68 research outputs found
Collective beating of artificial microcilia
We combine technical, experimental and theoretical efforts to investigate the
collective dynamics of artificial microcilia in a viscous fluid. We take
advantage of soft-lithography and colloidal self-assembly to devise microcapets
made of hundreds of slender magnetic rods. This novel experimental setup is
used to investigate the dynamics of extended cilia arrays driven by a
precessing magnetic field. Whereas the dynamics of an isolated cilium is a
rigid body rotation, collective beating results in a symmetry breaking of the
precession patterns. The trajectories of the cilia are anisotropic and
experience a significant structural evolution as the actuation frequency
increases. We present a minimal model to account for our experimental findings
and demonstrate how the global geometry of the array imposes the shape of the
trajectories via long range hydrodynamic interactions.Comment: 5 pages, 3 figure
Rotational dynamics of a soft filament: wrapping transition and propulsive forces
We analyze experimentally the shape of a long elastic filament rotating in a
viscous liquid. We identify a continuous but sharp transition from a straight
to an helical shape, resulting from the competition between viscous stresses
and elastic forces. This induced helicity generates a propulsive force along
the axis of rotation. In addition, we show that the shape transition is
associated with an unstable branch in the force-torque relation. A linearized
model of the fluid-structure interaction is proposed to account for all the
features of the non-linear filament dynamics
Effective equidistribution and the Sato-Tate law for families of elliptic curves
Extending recent work of others, we provide effective bounds on the family of
all elliptic curves and one-parameter families of elliptic curves modulo p (for
p prime tending to infinity) obeying the Sato-Tate Law. We present two methods
of proof. Both use the framework of Murty-Sinha; the first involves only
knowledge of the moments of the Fourier coefficients of the L-functions and
combinatorics, and saves a logarithm, while the second requires a Sato-Tate
law. Our purpose is to illustrate how the caliber of the result depends on the
error terms of the inputs and what combinatorics must be done.Comment: Version 1.1, 24 pages: corrected the interpretation of Birch's moment
calculations, added to the literature review of previous results
Phase Coexistence of a Stockmayer Fluid in an Applied Field
We examine two aspects of Stockmayer fluids which consists of point dipoles
that additionally interact via an attractive Lennard-Jones potential. We
perform Monte Carlo simulations to examine the effect of an applied field on
the liquid-gas phase coexistence and show that a magnetic fluid phase does
exist in the absence of an applied field. As part of the search for the
magnetic fluid phase, we perform Gibbs ensemble simulations to determine phase
coexistence curves at large dipole moments, . The critical temperature is
found to depend linearly on for intermediate values of beyond the
initial nonlinear behavior near and less than the where no
liquid-gas phase coexistence has been found. For phase coexistence in an
applied field, the critical temperatures as a function of the applied field for
two different are mapped onto a single curve. The critical densities
hardly change as a function of applied field. We also verify that in an applied
field the liquid droplets within the two phase coexistence region become
elongated in the direction of the field.Comment: 23 pages, ReVTeX, 7 figure
Force-Velocity Measurements of a Few Growing Actin Filaments
The authors propose a new mechanism for actin-based force generation based on results using chains of actin-grafted magnetic colloids
Magnetorheology in an aging, yield stress matrix fluid
Field-induced static and dynamic yield stresses are explored for magnetorheological (MR) suspensions in an aging, yield stress matrix fluid composed of an aqueous dispersion of Laponite® clay. Using a custom-built magnetorheometry fixture, the MR response is studied for magnetic field strengths up to 1 T and magnetic particle concentrations up to 30 v%. The yield stress of the matrix fluid, which serves to inhibit sedimentation of dispersed carbonyl iron magnetic microparticles, is found to have a negligible effect on the field-induced static yield stress for sufficient applied fields, and good agreement is observed between field-induced static and dynamic yield stresses for all but the lowest field strengths and particle concentrations. These results, which generally imply a dominance of inter-particle dipolar interactions over the matrix fluid yield stress, are analyzed by considering a dimensionless magnetic yield parameter that quantifies the balance of stresses on particles. By characterizing the applied magnetic field in terms of the average particle magnetization, a rheological master curve is generated for the field-induced static yield stress that indicates a concentration–magnetization superposition. The results presented herein will provide guidance to formulators of MR fluids and designers of MR devices who require a field-induced static yield stress and a dispersion that is essentially indefinitely stable to sedimentation.Petroleum Research Fund (ACS-PRF Grant No. 49956-ND9)American Chemical Society (ACS-PRF Grant No. 49956-ND9
The inhibition of the Rayleigh-Taylor instability by rotation
It is well-established that the Coriolis force that acts on fluid in a rotating system can act to stabilise otherwise unstable flows. Chandrasekhar considered theoretically the effect of the Coriolis force on the Rayleigh-Taylor instability, which occurs at the interface between a dense fluid lying on top of a lighter fluid under gravity, concluding that rotation alone could not stabilise this system indefinitely. Recent numerical work suggests that rotation may, nevertheless, slow the growth of the instability. Experimental verification of these results using standard techniques is problematic, owing to the practical difficulty in establishing the initial conditions. Here, we present a new experimental technique for studying the Rayleigh-Taylor instability under rotation that side-steps the problems encountered with standard techniques by using a strong magnetic field to destabilize an otherwise stable system. We find that rotation about an axis normal to the interface acts to retard the growth rate of the instability and stabilise long wavelength modes; the scale of the observed structures decreases with increasing rotation rate, asymptoting to a minimum wavelength controlled by viscosity. We present a critical rotation rate, dependent on Atwood number and the aspect ratio of the system, for stabilising the most unstable mode
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