Related papers: The $N$-link swimmer in three dimensions: controll…
The paper is about the parking 3-sphere swimmer ($\text{sPr}_3$). This is a low-Reynolds number model swimmer composed of three balls of equal radii. The three balls can move along three horizontal axes (supported in the same plane) that…
Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys.…
Combining geometric mechanics theory, laboratory robotic experiment and numerical simulation, we study the locomotion in granular media (GM) of the simplest non-inertial swimmer, the Purcell three-link swimmer. Using granular resistive…
Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers which is the regime of interest for micro-organisms and micro-robots. We focus on…
We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…
We propose minimal models of one-, two- and three-dimensional micro-swimmers at low Reynolds number with a periodic non-reciprocal motion. These swimmers are either "pushers" or "pullers" of fluid along the swimming axis, or combination of…
Simple, linear equations relate microscopic swimmers to the corresponding gliders and pumps. They have the following set of consequences: The swimming velocity of free swimmers can be inferred from the force on the tethered swimmer and vice…
In this paper we focus on a two-link swimmer called scallop which moves changing dynamics between two fluids regimes. We address and solve explicitly two optimal control problems, the minimum time one and the minimum quadratic cost needed…
We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body,…
A paradigmatic microswimmer is the three-linked-spheres model, which follows a minimalist approach for propulsion by shape shifting. As such, it has been the subject of numerous analytical and numerical studies. In this Rapid Communication,…
This paper formulates an optimal control problem for a system of rigid bodies that are connected by ball joints and immersed in an irrotational and incompressible fluid. The rigid bodies can translate and rotate in three-dimensional space,…
A recently introduced model for an autonomous swimmer at low Reynolds number that is comprised of three spheres connected by two arms is considered when one of the spheres has a large radius. The Stokes hydrodynamic flow associated with the…
Efficient swimming at low Reynolds numbers is a major concern of microbots. To compare the efficiencies of different swimmers we introduce the notion of ``swimming drag coefficient'' which allows for the ranking of swimmers. We find the…
We survey results of recent activity towards studying controllability and accessibility issues for equations of dynamics of incompressible fluids controlled by low-dimensional or, degenerate, forcing. New results concerning controllability…
We study the controllability of linearized shape-dependent operators for flow problems. The first operator is a mapping from the shape of the computational domain to the tangential wall velocity of the potential flow problem and the second…
We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly…
We investigate the behavior of a treadmilling microswimmer in a two-dimensional unbounded domain with a semi-infinite no-slip wall. The wall can also be regarded as a probe or pipette inserted into the flow. We solve the governing evolution…
This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…
The paper is devoted to the controllability problem for 3D compressible Euler system. The control is a finite-dimensional external force acting only on the velocity equation. We show that the velocity and density of the fluid are…
This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid. The objective is to minimize the hydrodynamic power…