831 research outputs found
Self-diffusion in two-dimensional hard ellipsoid suspensions
We studied the self-diffusion of colloidal ellipsoids in a monolayer near a
flat wall by video microscopy. The image processing algorithm can track the
positions and orientations of ellipsoids with sub-pixel resolution. The
translational and rotational diffusions were measured in both the lab frame and
the body frame along the long and short axes. The long-time and short-time
diffusion coefficients of translational and rotational motions were measured as
functions of the particle concentration. We observed sub-diffusive behavior in
the intermediate time regime due to the caging of neighboring particles. Both
the beginning and the ending times of the intermediate regime exhibit power-law
dependence on concentration. The long-time and short-time diffusion
anisotropies change non-monotonically with concentration and reach minima in
the semi-dilute regime because the motions along long axes are caged at lower
concentrations than the motions along short axes. The effective diffusion
coefficients change with time t as a linear function of (lnt)/t for the
translational and rotational diffusions at various particle densities. This
indicates that their relaxation functions decay according to 1/t which provides
new challenges in theory. The effects of coupling between rotational and
translational Brownian motions were demonstrated and the two time scales
corresponding to anisotropic particle shape and anisotropic neighboring
environment were measured
No many-scallop theorem: Collective locomotion of reciprocal swimmers
To achieve propulsion at low Reynolds number, a swimmer must deform in a way
that is not invariant under time-reversal symmetry; this result is known as the
scallop theorem. We show here that there is no many-scallop theorem. We
demonstrate that two active particles undergoing reciprocal deformations can
swim collectively; moreover, polar particles also experience effective
long-range interactions. These results are derived for a minimal dimers model,
and generalized to more complex geometries on the basis of symmetry and scaling
arguments. We explain how such cooperative locomotion can be realized
experimentally by shaking a collection of soft particles with a homogeneous
external field
Settling of an asymmetric dumbbell in a quiescent fluid
We compute the hydrodynamic torque on a dumbbell (two spheres linked by a
massless rigid rod) settling in a quiescent fluid at small but finite Reynolds
number. The spheres have the same mass densities but different sizes. When the
sizes are quite different the dumbbell settles vertically, aligned with the
direction of gravity, the largest sphere first. But when the size difference is
sufficiently small then its steady-state angle is determined by a competition
between the size difference and the Reynolds number. When the sizes of the
spheres are exactly equal then fluid inertia causes the dumbbell to settle in a
horizontal orientation.Comment: 11 pages, 1 figure, as publishe
Spatiotemporal and Wavenumber Resolved Bicoherence at the Low to High Confinement Transition in the TJ-II Stellarator
Plasma turbulence is studied using Doppler reflectometry at the TJ-II
stellarator. By scanning the tilt angle of the probing beam, different values
of the perpendicular wave numbers are probed at the reflection layer. In this
way, the interaction between zonal flows and turbulence is reported with (a)
spatial, (b) temporal, and (c) wavenumber resolution for the first time in any
magnetic confinement fusion device.
