Elia Bronzo & Arthur Plaud

- Elia Bronzo : Repulsion in minimal models for self-propelled rods: from microscopic model to continuum theories

Self-propelled elongated objects abound in nature, notably in the form of swimming or gliding bacteria, and their study occupies a prominent place in Active Matter Physics. Explicit rod-based models require exploring a large parameter space while often remaining strongly dependent on the specific implementation. Such models are also characterized by high computational cost and analytical complexity, which may limit our understanding of the many phases they exhibit. In this presentation, I will discuss an alternative approach consisting of particles that are circular and therefore easier to study with effective interactions that mimic the effects of collisions between elongated objects. I will present the effect of different types of repulsive interactions added to the nematic Vicsek model which consists only in point-like aligning self-propelled particles. Their impact will be analyzed both at the level of microscopic simulations and through continuum theories derived from these models using the Boltzmann–Ginzburg–Landau (BGL) approach.

- Arthur Plaud : Universal fluctuations in competitive exploration

Random exploration has so far been quantified mainly through observables that measure how fast new space is found collectively. In competitive exploration however, when foragers compete for food items or agents capture distributed targets, rewards are tied to first arrival. This collective description of exploration is thus no longer enough: one must also ask how first discoveries are divided between competitors. For this purpose, we introduce the discovery share measuring the fraction of the first n collective discoveries secured by a tagged searcher among two competitors, and show that its fluctuations obey a universal theory. Across transport processes ranging from ordinary diffusion to superdiffusion driven by long-range relocations and subdiffusion induced by geometry or memory, these fluctuations are governed by a single parameter dₛ called the spectral dimension, describing the return probability at the origin of a single searcher. This yields three regimes for the discovery share: persistent randomness in recurrent exploration when dₛ < 2, anomalously slow non-Gaussian concentration towards equal splitting for 2<dₛ<3, and Gaussian concentration for dₛ>3. In the asymptotically equal case dₛ>2, we obtain the variance exactly at leading order including prefactors. In the recurrent case while a general theory is absent, we focus on 1-dimensional Brownian motion and characterize fluctuations of the discovery share in the infinite time limit, both for one-sided exploration where sites are only discovered in one direction and in the general two-sided case. More broadly, the same phase structure persists under changes in geometry, competitor heterogeneity, number of competitors and memory, revealing a general fluctuation theory for how competitive inequalities persist or fade in exploration.