A simple criterion of transverse linear instability for solitary waves

We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.Comment: The main result has been improved and its proof simplifie

Simultaneous Induction Heating and Electromagnetic Stirring of a Molten Glass Bath

International audienceThis paper studies solutions for an efficient induction heating and a strong electromagnetic stirring of the molten glass bath through the action of Lorentz forces in a direct induction furnace. Different spatial configurations of AC magnetic fields - travelling, rotating or helicoidal, and the generated molten glass electromagnetic stirring are studied with one-way coupled electromagnetic and hydrodynamic models. For imposed value of the active power induced in the molten glass, the numerical experiments offers the values of the total inductor current and of the supply frequency for which an efficient electromagnetic stirring of molten glass is achieved

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument

Orbital motion of the young brown dwarf companion TWA 5 B

With more adaptive optics images available, we aim at detecting orbital motion for the first time in the system TWA 5 A+B. We measured separation and position angle between TWA 5 A and B in each high-resolution image available and followed their change in time, because B should orbit around A. The astrometric measurement precision is about one milli arc sec. With ten year difference in epoch, we can clearly detect orbital motion of B around A, a decrease in separation by ~ 0.0054 arc sec per year and a decrease in position angle by ~ 0.26 degrees per year. TWA 5 B is a brown dwarf with ~ 25 Jupiter masses (Neuh\"auser et al. 2000), but having large error bars (4 to 145 Jupiter masses, Neuh\"auser et al. 2009). Given its large projected separation from the primary star, ~ 86 AU, and its young age ~ 10 Myrs), it has probably formed star-like, and would then be a brown dwarf companion. Given the relatively large changes in separation and position angle between TWA 5 A and B, we can conclude that they orbit around each other on an eccentric orbit. Some evidence is found for a curvature in the orbital motion of B around A - most consistent with an elliptic (e=0.45) orbit. Residuals around the best-fit ellipse are detected and show a small-amplitude (~ 18 mas) periodic sinusoid with ~ 5.7 yr period, i.e., fully consistent with the orbit of the inner close pair TWA 5 Aa+b. Measuring these residuals caused by the photocenter wobble - even in unresolved images - can yield the total mass of the inner pair, so can test theoretical pre-main sequence models.Comment: 6 pages, 4 figures, accepted for publication in A&A; corrected typo in amplitude below Fig.

Astrometric and photometric monitoring of GQ Lup and its sub-stellar companion

Neuhaeuser et al. (2005) presented direct imaging evidence for a sub-stellar companion to the young T Tauri star GQ Lup. Common proper motion was highly significant, but no orbital motion was detected. Faint luminosity, low gravity, and a late-M/early-L spectral type indicated that the companion is either a planet or a brown dwarf. We have monitored GQ Lup and its companion in order to detect orbital and parallactic motion and variability in its brightness. We also search for closer and fainter companions. We have taken six more images with the VLT Adaptive Optics instrument NACO from May 2005 to Feb 2007, always with the same calibration binary from Hipparcos for both astrometric and photometric calibration. By adding up all the images taken so far, we search for additional companions. The position of GQ Lup A and its companion compared to a nearby non-moving background object varies as expected for parallactic motion by about one pixel (2 \pi with parallax \pi). We could not find evidence for variability of the GQ Lup companion in the K-band (standard deviation being \pm 0.08 mag), which may be due to large error bars. No additional companions are found with deep imaging. There is now exceedingly high significance for common proper motion of GQ Lup A and its companion. In addition, we see for the first time an indication for orbital motion (about 2 to 3 mas/yr decrease in separation, but no significant change in the position angle), consistent with a near edge-on or highly eccentric orbit. We measured the parallax for GQ Lup A to be \pi = 6.4 \pm 1.9 mas (i.e. 156 \pm 50 pc) and for the GQ Lup companion to be 7.2 \pm 2.1 mas (i.e. 139 \pm 45 pc), both consistent with being in the Lupus I cloud and bound to each other.Comment: A&A in pres

