1,954 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
Modulated phases of a 1D sharp interface model in a magnetic field
We investigate the ground states of 1D continuum models having short-range
ferromagnetic type interactions and a wide class of competing longer-range
antiferromagnetic type interactions. The model is defined in terms of an energy
functional, which can be thought of as the Hamiltonian of a coarse-grained
microscopic system or as a mesoscopic free energy functional describing various
materials. We prove that the ground state is simple periodic whatever the
prescribed total magnetization might be. Previous studies of this model of
frustrated systems assumed this simple periodicity but, as in many examples in
condensed matter physics, it is neither obvious nor always true that ground
states do not have a more complicated, or even chaotic structure.Comment: 12 pages, 3 figure
Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations
We discuss a numerical formulation for the cell problem related to a homogenization
approach for the study of wetting on micro rough surfaces. Regularity properties of the solution are
described in details and it is shown that the problem is a convex one. Stability of the solution with
respect to small changes of the cell bottom surface allows for an estimate of the numerical error, at least
in two dimensions. Several benchmark experiments are presented and the reliability of the numerical
solution is assessed, whenever possible, by comparison with analytical one. Realistic three dimensional
simulations confirm several interesting features of the solution, improving the classical models of study
of wetting on roughness
Reverse engineering the euglenoid movement
Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics
Checkerboards, stripes and corner energies in spin models with competing interactions
We study the zero temperature phase diagram of Ising spin systems in two
dimensions in the presence of competing interactions, long range
antiferromagnetic and nearest neighbor ferromagnetic of strength J. We first
introduce the notion of a "corner energy" which shows, when the
antiferromagnetic interaction decays faster than the fourth power of the
distance, that a striped state is favored with respect to a checkerboard state
when J is close to J_c, the transition to the ferromagnetic state, i.e., when
the length scales of the uniformly magnetized domains become large. Next, we
perform detailed analytic computations on the energies of the striped and
checkerboard states in the cases of antiferromagnetic interactions with
exponential decay and with power law decay r^{-p}, p>2, that depend on the
Manhattan distance instead of the Euclidean distance. We prove that the striped
phase is always favored compared to the checkerboard phase when the scale of
the ground state structure is very large. This happens for J\lesssim J_c if
p>3, and for J sufficiently large if 2<p<=3. Many of our considerations
involving rigorous bounds carry over to dimensions greater than two and to more
general short-range ferromagnetic interactions.Comment: 21 pages, 3 figure
Uniaxial and biaxial soft deformations of nematic elastomers
We give a geometric interpretation of the soft elastic deformation modes of
nematic elastomers, with explicit examples, for both uniaxial and biaxial
nematic order. We show the importance of body rotations in this non-classical
elasticity and how the invariance under rotations of the reference and target
states gives soft elasticity (the Golubovic and Lubensky theorem). The role of
rotations makes the Polar Decomposition Theorem vital for decomposing general
deformations into body rotations and symmetric strains. The role of the square
roots of tensors is discussed in this context and that of finding explicit
forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe
Dynamics of domain walls in magnetic nanostrips
We express dynamics of domain walls in ferromagnetic nanowires in terms of
collective coordinates generalizing Thiele's steady-state results. For weak
external perturbations the dynamics is dominated by a few soft modes. The
general approach is illustrated on the example of a vortex wall relevant to
recent experiments with flat nanowires. A two-mode approximation gives a
quantitatively accurate description of both the steady viscous motion of the
wall in weak magnetic fields and its oscillatory behavior in moderately high
fields above the Walker breakdown.Comment: 4 pages, update to published versio
- …