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- ItemThe double-well Bose Hubbard model with nearest-neighbor and cavity-mediated long-range interactions([Ithaca, NY] : Arxiv.org, 2023) Sicks, Johannes; Rieger, HeikoWe consider a one-dimensional Bose-Hubbard model (BHM) with on-site double-well potentials and study the effect of nearest-neighbor repulsion and cavity-mediated long-range interactions by calculating the ground-state phase diagrams with quantum Monte-Carlo simulations. We show that when the intra-well repulsion is as strong as the on-site repulsion a dimerized Mott insulator phase appears at the tip of the dimerized Density Wave phase for a density of one particle per double well. Furthermore, we find a dimerized Haldane insulator phase in the double-well BHM with nearest-neighbor interaction, which is identical to a dimerized BHM with repulsive interactions up to the third neighbor.
- ItemNon-Markovian and Collective Search Strategies([Ithaca, NY] : Arxiv.org, 2023) Meyer, Hugues; Rieger, HeikoAgents searching for a target can improve their efficiency by memorizing where they have already been searching or by cooperating with other searchers and using strategies that benefit from collective effects. This chapter reviews such concepts: non-Markovian and collective search strategies. We start with the first passage properties of continuous non-Markovian processes and then proceed to the discrete random walker with 1-step and n-step memory. Next we discuss the auto-chemotactic walker, a random walker that produces a diffusive chemotactic cue from which the walker tries to avoid. Then ensembles of agents searching for a single target are discussed, whence the search efficiency may comprise in addition to the first passage time also metabolic costs. We consider the first passage properties of ensembles of chemotactic random walkers and then the pursuit problem, in which searchers (or hunters / predators) see the mobile target over a certain distance. Evasion strategies of single or many targets are also elucidated. Finally we review collective foraging strategies comprising many searchers and many immobile targets. We finish with an outlook on future research directions comprising yet unexplored search strategies of immune cells and in swarm robotics.
- ItemStationary particle currents in sedimenting active matter wetting a wall([Ithaca, NY] : Arxiv.org, 2024) Mangeat, Matthieu; Chakraborty, Shaur; Wysocki, Adam; Rieger, HeikoRecently it was predicted, on the basis of a lattice gas model, that scalar active matter in a gravitational field would rise against gravity up a confining wall or inside a thin capillary - in spite of repulsive particle-wall interactions [Phys. Rev. Lett. 124, 048001 (2020)]. In this paper we confirm this prediction with sedimenting active Brownian particles (ABPs) in a box numerically and elucidate the mechanism leading to the formation of a meniscus rising above the bulk of the sedimentation region. The height of the meniscus increases with the activity of the system, algebraically with the Péclet number. The formation of the meniscus is determined by a stationary circular particle current, a vortex, centered at the base of the meniscus, whose size and strength increase with the ABP activity. The origin of these vortices can be traced back to the confinement of the ABPs in a box: already the stationary state of ideal (non-interacting) ABPs without gravitation displays circular currents that arrange in a highly symmetric way in the eight octants of the box. Gravitation distorts this vortex configuration downward, leaving two major vortices at the two side walls, with a strong downward flow along the walls. Repulsive interactions between the ABPs change this situation only as soon as motility induced phase separation (MIPS) sets in and forms a dense, sedimented liquid region at the bottom, which pushes the center of the vortex upwards towards the liquid-gas interface. Self-propelled particles therefore represent an impressive realization of scalar active matter that forms stationary particle currents being able to perform visible work against gravity or any other external field, which we predict to be observable experimentally in active colloids under gravitation.
- ItemSignificance of Elastic Coupling for Stresses and Leakage in Frictional Contacts([Ithaca, NY] : Arxiv.org, 2023) Müller, Christian; Müser, Martin H.; Carbone, Giuseppe; Menga, NicolaWe study how the commonly neglected coupling of normal and in-plane elastic response affects tribological properties when Hertzian or randomly rough indenters slide past an elastic body. Compressibility-induced coupling is found to substantially increase maximum tensile stresses, which cause materials to fail, and to decrease friction such that Amontons law is violated macroscopically even when it holds microscopically. Confinement-induced coupling increases friction and enlarges domains of high tension. Moreover, both types of coupling affect the gap topography and thereby leakage. Thus, coupling can be much more than a minor perturbation of a mechanical contact.
- ItemTopotaxis of Active Particles Induced by Spatially Heterogeneous Sliding along Obstacles(Ithaca, NY : Cornell University, 2023) Sadjadi, Zeinab; Rieger, HeikoMany biological active agents respond to gradients of environmental cues by redirecting their motion. Besides the well-studied prominent examples such as photo- and chemotaxis, there has been considerable recent interest in topotaxis, i.e.\ the ability to sense and follow topographic environmental cues. We numerically investigate the topotaxis of active agents moving in regular arrays of circular pillars. While a trivial topotaxis is achievable through a spatial gradient of obstacle density, here we show that imposing a gradient in the characteristics of agent-obstacle interaction can lead to an effective topotaxis in an environment with a spatially uniform density of obstacles. As a proof of concept, we demonstrate how a gradient in the angle of sliding around pillars -- as e.g.\ observed in bacterial dynamics near surfaces -- breaks the spatial symmetry and biases the direction of motion. We provide an explanation for this phenomenon based on effective reflection at the imaginary interface between pillars with different sliding angles. Our results are of technological importance for design of efficient taxis devices.
- ItemUnterschiedliche Startbedingungen von ländergemeinsamen, langfristig angelegten Bildungsprogrammen in der dritten Phase der Lehrkräftebildung am Beispiel des 10-Jahres Programms QuaMath(Hannover : Technische Informationsbibliothek, 2024) Hallemann, Svea[No abstract available]