1,124 research outputs found
Galois coverings of weakly shod algebras
We investigate the Galois coverings of weakly shod algebras. For a weakly
shod algebra not quasi-tilted of canonical type, we establish a correspondence
between its Galois coverings and the Galois coverings of its connecting
component. As a consequence, we show that a weakly shod algebra is simply
connected if and only if its first Hochschild cohomology group vanishes.Comment: Some references were added. The proof of Lemma 6.5 was modifie
Persistent correlation of constrained colloidal motion
We have investigated the motion of a single optically trapped colloidal
particle close to a limiting wall at time scales where the inertia of the
surrounding fluid plays a significant role. The velocity autocorrelation
function exhibits a complex interplay due to the momentum relaxation of the
particle, the vortex diffusion in the fluid, the obstruction of flow close to
the interface, and the harmonic restoring forces due to the optical trap. We
show that already a weak trapping force has a significant impact on the
velocity autocorrelation function C(t)= at times where the
hydrodynamic memory leads to an algebraic decay. The long-time behavior for the
motion parallel and perpendicular to the wall is derived analytically and
compared to numerical results. Then, we discuss the power spectral densities of
the displacement and provide simple interpolation formulas. The theoretical
predictions are finally compared to recent experimental observations.Comment: 12 pages, 6 figure
Non-equilibrium hydrodynamics of a rotating filament
The nonlinear dynamics of an elastic filament that is forced to rotate at its
base is studied by hydrodynamic simulation techniques; coupling between
stretch, bend, twist elasticity and thermal fluctuations is included. The
twirling-overwhirling transition is located and found to be strongly
discontinuous. For finite bend and twist persistence length, thermal
fluctuations lower the threshold rotational frequency, for infinite persistence
length the threshold agrees with previous analytical predictions
Particles held by springs in a linear shear flow exhibit oscillatory motion
The dynamics of small spheres, which are held by linear springs in a low
Reynolds number shear flow at neighboring locations is investigated. The flow
elongates the beads and the interplay of the shear gradient with the nonlinear
behavior of the hydrodynamic interaction among the spheres causes in a large
range of parameters a bifurcation to a surprising oscillatory bead motion. The
parameter ranges, wherein this bifurcation is either super- or subcritical, are
determined.Comment: 4 pages, 5 figure
Tilted algebras and short chains of modules
We provide an affirmative answer for the question raised almost twenty years
ago concerning the characterization of tilted artin algebras by the existence
of a sincere finitely generated module which is not the middle of a short
chain
Symmetric three-particle motion in Stokes flow: equilibrium for heavy spheres in contrast to "end-of-world" for point forces
A stationary stable solution of the Stokes equations for three identical
heavy solid spheres falling in a vertical plane is found. It has no analog in
the point-particle approximation. Three spheres aligned horizontally at equal
distances evolve towards the equilibrium relative configuration while the point
particles collapse onto a single point in a finite time.Comment: 4 pages, 7 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
Instabilities and turbulence-like dynamics in an oppositely driven binary particle mixture
Using extensive particle-based simulations, we investigate out-of-equilibrium
pattern dynamics in an oppositely driven binary particle system in two
dimensions. A surprisingly rich dynamical behavior including lane formation,
jamming, oscillation and turbulence-like dynamics is found. The ratio of two
friction coefficients is a key parameter governing the stability of lane
formation. When the friction coefficient transverse to the external force
direction is sufficiently small compared to the longitudinal one, the lane
structure becomes unstable to shear-induced disturbances, and the system
eventually exhibits a dynamical transition into a novel turbulence-like phase
characterized by random convective flows. We numerically construct an
out-of-equilibrium phase diagram. Statistical analysis of complex
spatio-temporal dynamics of the fully nonlinear turbulence-like phase suggests
its apparent reminiscence to the swarming dynamics in certain active matter
systems.Comment: 6 pages, 6 figures, accepted for publication in EP
Dynamics of non-equilibrium membrane bud formation
The dynamical response of a lipid membrane to a local perturbation of its
molecular symmetry is investigated theoretically. A density asymmetry between
the two membrane leaflets is predominantly released by in-plane lipid diffusion
or membrane curvature, depending upon the spatial extent of the perturbation.
It may result in the formation of non-equilibrium structures (buds), for which
a dynamical size selection is observed. A preferred size in the micrometer
range is predicted, as a signature of the crossover between membrane and
solvent dominated dynamical membrane response.Comment: 7 pages 3 figure
Arbitrarily slow, non-quasistatic, isothermal transformations
For an overdamped colloidal particle diffusing in a fluid in a controllable,
virtual potential, we show that arbitrarily slow transformations, produced by
smooth deformations of a double-well potential, need not be reversible. The
arbitrarily slow transformations do need to be fast compared to the barrier
crossing time, but that time can be extremely long. We consider two types of
cyclic, isothermal transformations of a double-well potential. Both start and
end in the same equilibrium state, and both use the same basic operations---but
in different order. By measuring the work for finite cycle times and
extrapolating to infinite times, we found that one transformation required no
work, while the other required a finite amount of work, no matter how slowly it
was carried out. The difference traces back to the observation that when time
is reversed, the two protocols have different outcomes, when carried out
arbitrarily slowly. A recently derived formula relating work production to the
relative entropy of forward and backward path probabilities predicts the
observed work average.Comment: 6 pages, 6 figure
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