407 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
Brownian motion in a non-homogeneous force field and photonic force microscope
The Photonic Force Microscope (PFM) is an opto-mechanical technique based on
an optical trap that can be assumed to probe forces in microscopic systems.
This technique has been used to measure forces in the range of pico- and
femto-Newton, assessing the mechanical properties of biomolecules as well as of
other microscopic systems. For a correct use of the PFM, the force field to
measure has to be invariable (homogeneous) on the scale of the Brownian motion
of the trapped probe. This condition implicates that the force field must be
conservative, excluding the possibility of a rotational component. However,
there are cases where these assumptions are not fulfilled Here, we show how to
improve the PFM technique in order to be able to deal with these cases. We
introduce the theory of this enhanced PFM and we propose a concrete analysis
workflow to reconstruct the force field from the experimental time-series of
the probe position. Furthermore, we experimentally verify some particularly
important cases, namely the case of a conservative or rotational force-field
A frictionless microswimmer
We investigate the self-locomotion of an elongated microswimmer by virtue of
the unidirectional tangential surface treadmilling. We show that the propulsion
could be almost frictionless, as the microswimmer is propelled forward with the
speed of the backward surface motion, i.e. it moves throughout an almost
quiescent fluid. We investigate this swimming technique using the special
spheroidal coordinates and also find an explicit closed-form optimal solution
for a two-dimensional treadmiler via complex-variable techniques.Comment: 6 pages, 4 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
Motion of a deformable drop of magnetic fluid on a solid surface in a rotating magnetic field
The behavior of a magnetic fluid drop lying on a solid horizontal surface and
surrounded by a nonmagnetic liquid under the action of a uniform magnetic field
which is rotating in a vertical plane with low frequency (of the order of 1 Hz)
has been investigated experimentally. Shape deformation and translatory motion
of the drop were observed and studied. The drop translation velocity for
different field amplitudes and field frequencies has been measured.Comment: 9 pages, 4 figure
Reduced model for H-mode sustainment in unfavorable drift configuration in ASDEX Upgrade
A recently developed reduced model of H-mode sustainment based on
interchange-drift-Alfv\'en turbulence description in the vicinity of the
separatrix matching experimental observations in ASDEX Upgrade has been
extended to experiments with the unfavorable drift. The combination
with the theory of the magnetic-shear-induced Reynolds stress offers a
possibility to quantitatively explain the phenomena. The extension of the
Reynolds stress estimate in the reduced model via the magnetic shear
contribution is able to reproduce the strong asymmetry in the access conditions
depending on the ion drift orientation in agreement with
experimental observations. The Reynolds stress profile asymmetry predicted by
the magnetic shear model is further extended by comparison with GRILLIX and
GENE-X simulations matched with comparable experiments in realistic X-point
geometry. The predictions of the radial electric field well depth and its
difference between the favorable and unfavorable configurations at the same
heating power from the extended model also show consistency with experimental
measurements.Comment: Submitted to Nuclear Fusio
Life at high Deborah number
In many biological systems, microorganisms swim through complex polymeric
fluids, and usually deform the medium at a rate faster than the inverse fluid
relaxation time. We address the basic properties of such life at high Deborah
number analytically by considering the small-amplitude swimming of a body in an
arbitrary complex fluid. Using asymptotic analysis and differential geometry,
we show that for a given swimming gait, the time-averaged leading-order
swimming kinematics of the body can be expressed as an integral equation on the
solution to a series of simpler Newtonian problems. We then use our results to
demonstrate that Purcell's scallop theorem, which states that time-reversible
body motion cannot be used for locomotion in a Newtonian fluid, breaks down in
polymeric fluid environments
Categorification of skew-symmetrizable cluster algebras
We propose a new framework for categorifying skew-symmetrizable cluster
algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with
the action of a finite group G, we construct a G-equivariant mutation on the
set of maximal rigid G-invariant objects of C. Using an appropriate cluster
character, we can then attach to these data an explicit skew-symmetrizable
cluster algebra. As an application we prove the linear independence of the
cluster monomials in this setting. Finally, we illustrate our construction with
examples associated with partial flag varieties and unipotent subgroups of
Kac-Moody groups, generalizing to the non simply-laced case several results of
Gei\ss-Leclerc-Schr\"oer.Comment: 64 page
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