10,850 research outputs found
A counter-example to the theorem of Hiemer and Snurnikov
A planar polygonal billiard is said to have the finite blocking property
if for every pair of points in there exists a finite number of
``blocking'' points such that every billiard trajectory from
to meets one of the 's. As a counter-example to a theorem of
Hiemer and Snurnikov, we construct a family of rational billiards that lack the
finite blocking property.Comment: 5 pages, 3 figure
On the finite blocking property
A planar polygonal billiard is said to have the finite blocking property
if for every pair of points in there exists a finite number of
``blocking'' points such that every billiard trajectory from
to meets one of the 's. Generalizing our construction of a
counter-example to a theorem of Hiemer and Snurnikov (see \cite{Mo}), we show
that the only regular polygons that have the finite blocking property are the
square, the equilateral triangle and the hexagon. Then we extend this result to
translation surfaces. We prove that the only Veech surfaces with the finite
blocking property are the torus branched coverings. We also provide a local
sufficient condition for a translation surface to fail the finite blocking
property. This enables us to give a complete classification for the L-shaped
surfaces as well as to obtain a density result in the space of translation
surfaces in every genus .Comment: 24 page
Spreading huge free software without internet connection, via self-replicating USB keys
We describe and discuss an affordable way to spread huge software without
relying on internet connection, via the use of self-replicating live USB keys.Comment: 5 pages, accepted to Extremecom 201
A necessary condition for lower semicontinuity of line energies
We are interested in some energy functionals concentrated on the
discontinuity lines of divergence-free 2D vector fields valued in the circle
. This kind of energy has been introduced first by P. Aviles and
Y. Giga. They show in particular that, with the cubic cost function ,
this energy is lower semicontinuous. In this paper, we construct a
counter-example which excludes the lower semicontinuity of line energies for
cost functions of the form with . We also show that, in this case,
the viscosity solution corresponding to a certain convex domain is not a
minimizer.Comment: 13 page
Identification of mode couplings in nonlinear vibrations of the steelpan
The authors are grateful to Bertrand David (Telecom-ParisTech) for computing the code allowing the STFT filtering procedure used in Section 5.1. The filter has been designed in the framework of the PAFI project (Plateforme dâAide la facture Instrumentale, www.pafi.fr) which is also thanked.The vibrations and sounds produced by two notes of a double second steelpan are investigated, the main objective being to quantify the nonlinear energy exchanges occurring between vibration modes that are responsible of the peculiar sound of the instrument. A modal analysis first reveals the particular tuning of the modes and the systematic occurence of degenerate modes, from the second one, this feature being a consequence of the tuning and the mode localization. Forced vibrations experiments are then performed to follow precisely the energy exchange between harmonics of the vibration and thus quantify properly the mode couplings. In particular, it is found that energy exchanges are numerous, resulting in complicated frequency response curves even for very small levels of vibration amplitude. Simple models displaying 1:2:2 and 1:2:4 internal resonance are then fitted to the measurements, allowing to identify the values of the nonlinear quadratic coupling coefficients resulting from the geometric nonlinearity. The identified 1:2:4 model is finally used to recover the time domain variations of an impacted note in normal playing condition, resulting in an excellent agreement for the temporal behaviour of the first four harmonics
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