Related papers: Microorganism Billiards
We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain ${\mathcal D} \subset {\mathbb R}^d$ until it hits the boundary and bounces randomly inside according to some reflection…
Microswimmers are exposed in nature to crowded environments and their transport properties depend in a subtle way on the interaction with obstacles. Here, we investigate a model for a single ideal circle swimmer exploring a two-dimensional…
Microswimmers typically operate in complex environments. In biological systems, often diverse species are simultaneously present and interact with each other. Here, we derive a (time-dependent) particle-scale statistical description, namely…
It is shown that nonsymmetric microobjects orient while settling under gravity in a viscous fluid. To analyze this process, a simple shape is chosen: a non-deformable `chain'. The chain consists of two straight arms, made of touching solid…
In this review, we provide a theoretical introduction to Jeffery's equations for the orientation dynamics of an axisymmetric object in a flow at low Reynolds number, and review recent theoretical extensions and applications to the motions…
Inspired by the classical Kepler and Rutherford problem, we investigate an analogous set-up in the context of active microswimmers: the behavior of a deformable microswimmer in a swirl flow. First we identify new steady bound states in the…
Swimming of microorganisms is further developed from a viewpoint of strings and membranes swimming in the incompressible fluid of low Reynolds number. In our previous paper the flagellated motion was analyzed in two dimensional fluid, by…
Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to…
Many microorganisms live and evolve in complex fluids. Examples include mammalian spermatozoa in cervical mucus, worms (e.g., \textit{C. elegans}) in wet soil, and bacteria (e.g., \textit{H. pylori}) in our stomach lining. Due to the…
We present and analyze a theoretical model for the dynamics and interactions of "capillary surfers," which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [1], we…
Biological and artificial microswimmers often self-propel in external flows of vortical nature; relevant examples include algae in small-scale ocean eddies, spermatozoa in uterine peristaltic flows and bacteria in microfluidic devices. A…
We investigate the hydrodynamic interactions between microorganisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a…
We show that a two-dimensional system of flocking microswimmers interacting hydrodynamically can be expressed using a Hamiltonian formalism. The Hamiltonian depends strictly on the angles between the particles and their swimming…
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…
A variety of swimming microorganisms, called ciliates, exploit the bending of a large number of small and densely-packed organelles, termed cilia, in order to propel themselves in a viscous fluid. We consider a spherical envelope model for…
We study dissipative polygonal outer billiards, i.e. outer billiards about convex polygons with a contractive reflection law. We prove that dissipative outer billiards about any triangle and the square are asymptotically periodic, i.e. they…
We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming…
We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case,…