Auswahl der wissenschaftlichen Literatur zum Thema „Run-And-Tumble particles“

We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker–Planck equations in one space dimension, we derive some known exact results in simple physical situations (free run-and-tumble particles and harmonic confinement). We then extend the calculation to the case of anisotropic motion (different speeds and tumbling rates for right- and left-oriented particles), obtaining exact expressions of the entropy production rate. We conclude by discussing the general case of heterogeneous run-and-tumble motion described by space-dependent parameters and extending the analysis to the case of d-dimensional motions.

We study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein-Uhlenbeck process. We also consider an interacting case, where the particles are subjected to exclusion. We then study the fluctuations of the total density, which is a non-Markovian Gaussian process, and obtain its covariance in closed form. By considering small noise limits of this non-Markovian Gaussian process, we obtain in a concrete example a large deviation rate function containing memory terms.

Cette thèse étudie le comportement en temps long des particules run-and-tumble (RTPs), un modèle pour les bactéries en physique statistique hors équilibre, en utilisant des processus de Markov déterministes par morceaux (PDMPs). La motivation est d'améliorer la compréhension au niveau particulaire des phénomènes actifs, en particulier la séparation de phase induite par la motilité (MIPS). La mesure invariante pour deux RTPs avec jamming sur un tore 1D est déterminée pour mécanismes de tumble et jamming généraux, révélant deux classes d'universalité hors équilibre. De plus, la dépendance du temps de mélange en fonction des paramètres du modèle est déterminée en utilisant des techniques de couplage et le modèle continu PDMP est rigoureusement relié à un modèle sur réseau connu. Dans le cas de deux RTPs avec jamming sur la droite réelle et interagissant à travers un potentiel attractif, la mesure invariante présente des différences qualitatives en fonction des paramètres du modèle, rappelant des transitions de forme et des classes d'universalité. Des taux de convergence fins sont à nouveau obtenus par des techniques de couplage. Par ailleurs, la mesure invariante explicite de trois RTPs se bloquant sur le tore 1D est calculée. Enfin, les résultats de convergence hypocoercive sont étendus aux RTPs, obtenant ainsi des taux de convergence \( L^2 \) fins dans un cadre général qui couvre également les PDMPs utilisés pour l'échantillonnage et Langevin cinétique
This thesis investigates the long-time behavior of run-and-tumble particles (RTPs), a model for bacteria's moves and interactions in out-of-equilibrium statistical mechanics, using piecewise deterministic Markov processes (PDMPs). The motivation is to improve the particle-level understanding of active phenomena, in particular motility induced phase separation (MIPS). The invariant measure for two jamming RTPs on a 1D torus is determined for general tumbling and jamming, revealing two out-of-equilibrium universality classes. Furthermore, the dependence of the mixing time on model parameters is established using coupling techniques and the continuous PDMP model is rigorously linked to a known on-lattice model. In the case of two jamming RTPs on the real line interacting through an attractive potential, the invariant measure displays qualitative differences based on model parameters, reminiscent of shape transitions and universality classes. Sharp quantitative convergence bounds are again obtained through coupling techniques. Additionally, the explicit invariant measure of three jamming RTPs on the 1D torus is computed. Finally, hypocoercive convergence results are extended to RTPs, achieving sharp \( L^2 \) convergence rates in a general setting that also covers kinetic Langevin and sampling PDMPs

Abstract Active fluids refer to the fluids that contain self-propelled particles such as bacteria or micro-algae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion; with high-motility “run” periods separated by low-motility “tumble” periods. The average motion can be modified with external stresses, such as nutrient or light gradient, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp.PCC 6803, a model micro-organism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and non-isotropic conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical time of about 1 hour, when initial probability is recovered. Our results are well described by a model based on the linear response theory. When the perturbation is anisotropic, the characteristic time of runs is longer whatever the direction, similar to what is observed with isotropic conditions. Yet we observe a collective motion toward the light source (phototaxis) and show that the bias emerges because of more frequent runs towards the light.