

Exact spatial correlations in single-file diffusion.

Single-file diffusion refers to the motion of diffusive particles in narrow channels, so that they cannot bypass each other. This constraint leads to the subdiffusion of a tagged particle, called the tracer. This anomalous behavior results from the strong correlations that arise in this geometry between the tracer and the surrounding bath particles.

Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond.

Tracer dynamics in the symmetric exclusion process (SEP), where hard-core particles diffuse on an infinite one-dimensional lattice, is a paradigmatic model of anomalous diffusion. While the equilibrium situation has received a lot of attention, the case where the tracer is driven by an external force, which provides a minimal model of nonequilibrium transport in confined crowded environments, remains largely unexplored. Indeed, the only available analytical results concern the means of both the position of the tracer and the lattice occupation numbers in its frame of reference and higher-order moments but only in the high-density limit.

Diffusion of a tracer in a dense mixture of soft particles connected to different thermostats.

We study the dynamics of a tracer in a dense mixture of particles connected to different thermostats. Starting from the overdamped Langevin equations that describe the evolution of the system, we derive the expression of the self-diffusion coefficient of a tagged particle in the suspension, in the limit of soft interactions between the particles. Our derivation, which relies on the linearization of the Dean-Kawasaki equations obeyed by the density fields and on a path-integral representation of the dynamics of the tracer, extends previous derivations that held for tracers in contact with a single bath.

Conditions for the propulsion of a colloid surrounded by a mesoscale phase separation.

We study a two-dimensional model of an active isotropic colloid whose propulsion is linked to the interactions between solute particles of the bath. The colloid catalyzes a chemical reaction in its vicinity, that yields a local phase separation of solute particles. The density fluctuations of solute particles result in the enhanced diffusion of the colloid.

Exact time dependence of the cumulants of a tracer position in a dense lattice gas.

We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant-generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position, a regime in which few results are known.

Exact closure and solution for spatial correlations in single-file diffusion.

In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension.

Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment.

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system.

Generalized Correlation Profiles in Single-File Systems.

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other, and leads to tracer subdiffusion. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only. Here, we go beyond this standard description by introducing and providing analytical results for generalized correlation profiles (GCPs) in the frame of the tracer.

Synchronization and Enhanced Catalysis of Mechanically Coupled Enzymes.

We examine the stochastic dynamics of two enzymes that are mechanically coupled to each other, e.g., through an elastic substrate or a fluid medium.

Spontaneous propulsion of an isotropic colloid in a phase-separating environment.

The motion of active colloids is generally achieved through their anisotropy, as exemplified by Janus colloids. Recently, there was a growing interest in the propulsion of isotropic colloids, which requires some local symmetry breaking. Although several mechanisms for such propulsion were proposed, little is known about the role played by the interactions within the environment of the colloid, which can have a dramatic effect on its propulsion.

Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes.

The symmetric exclusion process (SEP), where particles hop on a one-dimensional lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions-annealed or quenched-has a quantitative impact on the long-time properties of tracer diffusion. However, so far, the cumulant generating function in the quenched case was only determined in the low-density limit and for the specific case of a half-filled system.

Speed-dispersion-induced alignment: A one-dimensional model inspired by swimming droplets experiments.

We investigate the collective dynamics of self-propelled droplets, confined in a one-dimensional microfluidic channel. On the one hand, neighboring droplets align and form large trains of droplets moving in the same direction. On the other hand, the droplets condensate, leaving large regions with very low density.

Cooperatively enhanced reactivity and "stabilitaxis" of dissociating oligomeric proteins.

Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer on them a functional advantage with respect to nondissociating proteins.

Experimental observation of flow fields around active Janus spheres.

The phoretic mechanisms at stake in the propulsion of asymmetric colloids have been the subject of debates during the past years. In particular, the importance of electrokinetic effects on the motility of Pt-PS Janus sphere was recently discussed. Here, we probe the hydrodynamic flow field around a catalytically active colloid using particle tracking velocimetry both in the freely swimming state and when kept stationary with an external force.

Fluctuation-induced hydrodynamic coupling in an asymmetric, anisotropic dumbbell.

We recently introduced a model of an asymmetric dumbbell made of two hydrodynamically coupled subunits as a minimal model for a macromolecular complex, in order to explain the observation of enhanced diffusion of catalytically active enzymes. It was shown that internal fluctuations lead to a negative contribution to the overall diffusion coefficient and that the fluctuation-induced contribution is controlled by the strength of the interactions between the subunits and their asymmetry. We develop the model by studying the effect of anisotropy on the diffusion properties of a modular structure.

Enhanced Diffusion and Chemotaxis at the Nanoscale.

Enzymes have been recently proposed to have mechanical activity associated with their chemical activity. In a number of recent studies, it has been reported that enzymes undergo enhanced diffusion in the presence of their corresponding substrate when this substrate is uniformly distributed in solution. Moreover, if the concentration of the substrate is nonuniform, enzymes and other small molecules have been reported to show chemotaxis (biased stochastic movement in the direction of the substrate gradient), typically toward higher concentrations of this substrate, with a few exceptions.