Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1

In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has been performed on a thermoplastic lattice produced with a 3d printing technology. A theoretical analysis of the effective properties has been performed and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis has been performed on three micro-geometry leading to an isotropic behaviour for the cases of three-fold and six-fold symmetry and to a cubic behaviour for the case of four-fold symmetry.Comment: 26 pages, 12 figures (26 subfigures

Measuring non-linear functionals of quantum harmonic oscillator states

Using only linear interactions and a local parity measurement we show how entanglement can be detected between two harmonic oscillators. The scheme generalizes to measure both linear and non-linear functionals of an arbitrary oscillator state. This leads to many applications including purity tests, eigenvalue estimation, entropy and distance measures - all without the need for non-linear interactions or complete state reconstruction. Remarkably, experimental realization of the proposed scheme is already within the reach of current technology with linear optics.Comment: 5 pages, 2 figures. Minor corrections and some new references adde

Global Dynamics of Subsurface Solar Active Regions

We present three-dimensional numerical simulations of a magnetic loop evolving in either a convectively stable or unstable rotating shell. The magnetic loop is introduced in the shell in such a way that it is buoyant only in a certain portion in longitude, thus creating an \Omega-loop. Due to the action of magnetic buoyancy, the loop rises and develops asymmetries between its leading and following legs, creating emerging bipolar regions whose characteristics are similar to the ones of observed spots at the solar surface. In particular, we self-consistently reproduce the creation of tongues around the spot polarities, which can be strongly affected by convection. We moreover emphasize the presence of ring-shaped magnetic structures around our simulated emerging regions, which we call "magnetic necklace" and which were seen in a number of observations without being reported as of today. We show that those necklaces are markers of vorticity generation at the periphery and below the rising magnetic loop. We also find that the asymmetry between the two legs of the loop is crucially dependent on the initial magnetic field strength. The tilt angle of the emerging regions is also studied in the stable and unstable cases and seems to be affected both by the convective motions and the presence of a differential rotation in the convective cases.Comment: 23 pages (ApJ 2-column format), 19 figures, accepted for publication in Ap

Exploring the PcycP_{cyc} vs ProtP_{rot} relation with flux transport dynamo models of solar-like stars

Aims: To understand stellar magnetism and to test the validity of the Babcock-Leighton flux transport mean field dynamo models with stellar activity observations Methods: 2-D mean field dynamo models at various rotation rates are computed with the STELEM code to study the sensitivity of the activity cycle period and butterfly diagram to parameter changes and are compared to observational data. The novelty is that these 2-D mean field dynamo models incorporate scaling laws deduced from 3-D hydrodynamical simulations for the influence of rotation rate on the amplitude and profile of the meridional circulation. These models make also use of observational scaling laws for the variation of differential rotation with rotation rate. Results: We find that Babcock-Leighton flux transport dynamo models are able to reproduce the change in topology of the magnetic field (i.e. toward being more toroidal with increasing rotation rate) but seem to have difficulty reproducing the cycle period vs activity period correlation observed in solar-like stars if a monolithic single cell meridional flow is assumed. It may however be possible to recover the $P_{cyc}$ vs $P_{rot}$ relation with more complex meridional flows, if the profile changes in a particular assumed manner with rotation rate. Conclusions: The Babcock-Leighton flux transport dynamo model based on single cell meridional circulation does not reproduce the $P_{cyc}$ vs $P_{rot}$ relation unless the amplitude of the meridional circulation is assumed to increase with rotation rate which seems to be in contradiction with recent results obtained with 3-D global simulations.Comment: 12 pages, 8 figures, accepted for publication by A&A 1: AIM, CEA/DSM-CNRS-Univ. Paris 7, IRFU/SAp, France, 2: D.A.M.T.P., Centre for Mathematical Sciences, Univ. of Cambridge, UK, 3: JILA and Department of Astrophysical and Planetary Sciences, Univ. of Colorado, US

Polar cap magnetic field reversals during solar grand minima: could pores play a role?

We study the magnetic flux carried by pores located outside active regions with sunspots and investigate their possible contribution to the reversal of the global magnetic field of the Sun. We find that they contain a total flux of comparable amplitude to the total magnetic flux contained in polar caps. The pores located at distances of 40--100~Mm from the closest active region have systematically the correct sign to contribute to the polar cap reversal. These pores can predominantly be found in bipolar magnetic regions. We propose that during grand minima of solar activity, such a systematic polarity trend, akin to a weak magnetic (Babcock-Leighton-like) source term could still be operating but was missed by the contemporary observers due to the limited resolving power of their telescopes.Comment: 11 pages, 9 figures, accepted for publication in Astronomy&Astrophysic

Impingement of Water Droplets on an Ellipsoid with Fineness Ratio 5 in Axisymmetric Flow

The presence of radomes and instruments that are sensitive to water films or ice formations in the nose section of all-weather aircraft and missiles necessitates a knowledge of the droplet impingement characteristics of bodies of revolution. Because it is possible to approximate many of these bodies with an ellipsoid of revolution, droplet trajectories about an ellipsoid of revolution with a fineness ratio of 5 were computed for incompressible axisymmetric air flow. From the computed droplet trajectories, the following impingement characteristics of the ellipsoid surface were obtained and are presented in terms of dimensionless parameters: (1) total rate of water impingement, (2) extent of droplet impingement zone, (3) distribution of impinging water, and (4) local rate of water impingement