1,166 research outputs found
Which canonical algebras are derived equivalent to incidence algebras of posets?
We give a full description of all the canonical algebras over an
algebraically closed field that are derived equivalent to incidence algebras of
finite posets. These are the canonical algebras whose number of weights is
either 2 or 3.Comment: 8 pages; slight revision; to appear in Comm. Algebr
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
Microscale swimming: The molecular dynamics approach
The self-propelled motion of microscopic bodies immersed in a fluid medium is
studied using molecular dynamics simulation. The advantage of the atomistic
approach is that the detailed level of description allows complete freedom in
specifying the swimmer design and its coupling with the surrounding fluid. A
series of two-dimensional swimming bodies employing a variety of propulsion
mechanisms -- motivated by biological and microrobotic designs -- is
investigated, including the use of moving limbs, changing body shapes and fluid
jets. The swimming efficiency and the nature of the induced, time-dependent
flow fields are found to differ widely among body designs and propulsion
mechanisms.Comment: 5 pages, 3 figures (minor changes to text
Hydrodynamics of flagellated microswimmers near free-slip interfaces
The hydrodynamics of a flagellated microorganism is investigated when
swimming close to a planar free-slip surface by means of numerical solu- tions
of the Stokes equations obtained via a Boundary Element Method. Depending on
the initial condition, the swimmer can either escape from the free-slip surface
or collide with the boundary. Interestingly, the mi- croorganism does not
exhibit a stable orbit. Independently of escape or attraction to the interface,
close to a free-slip surface, the swimmer fol- lows a counter-clockwise
trajectory, in agreement with experimental find- ings, [15]. The hydrodynamics
is indeed modified by the free-surface. In fact, when the same swimmer moves
close to a no-slip wall, a set of initial conditions exists which result in
stable orbits. Moreover when moving close to a free-slip or a no-slip boundary
the swimmer assumes a different orientation with respect to its trajectory.
Taken together, these results contribute to shed light on the hydrodynamical
behaviour of microorgan- isms close to liquid-air interfaces which are relevant
for the formation of interfacial biofilms of aerobic bacteria
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
Faxen relations in solids - a generalized approach to particle motion in elasticity and viscoelasticity
A movable inclusion in an elastic material oscillates as a rigid body with
six degrees of freedom. Displacement/rotation and force/moment tensors which
express the motion of the inclusion in terms of the displacement and force at
arbitrary exterior points are introduced. Using reciprocity arguments two
general identities are derived relating these tensors. Applications of the
identities to spherical particles provide several new results, including simple
expressions for the force and moment on the particle due to plane wave
excitation.Comment: 11 pages, 4 figure
Rotational and translational self-diffusion in concentrated suspensions of permeable particles
In our recent work on concentrated suspensions of uniformly porous colloidal
spheres with excluded volume interactions, a variety of short-time dynamic
properties were calculated, except for the rotational self-diffusion
coefficient. This missing quantity is included in the present paper. Using a
precise hydrodynamic force multipole simulation method, the rotational
self-diffusion coefficient is evaluated for concentrated suspensions of
permeable particles. Results are presented for particle volume fractions up to
45%, and for a wide range of permeability values. From the simulation results
and earlier results for the first-order virial coefficient, we find that the
rotational self-diffusion coefficient of permeable spheres can be scaled to the
corresponding coefficient of impermeable particles of the same size. We also
show that a similar scaling applies to the translational self-diffusion
coefficient considered earlier. From the scaling relations, accurate analytic
approximations for the rotational and translational self-diffusion coefficients
in concentrated systems are obtained, useful to the experimental analysis of
permeable-particle diffusion. The simulation results for rotational diffusion
of permeable particles are used to show that a generalized
Stokes-Einstein-Debye relation between rotational self-diffusion coefficient
and high-frequency viscosity is not satisfied.Comment: 4 figure
Colloidal transport through optical tweezer arrays
Viscously damped particles driven past an evenly spaced array of potential
energy wells or barriers may become kinetically locked in to the array, or else
may escape from the array. The transition between locked-in and free-running
states has been predicted to depend sensitively on the ratio between the
particles' size and the separation between wells. This prediction is confirmed
by measurements on monodisperse colloidal spheres driven through arrays of
holographic optical traps.Comment: 4 pages, 4 figure
Low-Reynolds number swimming in gels
Many microorganisms swim through gels, materials with nonzero zero-frequency
elastic shear modulus, such as mucus. Biological gels are typically
heterogeneous, containing both a structural scaffold (network) and a fluid
solvent. We analyze the swimming of an infinite sheet undergoing transverse
traveling wave deformations in the "two-fluid" model of a gel, which treats the
network and solvent as two coupled elastic and viscous continuum phases. We
show that geometric nonlinearities must be incorporated to obtain physically
meaningful results. We identify a transition between regimes where the network
deforms to follow solvent flows and where the network is stationary. Swimming
speeds can be enhanced relative to Newtonian fluids when the network is
stationary. Compressibility effects can also enhance swimming velocities.
Finally, microscopic details of sheet-network interactions influence the
boundary conditions between the sheet and network. The nature of these boundary
conditions significantly impacts swimming speeds.Comment: 6 pages, 5 figures, submitted to EP
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