7,337 research outputs found
Liquid jet eruption from hollow relaxation
A cavity hollowed out on a free liquid surface is relaxing, forming an
intense liquid jet. Using a model experiment where a short air pulse sculpts an
initial large crater, we depict the different stages in the gravitational
cavity collapse and in the jet formation. Prior eversion, all cavity profiles
are found to exhibit a shape similarity. Following hollow relaxation, a
universal scaling law establishing an unexpected relation between the jet
eruption velocity, the initial cavity geometry and the liquid viscosity is
evidenced experimentally. On further analysing the jet forms we demonstrate
that the stretched liquid jet also presents shape similarity. Considering that
the jet shape is a signature of the initial flow focusing, we elaborate a
simple model capturing the key features of the erupting jet velocity scaling
On the density of sets of the Euclidean plane avoiding distance 1
A subset is said to avoid distance if: In this paper we study the number
which is the supremum of the upper densities of measurable
sets avoiding distance 1 in the Euclidean plane. Intuitively, represents the highest proportion of the plane that can be filled by a
set avoiding distance 1. This parameter is related to the fractional chromatic
number of the plane.
We establish that and .Comment: 11 pages, 5 figure
Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS
This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful
On the physics of fizzing: How bubble bursting controls droplets ejection
Bubbles at a free surface surface usually burst in ejecting myriads of
droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we
propose a simple scaling for the jet velocity and we unravel experimentally the
intricate roles of bubble shape, capillary waves, gravity and liquid
properties. We demonstrate that droplets ejection unexpectedly changes with
liquid properties. In particular, using damping action of viscosity,
self-similar collapse can be sheltered from capillary ripples and continue
closer to the singular limit, therefore producing faster and smaller
droplets.These results pave the road to the control of the bursting bubble
aerosols
On the density of sets avoiding parallelohedron distance 1
The maximal density of a measurable subset of R^n avoiding Euclidean
distance1 is unknown except in the trivial case of dimension 1. In this paper,
we consider thecase of a distance associated to a polytope that tiles space,
where it is likely that the setsavoiding distance 1 are of maximal density
2^-n, as conjectured by Bachoc and Robins. We prove that this is true for n =
2, and for the Vorono\"i regions of the lattices An, n >= 2
On homotopies with triple points of classical knots
We consider a knot homotopy as a cylinder in 4-space. An ordinary triple
point of the cylinder is called {\em coherent} if all three branches
intersect at pairwise with the same index. A {\em triple unknotting} of a
classical knot is a homotopy which connects with the trivial knot and
which has as singularities only coherent triple points. We give a new formula
for the first Vassiliev invariant by using triple unknottings. As a
corollary we obtain a very simple proof of the fact that passing a coherent
triple point always changes the knot type. As another corollary we show that
there are triple unknottings which are not homotopic as triple unknottings even
if we allow more complicated singularities to appear in the homotopy of the
homotopy.Comment: 10 pages, 13 figures, bugs in figures correcte
Incremental complexity of a bi-objective hypergraph transversal problem
The hypergraph transversal problem has been intensively studied, from both a
theoretical and a practical point of view. In particular , its incremental
complexity is known to be quasi-polynomial in general and polynomial for
bounded hypergraphs. Recent applications in computational biology however
require to solve a generalization of this problem, that we call bi-objective
transversal problem. The instance is in this case composed of a pair of
hypergraphs (A, B), and the aim is to find minimal sets which hit all the
hyperedges of A while intersecting a minimal set of hyperedges of B. In this
paper, we formalize this problem, link it to a problem on monotone boolean
-- formulae of depth 3 and study its incremental complexity
Enhancing the area of a Raman atom interferometer using a versatile double-diffraction technique
IIn this paper we demonstrate a new scheme for Raman transitions which
realize a symmetric momentum-space splitting of , deflecting the
atomic wave-packets into the same internal state. Combining the advantages of
Raman and Bragg diffraction, we achieve a three pulse state labelled
interferometer, intrinsically insensitive to the main systematics and
applicable to all kind of atomic sources. This splitting scheme can be extended
to momentum transfer by a multipulse sequence and is implemented
on a interferometer. We demonstrate the area enhancement by
measuring inertial forces
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