103 research outputs found

### Purcell magneto-elastic swimmer controlled by an external magnetic field

International audienceThis paper focuses on the mechanism of propulsion of a Purcell swimmer whose segments are magnetized and react to an external magnetic field applied into the fluid. By an asymptotic analysis, we prove that it is possible to steer the swimmer along a chosen direction when the control functions are prescribed as an oscillating field. Moreover, we discuss what are the main obstructions to overcome in order to get classical controllability result for this system

### Three-sphere low-Reynolds-number swimmer with a passive elastic arm

One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer\u2019s geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers

### Modeling and steering magneto-elastic micro-swimmers inspired by the motility of sperm cells

Controlling artificial devices that mimic the motion of real microorganisms, is attracting increasing interest, both from the mathematical point of view and applications. A model for a magnetically driven slender micro-swimmer, mimicking a sperm cell is presented, supported by two examples showing how to steer it. Using the Resistive Force Theory (RTF) approach [J. Gray and J. Hancock, J. Exp. Biol. 32, 802 (1955)] to describe the hydrodynamic forces, the micro-swimmer can be described by a driftless affine control system where the control is an external magnetic field. Moreover we discuss through at first an asymptotic analysis and then by numerical simulations how to realize different kinds of paths

### Homogenization of a model for the propagation of sound in the lungs

International audienceIn this paper, we are interested in the mathematical modeling of the propagation of sound waves in the lung parenchyma, which is a foam-like elastic material containing millions of air-filled alveoli. In this study, the parenchyma is governed by the linearized elasticity equations, and the air by the acoustic wave equations. The geometric arrangement of the alveoli is assumed to be periodic with a small period Î” > 0. We consider the time-harmonic regime forced by vibrations induced by volumic forces. We use the two-scale convergence theory to study the asymptotic behavior as Î” goes to zero and prove the convergence of the solutions of the coupled fluid-structure problem to the solution of a linear-elasticity boundary value problem

### On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability

In this paper we investigate the role of Parodi's relation in the
well-posedness and stability of the general Ericksen-Leslie system modeling
nematic liquid crystal flows. First, we give a formal physical derivation of
the Ericksen-Leslie system through an appropriate energy variational approach
under Parodi's relation, in which we can distinguish the
conservative/dissipative parts of the induced elastic stress. Next, we prove
global well-posedness and long-time behavior of the Ericksen-Leslie system
under the assumption that the viscosity $\mu_4$ is sufficiently large. Finally,
under Parodi's relation, we show the global well-posedness and Lyapunov
stability for the Ericksen-Leslie system near local energy minimizers. The
connection between Parodi's relation and linear stability of the
Ericksen-Leslie system is also discussed

### A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO(n)

In this paper we consider an energy functional depending on the norm of the gradient and seek to extremise it over an admissible class of Sobolev maps defined on an annulus and taking values on the unit sphere whilst satisfying suitable boundary conditions. We establish the existence of an infinite family of solutions with certain symmetries to the associated nonlinear Euler-Lagrange system in even dimensions and discuss the stability of such extremisers by way of examining the positivity of the second variation of the energy at these solutions

### The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to
modern results- of the problem of rolling two Riemannian manifolds one on the
other, with the restrictions that they cannot instantaneously slip or spin one
with respect to the other. On the way we show how this problem has profited
from the development of intrinsic Riemannian geometry, from geometric control
theory and sub-Riemannian geometry. We also mention how other areas -such as
robotics and interpolation theory- have employed the rolling model.Comment: 20 page

### Topological Defects in Nematic Droplets of Hard Spherocylinders

Using computer simulations we investigate the microscopic structure of the
singular director field within a nematic droplet. As a theoretical model for
nematic liquid crystals we take hard spherocylinders. To induce an overall
topological charge, the particles are either confined to a two-dimensional
circular cavity with homeotropic boundary or to the surface of a
three-dimensional sphere. Both systems exhibit half-integer topological point
defects. The isotropic defect core has a radius of the order of one particle
length and is surrounded by free-standing density oscillations. The effective
interaction between two defects is investigated. All results should be
experimentally observable in thin sheets of colloidal liquid crystals.Comment: 13 pages, 16 figures, Phys. Rev.

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