Fernando Peruani (LPTM, Cergy Paris Université)

Cluster formation, order, and aggregation in Active Matter

Active matter is strongly based on idealized models and processes. The underlying assumption is that, as in equilibrium, “universality classes” depend only on the symmetry and range of the interactions, as well as on the presence or absence of conserved quantities. For example, the emergence of polar order is explained assuming the existence of a short-range velocity alignment mechanism, which is believed to lead generically to active polar fluids that fall into the Toner-Tu class. Similarly, phase separation in active systems is usually rationalized in the context of short-range repulsive active Brownian particles that fall into the mobility-induced phase separation (MIPS) class. However, it can be argued that in general the emergence of order and phase separation are closely interconnected in several active systems. For instance, in self-propelled rods the emergence of (local) polar order precludes MIPS and leads to a phase separation process that exhibits statistical features that are different from those reported in MIPS. Similarly, active particles with non-reciprocal attractive interactions phase separate via a distinct process, inconsistent with MIPS, into high-density structures displaying either polar, neutral, or nematic order depending on noise value and the non-reciprocity parameter. We will also see that it is possible to conceive a model that exhibits short-range polar velocity alignment and short-range attraction and repulsion, where particle aggregation and emergence of order are intrinsically interconnected, that displays a novel type of phase transition to polar order fundamentally different to the one observed in the Vicsek model and inconsistent with Toner-Tu ordered phase.

Hugues Meyer (Theoretical Physics department, Saarland University, Germany)

Optimizing search strategies with memory: general results and application to autochemotactic walkers

The term search process refers to any process in which agents are looking for targets in a well-defined domain. This general definition encompasses a broad scope of phenomena, from foraging in animal species to the search of toxic bodies by immune cells. In most cases, the searching agents need to optimize their strategy in order to maximize the search efficiency, often quantified in terms of first-passage times in statistical physics. In this talk, we will discuss how a search can be optimized if the agents have memory of the locations they have previously visited. This question can be formalized and solved in general terms in order to infer the very optimal strategy for a searcher with a given memory time and to define a lower bound for the mean first-passage time. We will then discuss the concrete case of autochemotactic particles, i.e. agents that generate a self-repeling chemical cue. This phenomenon is for instance observed in ants looking for food, or in some immune cells searching for organisms to eliminate. The chemical information that they produce can be effectively used as a way to memorize the previously visited locations and as a non-local communication channel between particles. For such systems, we will first evaluate how search efficiency can be optimized in the low density regime, and how it compares to the theoretically optimal efficiency. Then, we will show how the search process is impacted as the density of searchers increases. While one might intuitively think that search should be more efficient with more searchers, the formation of bands under certain conditions can make it particularly inefficient. We will discuss the mechanism and conditions for such bands to form.

Thomas Franosch (Institut für Theoretische Physik, Universität Innsbruck, Austria)

Gravitaxis of a single active particle

The active Brownian particle (ABP) model has become a paradigm for dynamics far from equilibrium and has attracted considerable attention in the statistical-physics/soft-matter community [1,2]. In this model particles undergo directed motion along their axis of orientation which is subject to orientational diffusion. While it is rather easy to simulate the dynamics of such agents in a prescribed potential landscape, analytical progress even for the simplest set-ups has been difficult. Here I present an exact solution for the dynamics of active Brownian particle in a uniform gravitational field as described by the equations of motion of Ref. [3]. We show that the problem maps to the noisy overdamped pendulum or dynamics in a tilted washboard potential. Close to the underlying classical bifurction we unravel a resonance for the diffusion coefficient. We derive the corresponding Fokker-Planck equation and use techniques familiar from quantum mechanics to provide a complete solution. The scaling behavior at the resonance is rationalized in terms of a simple harmonic oscillator picture.

[1] C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).

[2] C. Kurzthaler, C. Devailly, J. Arlt, T. Franosch, W. C. K. Poon, V. A. Martinez, and A. T. Brown, Probing the spatiotemporal dynamics of catalytic janus particles with single-particle tracking and differential dynamic microscopy, Physical Review Letters 121, 078001 (2018).

[3] B. ten Hagen, F. Kümmel, R. Wittkowski, D. Takagi, H. Löwen, and C. Bechinger, Gravitaxis of asymmetric self-propelled colloidal particles, Nature Communications 5, 4829 (2014).

Kirill Polovnikov (LPTMS (visitor), Skoltech & Laboratoire Poncelet)

Constrained fractal polymer chain in curved geometry: how far is KPZ?

Can intrinsic curvature of the space yield a similar regime of fluctuations as a certain type of random potentials? In this talk by means of scaling analyses of the free energy and computer simulations I will discuss stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. The typical excursions of the polymer away from the surface scale as \Delta \sim R^{\beta}, with the Kardar-Parisi-Zhang (KPZ) growth exponent \beta=1/3 and the curvature-induced correlation length is described by the KPZ exponent z=3/2. Remarkably, the uncovered KPZ scaling is independent of the fractal dimension of the polymer and, thus, is universal across the classical polymer models, e.g. SAW, randomly-branching polymers, crumpled unknotted rings. The one-point distribution of fluctuations, as found in simulations, can be well described by the squared Airy law, connecting our 2D polymer problem with the (1+1)D Ferrari-Spohn universality class of constrained random walks. A relation between directed polymers in quenched random potential (KPZ) and stretched polymers above the semicircle will be explained.