No abstract

While active systems possess notable potential to form the foundation of new classes of autonomous materials, designing systems that can extract functional work from active surroundings has proven challenging. In this work, we extend these efforts to the realm of designed active liquid crystal/colloidal composites. We propose suspending colloidal particles with Janus anchoring conditions in an active nematic medium. These passive Janus particles become effectively self-propelled once immersed into an active nematic bath. The self-propulsion of passive Janus particles arises from the effective +1/2 topological charge their surface enforces on the surrounding active fluid. We analytically study their dynamics and the orientational dependence on the position of a companion −1/2 defect. We predict that at sufficiently small activity, the colloid and companion defect remain bound to each other, with the defect strongly orienting the colloid to propel either parallel or perpendicular to the nematic. At sufficiently high activity, we predict an unbinding of the colloid/defect pair. This work demonstrates how suspending engineered colloids in active liquid crystals may present a path to extracting activity to drive functionality.

The purpose of this manuscript is to present a series of lecture notes on isoperimetric inequalities for the Laplacian, for the Schrödinger operator, and related problems.

No abstract

Systems composed of strongly interacting self-propelled particles can form a spontaneously flowing polar active fluid. The study of the connection between the microscopic dynamics of a single such particle and the macroscopic dynamics of the fluid can yield insights into experimentally realizable active flows, but this connection is well understood in only a few select cases. We introduce a model of self-propelled particles based on an analogy with the motion of electrons that have strong spin-orbit coupling. We find that, within our model, self-propelled particles are subject to an analog of the Heisenberg uncertainty principle that relates translational and rotational noise. Furthermore, by coarse-graining this microscopic model, we establish expressions for the coefficients of the Toner-Tu equations-the hydrodynamic equations that describe an active fluid composed of these 'active spins.' The connection between stochastic self-propelled particles and quantum particles with spin may help realize exotic phases of matter using active fluids via analogies with systems composed of strongly correlated electrons.Active liquids exhibit striking phenomena due to the unusual nature of their hydrodynamics [1]. Such phenomena have been observed in naturally occurring collections of live animals [2-4] and cells [5-9], as well as synthetically prepared systems of granules [10, 11], robots [12], colloids [13][14][15], and molecules [16][17][18][19].Coarse-grained descriptions that capture these phenomena may be either constructed based solely on symmetry and lengthscale considerations or derived from simple particle-based models [15,[20][21][22]. A crucial advantage of the latter, microscopic, approach is that it connects the hydrodynamic coefficients (such as viscosity, diffusivity, and compressibility) to the microscopic parameters of the model. In experimental realizations of active fluids, this connection between microscopics and hydrodynamics can be used to construct design principles for the realization of novel materials and devices. For example, recent work has focused on the robustness of active liquids against disorder [23], the design of flow patterns in confined active fluids [24-28], and the use of such channel networks for the design of topological metamaterials [29] and logic gates [30].In this work, we introduce a minimal model of self-propelled particles, and we explore their individual and collective statistical dynamics in order to arrive at a hydrodynamic description. The motivation for the model we consider comes from an analogy between the stochastic classical dynamics of self-propelled particles and the Schrödinger equation describing the dynamics of quantum particles. Our goal is to use well-known results from quantum mechanics to develop physical intuition for both individual self-propelled particles and many-particle active fluids. For example, we describe active-fluid analogs of such well-known quantum-mechanical concepts as spin, spin-orbit coupling, and the Heisenberg uncertainty principle. We di...