Erratum : Existence of 3D Skyrmions. Complete version

This erratum corrects the proof given in \cite{E1,E2} about the existence of $3D$ Skyrmions. This is done by changing the arguments of the proof while remaining in the same framework of concentration-compactness. Note however that the use of this method is here different of most of what has been done with it so far. In that sense, this new proof has some interest by itself. The proof given here is self-contained. I thank F. Lin and Y. Yang for having pointed out to me that there were gaps in my proofs.Comment: 10 page

Dog Owners’ Liability: Statutory Effects

The Triboindenter present many advantages for the measurement of friction and wear at the nanoscale. A reciprocating multi-cycle linear test can be programmed, from where it is possible to obtain simultaneously the friction force and wear rate from the lateral force and vertical displacement sensors, respectively. The friction values have high precision but the wear data is usually wrong in long duration tests because the drift rate is only measured just before the test start. Alternatively, one can program the SPM scanning mode of the instrument with a high load in order to produce the wear of the surface. At the end of the experiment, a squared hole is produced which can be measured using the SPM facility of the system. However, this wear experiment does not allow the simultaneous measurement of the friction coefficient.In this talk I will present a new methodology to measure in-situ the friction and wear of thin films using a Triboindenter TI-950 from Hysitron. I will show how the possible changes of drift rate during long-time tests can be overcome, obtaining simultaneous precise values of friction and wear rate as a function of time. I will discuss how the Triboimage® software can be adapted to this methodology in order to get realistic values of friction and wear. Finally I will show some results for soft (H < 1GPa) Pb films and very hard (H ~ 35 GPa) nitride coating

Electron neutrino opacity in magnetised media

We study the effects of strong magnetic fields ($B> 10^{13}$~G) in the cross section for $\nu_e n\to p e$ scattering in the presence of a degenerate electron background. This can be relevant for the $\nu_e$ propagation in the proto-neutron star stage after supernovae collapse. We find that for field strengths $B> 10^{16}$~G$(E_\nu/10$ MeV$)^2$ the $\nu_e$ opacity is sizeably affected by the magnetic field and can lead to a shift in the location of the electron neutrino sphere towards lower densities. We discuss the implications that this may have for scenarios proposed to explain the observed pulsar velocities

Results from the Pierre Auger Observatory

I describe some of the results on ultrahigh-energy cosmic rays that have been obtained with the Pierre Auger Observatory. These include measurements of the spectrum, composition and anisotropies. Possible astrophysical scenarios that account for these results are discussed.Comment: Proceedings of the 7th Roma International Conference on Astroparticle Physic

A hydrodynamic approach to boost invariant free streaming

We consider a family of exact boost invariant solutions of the transport equation for free streaming massless particles, where the one particle distribution function is defined in terms of a function of a single variable. The evolution of second and third moments of the one particle distribution function (the second moment being the energy momentum tensor (EMT) and the third moment the non equilibrium current (NEC)) depends only on two moments of that function. Given those two moments we show how to build a non linear hydrodynamic theory which reproduces the early time evolution of the EMT and the NEC. The structure of these theories may give insight on nonlinear hydrodynamic phenomena on short time scales.Comment: 20 pages, 8 figures. Accepted for publication in Phys. Rev.

Recent results from the Pierre Auger Observatory

The results obtained after the first decade of operation of the Pierre Auger Observatory are reviewed.Comment: Proceedings X SILAFAE Medellin-201