Motility-induced clustering and meso-scale turbulence in active polar fluids

Meso-scale turbulence was originally observed experimentally in various suspensions of swimming bacteria, as well as in the collective motion of active colloids. The corresponding large scale dynamical patterns were reproduced in a simple model of a polar fluid, assuming a constant density of active particles. Recent, more detailed studies in a variety of experimental realizations of active polar fluids revealed additional interesting aspects, such as anomalous velocity statistics and clustering phenomena. Those phenomena cannot be explained by currently available models for active polar fluids. Herein, we extend the continuum model suggested by Dunkel et al to include density variations and a local feedback between the local density and self-propulsion speed of the active polar particles. If the velocity decreases strong enough with the density, a linear stability analysis of the resulting model shows that, in addition to the short-wavelength instability of the original model, a long-wavelength instability occurs. This is typically observed for high densities of polar active particles and is analogous to the well-known phenomenon of motility-induced phase separation (MIPS) in scalar active matter. We determine a simple phase diagram indicating the linear instabilities and perform systematic numerical simulations for the various regions in the corresponding parameter space. The interplay between the well understood short-range instability (leading to meso-scale turbulence) and the long-range instability (associated with MIPS) leads to interesting dynamics and novel phenomena concerning nucleation and coarsening processes. Our simulation results display a rich variety of novel patterns, including phase separation into domains with dynamically changing irregularly shaped boundaries. Anomalous velocity statistics are observed in all phases where the system segregates into regions of high and low densities. This offers a simple explanation for their occurrence in recent experiments with bacterial suspensions.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Statistical Analysis of Spherical Harmonics Representations of Soil Particles

RÉSUMÉ :Grâce aux avancées en micro-tomographie par rayons-X, il est désormais possible d’obtenir des représentations en 3D haute résolution de milliers de particules échantillonnées depuis diverses sources géologiques. La représentation plus précise des particules pourrait éventuellement permettre d’obtenir des simulations numériques plus fidèles des comportements de matériaux granulaires par la méthode des éléments discrets (DEM, Discrete Element Method en anglais). Cependant, l’accès à des descriptions fines demande aussi de développer de nouveaux outils numériques pour la caractérisation géométrique et l’analyse statistique d’ensembles de particules. Ce mémoire se concentre sur la modélisation géométrique des particules de sol par la représentation de leur surface à l’aide de la décomposition en harmoniques sphériques. Plus précisément, nous discutons de l’utilisation des représentations en harmoniques sphériques pour développer un modèle statistique permettant de générer des assemblages virtuels de particules à partir des données de plusieurs centaines de grains. La haute dimension de tels ensembles de données a longtemps été une complication majeure, mais avec les récentes avancées en apprentissage automatique dans l’analyse des mégadonnées, il y a espoir que ces nouveaux algorithmes puissent surmonter cette limitation.----------ABSTRACT : Advancements in X-ray micro-computed tomography allow one to obtain high resolution 3D representations of particles collected from multiple geological sources. The representational power enabled by this new technology could allow for more accurate numerical simulations of granular materials using the celebrated Discrete Element Method (DEM). However, access to realistic representations of particles requires the development of more advanced geometrical and statistical characterization techniques. This thesis focuses on the use of the Spherical Harmonics decomposition of soil particles to model the surface of the particles. More precisely, we discuss the application of the Spherical Harmonics decomposition of particles to develop generative models of virtual assemblies that are calibrated based on datasets made of hundreds of grains. For long, the high dimensionality of the data has been a major challenge to the developpement of such statistical models. However, with recent advances of machine learning algorithms in the context of Big Data, there is hope that these new techniques can be utilized to overcome this limitation and obtain very accurate generative models of assemblies