Some aspects of dispersive horizons: lessons from surface waves

Hydrodynamic surface waves propagating on a moving background flow experience an effective curved space-time. We discuss experiments with gravity waves and capillary-gravity waves in which we study hydrodynamic black/white-hole horizons and the possibility of penetrating across them. Such possibility of penetration is due to the interaction with an additional "blue" horizon, which results from the inclusion of surface tension in the low-frequency gravity-wave theory. This interaction leads to a dispersive cusp beyond which both horizons completely disappear. We speculate the appearance of high-frequency "superluminal" corrections to be a universal characteristic of analogue gravity systems, and discuss their relevance for the trans-Planckian problem. We also discuss the role of Airy interference in hybridising the incoming waves with the flowing background (the effective spacetime) and blurring the position of the black/white-hole horizon.Comment: 29 pages. Lecture Notes for the IX SIGRAV School on "Analogue Gravity", Como (Italy), May 201

Horizon effects for surface waves in wave channels and circular jumps

Surface waves in classical fluids experience a rich array of black/white hole horizon effects. The dispersion relation depends on the characteristics of the fluid (in our case, water and silicon oil) as well as on the fluid depth and the wavelength regime. In some cases, it can be tuned to obtain a relativistic regime plus high-frequency dispersive effects. We discuss two types of ongoing analogue white-hole experiments: deep water waves propagating against a counter-current in a wave channel and shallow waves on a circular hydraulic jump.Comment: 4 pages, 2 figs. To appear in: Proceedings of the Spanish Relativity Meeting (ERE2010

Modelling the electric field applied to a tokamak

The vector potential for the Ohmic heating coil system of a tokamak is obtained in semi-analytical form. Comparison is made to the potential of a simple, finite solenoid. In the quasi-static limit, the time rate of change of the potential determines the induced electromotive force through the Maxwell-Lodge effect. Discussion of the gauge constraint is included.Comment: 13 pages, 7 figures, final versio

Developing microwave chemistry under process engineering principles

[EN] It is nowadays admitted that microwaves are frequently used in organic chemistry labs [1] (even if not as much as it was predicted 20 years ago, one must say [2]). On the other side it is also certain that this technology has not yet found its place in chemical industry: application at a production scale are very scarce [3][4] and this despite the potential advantages of the technology (selective heating, high heating rate, low thermal inertia…). The point is that mastering all the aspects of microwaves assisted synthesis at industrial scale demands a lot of different skills to work together: chemistry, process engineering, microwave engineering, materials science. This is so challenging that tools and methodologies for quantification of industrial microwave interest and scaling-up of lab results are missing. In this work we present our contributions to the deployment of microwaves for synthesis in the chemical industry which are mainly The development of small pilot reactors (1 L) in stainless steel, capable to withstand temperature and pressureThe application of a chemical engineering methodology to microwave assisted synthesisAn example of intensification (see table) of an industrially interesting reaction using microwave to access NPW (high temperature and pressure)A tentative of rationalization of process criteria to identify a priori the interest of microwave heating for a specific application [1]. Diaz-Ortiz et al., Chem. Rec. 2019, 19, 85–97 [2]. Kappe, Chem. Rec. 2019, 19, 15–39 [3]. Aldivia, brevet WO2004/066683A1 [4]. https://cen.acs.org/articles/94/i36/Microwaving-ton.htmlTioni, E.; Breysse, J.; Rousseaux, P. (2019). Developing microwave chemistry under process engineering principles. En AMPERE 2019. 17th International Conference on Microwave and High Frequency Heating. Editorial Universitat Politècnica de València. 174-180. https://doi.org/10.4995/AMPERE2019.2019.9901OCS17418

Les crédits aux sociétés non financières en France : évolutions récentes.

Particulièrement soutenue jusqu’à ces derniers mois, la croissance des crédits aux entreprises donne, depuis peu, des signes de modération, dans un contexte de consolidation des bilans bancaires et de dégradation de l’environnement macroéconomique.Crédits aux entreprises, taux débiteurs, réintermédiation, financement des entreprises, conditions du crédit.

Lorenz or Coulomb in Galilean Electromagnetism ?

Galilean Electromagnetism was discovered thirty years ago by Levy-Leblond & Le Bellac. However, these authors only explored the consequences for the fields and not for the potentials. Following De Montigny & al., we show that the Coulomb gauge condition is the magnetic limit of the Lorenz gauge condition whereas the Lorenz gauge condition applies in the electric limit of L\'{e}vy-Leblond & Le Bellac. Contrary to De Montigny & al. who used Galilean tensor calculus, we use orders of magnitude based on physical motivations in our derivation.Comment: PDF versio

Effects of interdot dipole coupling in mesoscopic epitaxial Fe(100) dot arrays

The domain structure and the coercivity of epitaxial Fe(100) circular dot arrays of different diameters and separations have been studied using magnetic force microscopy (MFM) and focused magneto-optical Kerr effect (MOKE). The MFM images of the 1 µm diameter single domain dot arrays show direct evidence of strong interdot dipole coupling when the separation is reduced down to 0.1 µm. The coercivity of the dots is also found to be dependent on the separation, indicating the effect of the interdot dipole coupling on the magnetization reversal process

Granular size segregation in underwater sand ripples

We report an experimental study of a binary sand bed under an oscillating water flow. The formation and evolution of ripples is observed. The appearance of a granular segregation is shown to strongly depend on the sand bed preparation. The initial wavelength of the mixture is measured. In the final steady state, a segregation in volume is observed instead of a segregation at the surface as reported before. The correlation between this phenomenon and the fluid flow is emphasised. Finally, different ``exotic'' patterns and their geophysical implications are presented.Comment: 8 page

Horizon effects with surface waves on moving water

Surface waves on a stationary flow of water are considered, in a linear model that includes the surface tension of the fluid. The resulting gravity-capillary waves experience a rich array of horizon effects when propagating against the flow. In some cases three horizons (points where the group velocity of the wave reverses) exist for waves with a single laboratory frequency. Some of these effects are familiar in fluid mechanics under the name of wave blocking, but other aspects, in particular waves with negative co-moving frequency and the Hawking effect, were overlooked until surface waves were investigated as examples of analogue gravity [Sch\"utzhold R and Unruh W G 2002 Phys. Rev. D 66 044019]. A comprehensive presentation of the various horizon effects for gravity-capillary waves is given, with emphasis on the deep water/short wavelength case kh>>1 where many analytical results can be derived. A similarity of the state space of the waves to that of a thermodynamic system is pointed out.Comment: 30 pages, 15 figures. Minor change

Hawking Radiation on an Ion Ring in the Quantum Regime

This paper discusses a recent proposal for the simulation of acoustic black holes with ions. The ions are rotating on a ring with an inhomogeneous, but stationary velocity profile. Phonons cannot leave a region, in which the ion velocity exceeds the group velocity of the phonons, as light cannot escape from a black hole. The system is described by a discrete field theory with a nonlinear dispersion relation. Hawking radiation is emitted by this acoustic black hole, generating entanglement between the inside and the outside of the black hole. We study schemes to detect the Hawking effect in this setup.Comment: 42 pages (one column), 17 figures, published revised versio