Condensed Matter Theory

Abstract:

The energy dissipation and entropy production by self-propelled microswimmers differ profoundly from passive particles pulled by external forces. The difference extends both to the shape of the flow around the swimmer, as well as to the internal dissipation of the propulsion mechanism. Here we derive a general theorem that provides an exact lower bound on the total, external and internal, dissipation by a microswimmer. The problems that can be solved include an active surface-propelled droplet, swimmers with an extended propulsive layer and swimmers with an effective internal dissipation. We apply the theorem to determine the swimmer shapes that minimize the total dissipation while keeping the volume constant. Our results show that the entropy production by active microswimmers is subject to different fundamental limits than the entropy production by externally driven particles.Comment: 16 pages, 6 figure

Abstract:

Particles that are catalytically-active and chemotactic can interact through the concentration fields upon which they act, which in turn may lead to wide-scale spatial self-organization. When these active particles interact through several fields, these interactions gain an additional structure, which can result in new forms of collective behavior. Here, we study a mixture of active species which catalyze the conversion of a substrate chemical into a product chemical, and chemotax in concentration gradients of both substrate and product. Such species develop non-reciprocal, specific interactions that we coarse-grain into attractive and repulsive, which can lead to a potentially complex interaction network. We consider the particular case of a metabolic cycle of three species, each of which interacts with itself and both other species in the cycle. We find that the stability of a cycle of species that only chemotax in gradients of their substrate is piloted by a set of two parameter-free conditions, which we use to classify the low number of corresponding interaction networks. In the more general case of substrate- and product-chemotactic species, we can derive a set of two high-dimensional stability conditions, which can be used to classify the stability of all the possible interaction networks based on the self- and pair-interaction motifs they contain. The classification scheme that we introduce can help guide future studies on the dynamics of complex interaction networks and explorations of the corresponding large parameter spaces in such metabolically active complex systems