We report measurements of the bicoherence across the Low to High (L--H)
confinement transition at TJ-II. We examine both fast transitions and slow
transitions characterized by an intermediate (I) phase. The bicoherence,
understood to reflect the non-linear coupling between the perpendicular
velocity (zonal flow) and turbulence amplitude, is significantly enhanced in a
time window of several tens of ms around the time of the L--H transition. It is
found to peak at a specific radial position (slightly inward from the radial
electric field shear layer in H mode), and is associated with a specific
perpendicular wave number ( cm, ). In all cases, the bicoherence is due to the interaction between
high frequencies ( MHz) and a rather low frequency (
kHz), as expected for a zonal flow.Comment: 11 pages, 3 figure
Multidimensional optical fractionation with holographic verification
The trajectories of colloidal particles driven through a periodic potential
energy landscape can become kinetically locked in to directions dictated by the
landscape's symmetries. When the landscape is realized with forces exerted by a
structured light field, the path a given particle follows has been predicted to
depend exquisitely sensitively on such properties as the particle's size and
refractive index These predictions, however, have not been tested
experimentally. Here, we describe measurements of colloidal silica spheres'
transport through arrays of holographic optical traps that use holographic
video microscopy to track individual spheres' motions in three dimensions and
simultaneously to measure each sphere's radius and refractive index with
part-per-thousand resolution. These measurements confirm previously untested
predictions for the threshold of kinetically locked-in transport, and
demonstrate the ability of optical fractionation to sort colloidal spheres with
part-per-thousand resolution on multiple characteristics simultaneously.Comment: 4 pages, 2 figures. Accepted for publication in Physical Review
Letter
The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods
The short--time self diffusion coefficient of a sphere in a suspension of
rigid rods is calculated in first order in the rod volume fraction. For low rod
concentrations the correction to the Einstein diffusion constant of the sphere
is a linear function of the rod volume fraction with the slope proportional to
the equilibrium averaged mobility diminution trace of the sphere interacting
with a single freely translating and rotating rod. The two--body hydrodynamic
interactions are calculated using the so--called bead model in which the rod is
replaced by a stiff linear chain of touching spheres. The interactions between
spheres are calculated numerically using the multipole method. Also an
analytical expression for the diffusion coefficient as a function of the rod
aspect ratio is derived in the limit of very long rods. We show that in this
limit the correction to the Einstein diffusion constant does not depend on the
size of the tracer sphere. The higher order corrections depending on the
applied model are computed numerically. An approximate expression is provided,
valid for a wide range of aspect ratios.Comment: 11 pages, 6 figure
Influence of flow confinement on the drag force on a static cylinder
The influence of confinement on the drag force on a static cylinder in a
viscous flow inside a rectangular slit of aperture has been investigated
from experimental measurements and numerical simulations. At low enough
Reynolds numbers, varies linearly with the mean velocity and the viscosity,
allowing for the precise determination of drag coefficients and
corresponding respectively to a mean flow parallel and
perpendicular to the cylinder length . In the parallel configuration, the
variation of with the normalized diameter of the
cylinder is close to that for a 2D flow invariant in the direction of the
cylinder axis and does not diverge when . The variation of
with the distance from the midplane of the model reflects the
parabolic Poiseuille profile between the plates for while it
remains almost constant for . In the perpendicular configuration,
the value of is close to that corresponding to a 2D system
only if and/or if the clearance between the ends of the cylinder
and the side walls is very small: in that latter case,
diverges as due to the blockage of the flow. In other cases, the
side flow between the ends of the cylinder and the side walls plays an
important part to reduce : a full 3D description of the flow is
needed to account for these effects
On Berenstein-Douglas-Seiberg Duality
I review the proposal of Berenstein-Douglas for a completely general
definition of Seiberg duality. To give evidence for their conjecture I present
the first example of a physical dual pair and explicitly check that it
satisfies the requirements. Then I explicitly show that a pair of toric dual
quivers is also dual according to their proposal. All these computations go
beyond tilting modules, and really work in the derived category. I introduce
all necessary mathematics where needed.Comment: 22 pages, LaTe
First-order virial expansion of short-time diffusion and sedimentation coefficients of permeable particles suspensions
For suspensions of permeable particles, the short-time translational and
rotational self-diffusion coefficients, and collective diffusion and
sedimentation coefficients are evaluated theoretically. An individual particle
is modeled as a uniformly permeable sphere of a given permeability, with the
internal solvent flow described by the Debye-Bueche-Brinkman equation. The
particles are assumed to interact non-hydrodynamically by their excluded
volumes. The virial expansion of the transport properties in powers of the
volume fraction is performed up to the two-particle level. The first-order
virial coefficients corresponding to two-body hydrodynamic interactions are
evaluated with very high accuracy by the series expansion in inverse powers of
the inter-particle distance. Results are obtained and discussed for a wide
range of the ratio, x, of the particle radius to the hydrodynamic screening
length inside a permeable sphere. It is shown that for x >= 10, the virial
coefficients of the transport properties are well-approximated by the
hydrodynamic radius (annulus) model developed by us earlier for the effective
viscosity of porous-particle suspensions
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