Joint evolution of multiple social traits: a kin selection analysis

General models of the evolution of cooperation, altruism and other social behaviours have focused almost entirely on single traits, whereas it is clear that social traits commonly interact. We develop a general kin-selection framework for the evolution of social behaviours in multiple dimensions. We show that whenever there are interactions among social traits new behaviours can emerge that are not predicted by one-dimensional analyses. For example, a prohibitively costly cooperative trait can ultimately be favoured owing to initial evolution in other (cheaper) social traits that in turn change the cost-benefit ratio of the original trait. To understand these behaviours, we use a two-dimensional stability criterion that can be viewed as an extension of Hamilton's rule. Our principal example is the social dilemma posed by, first, the construction and, second, the exploitation of a shared public good. We find that, contrary to the separate one-dimensional analyses, evolutionary feedback between the two traits can cause an increase in the equilibrium level of selfish exploitation with increasing relatedness, while both social (production plus exploitation) and asocial (neither) strategies can be locally stable. Our results demonstrate the importance of emergent stability properties of multidimensional social dilemmas, as one-dimensional stability in all component dimensions can conceal multidimensional instability

The phase shift of line solitons for the KP-II equation

The KP-II equation was derived by [B. B. Kadomtsev and V. I. Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of line solitary waves of shallow water. Stability of line solitons has been proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi, Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the local phase shift of modulating line solitons are not uniform in the transverse direction. In this paper, we obtain the $L^\infty$-bound for the local phase shift of modulating line solitons for polynomially localized perturbations

Effet d’un programme d’activité physique intermittent de haute intensité sur la perte de masse grasse abdominale chez la femme DT2 ménopausée

Contexte : A la ménopause, la diminution des taux d’estrogènes favorise un dépôt de masse grasse (MG) abdominal (sous-cutané et viscéral). La MG viscérale est corrélée aux maladies cardio-vasculaires (MCV). Ce risque est accentué chez les sujets présentant un diabète de type 2 (DT2).Objectif : Comparer deux modalités d’entraînement, continu de moyenne intensité (SSE) vs. intermittent de haute intensité (HIIE), sur la perte de MG abdominale (dont viscérale) chez des femmes DT2 ménopausées.Matériels et méthode : Seize femmes DT2 ménopausées (69±1ans; IMC : 31±1 kg/m²) ont été réparties aléatoirement en deux groupes. Pendant quatre mois, deux fois par semaine, 8 d’entre elles ont réalisé un entraînement SSE (40 min de pédalage à 50% de la FCmax de réserve), et 8 ont réalisé un entraînement HIIE (8s de sprint suivies de 12s de récupération active, pendant 20 min). Pré (T0) et post entraînement (T4), la composition corporelle et la MG abdominale totale ont été mesurées par DXA (Dual Energy X-ray Absorptiometry). La MG viscérale a été estimée à partir de la méthode de Martin et Jensen1. A T0 et T4, les apports énergétiques et le niveau d’activité physique ont été déterminés (questionnaires et accéléromètrie validée2 intégrée sur smartphone).Résultats : Après 16 semaines d’intervention, sans modification des apports énergétiques et du niveau d’activité physique total, une perte de MG totale et un gain de masse maigre est observé (effet temps, p<0.05). La diminution de MG abdominale est supérieure dans le groupe HIIE (0.32% ± 2.07 vs 8.32 % ± 2.19, p<0.05) et la perte de MG viscérale n’est observée que dans le groupe HIIE (p<0.05).Conclusion : L’entraînement de type HIIE apparait comme un programme alternatif intéressant chez la femme DT2 ménopausée en diminuant significativement la MG abdominale totale et viscérale

Remotely Operated Train for Inspection and Measurement in CERN's LHC Tunnel

Personnel access to the LHC tunnel will be restricted to varying extents during the life of the machine due to radiation and cryogenic hazards. For this reason a remotely operated modular inspection train, (TIM) running on the LHC tunnel’s overhead monorail has been developed. In order to be compatible with the LHC personnel access system, a small section train that can pass through small openings at the top of sector doors has now been produced. The basic train can be used for remote visual inspection; additional modules give the capability of carrying out remote measurement of radiation levels, environmental conditions around the tunnel, and even remote measurement of the precise position of machine elements such as collimators. The paper outlines the design, development and operation of the equipment including preparation of the infrastructure. Key features of the trains are described along with future developments and intervention scenarios