A rescaled method for RBF approximation

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties

A rescaled method for RBF approximation

A new method to compute stable kernel-based interpolants has been presented by the second and third authors. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties. First, we prove that the method is an instance of the Shepard\u2019s method, when certain weight functions are used. In particular, the method can reproduce constant functions. Second, it is possible to define a modified set of cardinal functions strictly related to the ones of the not-rescaled kernel. Through these functions, we define a Lebesgue function for the rescaled interpolation process, and study its maximum - the Lebesgue constant - in different settings. Also, a preliminary theoretical result on the estimation of the interpolation error is presented. As an application, we couple our method with a partition of unity algorithm. This setting seems to be the most promising, and we illustrate its behavior with some experiments

Magnetic Anisotropy of Co2+ as Signature of Intrinsic Ferromagnetism in ZnO:Co

We report on the magnetic properties of thoroughly characterized Zn1-xCoxO epitaxial thin films, with low Co concentration, x=0.003-0.005. Magnetic and EPR measurements, combined with crystal field theory, reveal that isolated Co2+ ions in ZnO possess a strong single ion anisotropy which leads to an "easy plane" ferromagnetic state when the ferromagnetic Co-Co interaction is considered. We suggest that the peculiarities of the magnetization process of this state can be viewed as a signature of intrinsic ferromagnetism in ZnO:Co materials.Comment: 4 pages, 4 figure

Ferromagnetism in Co-doped ZnO films grown by molecular beam epitaxy: magnetic, electrical and microstructural studies

We studied structural, optical and magnetic properties of high-quality 5 and 15% Co-doped ZnO films grown by plasma-assisted molecular beam epitaxy (MBE) on (0001)-sapphire substrates. Magnetic force microscopy (MFM) and magnetic measurements with SQUID magnetometer show clear ferromagnetic behavior of the films up to room temperature whereas they are antiferromagnetic below 200 K approximately. Temperature dependence of the carrier mobility was determined using Raman line shape analysis of the longitudinal-optical-phonon-plasmon coupled modes. It shows that the microscopic mechanism for ferromagnetic ordering is coupling mediated by free electrons between spins of Co atoms. These results bring insight into a subtle interplay between charge carriers and magnetism in MBE-grown Zn(1-x)CoxO films.Comment: 10 pages, 9 figures, 2 table

Toward an experimental proof of superhydrophobicity enhanced by quantum fluctuations freezing on a broadband-absorber metamaterial

Previous theoretical works suggested that superhydrophobicity could be enhanced through partial inhibition of the quantum vacuum modes at the surface of a broadband-absorber metamaterial which acts in the extreme ultraviolet frequency domain. This effect would then compete with the classical Cassie-Baxter interpretation of superhydrophobicity. In this article, we first theoretically establish the expected phenomenological features related to such a kind of "quantum" superhydrophobicity. Then, relying on this theoretical framework, we experimentally study patterned silicon surfaces on which organosilane molecules were grafted, all the coated surfaces having similar characteristic pattern sizes but different profiles. Some of these surfaces can indeed freeze quantum photon modes while others cannot. While the latter ones allow hydrophobicity, only the former ones allow for superhydrophobicity. We believe these results lay the groundwork for further complete assessment of superhydrophobicity induced by quantum fluctuations freezing.Comment: 10 pages, 5 figures, final version, accepted for publication in Journal of Applied Physic

Assessment of CO2 health risk in indoor air following a leakage reaching unsaturated zone: results from the first representative scale experiment

International audienceLeakage of CO2 from geological reservoirs is one of the most fearsome unexpected scenarios for CO2 storage activities. If a leakage reaches the ground level, exposure to high CO2 concentrations is more likely to occur in low ventilated spaces (pit dug in the ground, basement, building) where CO2 could accumulate to high concentrations. Significant literature and models about indoor exposure resulting from intrusion of soils gases in building are available in several domains (e.g., contaminated soils, radon, etc.). However, there is no guarantee that those approaches are appropriate for the assessment of consequences of CO2 leakage due the specificity of CO2 and due to the singularities of the source in case of leakage from anthropic reservoirs. Furthermore, another singularity compared to conventional approaches is that the risk due to CO2 exposure should be evaluated considering acute concentrations rather than long term exposure to low concentrations. Thus, a specific approach is needed to enable a quantitative assessment of the risk for health and living in indoor environment in case of leakage from a reservoir reaching the unsaturated zone below the buildings. We present the results of the IMPACT-CO2 project that aims at understanding the possible migration of CO2 to indoor environment and to develop an approach to evaluate the risks. The approach is based on modelling and experiments at laboratory scale and at field representative scale. The aim of the experiment is to capture the main phenomena that control the migration of CO2 through unsaturated zone, and its intrusion and accumulation in buildings. The experimental results will also enable numerical confrontation with tools used for risk assessment. Experiments at representative scale (Figure 1) are performed on the PISCO2 platform (Ponferrada, Spain) specifically instrumented and designed for understanding the impacts of CO2 migration towards the soil surface. The experiment is composed of a 2.2 m deep basin filled with sand upon which a specifically designed cylindrical device representing the indoor condition of a building (with controlled depressurization and ventilation) is set up. The device includes a calibrated interface that represents a cracked slab of a building. The injection of CO2 is performed at the bottom of the basin with a flow rate in the range of hundreds of g/d/m². The first results show that the presence of a building influences significantly the transport of CO2 in the surrounding soil leading to two competing phenomena: 1) seepage in the atmosphere mainly controlled by diffusion gradient and 2) advective/diffusive flux entering the building due to the depressurization. Models have been established to quantitatively assess the proportion of CO

The inhomogeneous reionization times of present-day galaxies

Today's galaxies experienced cosmic reionization at different times in different locations. For the first time, reionization (50% ionized) redshifts, z R , at the location of their progenitors are derived from new, fully coupled radiation-hydrodynamics simulation of galaxy formation and reionization at z > 6, matched to N-body simulation to z = 0. Constrained initial conditions were chosen to form the well-known structures of the local universe, including the Local Group and Virgo, in a (91 Mpc)3 volume large enough to model both global and local reionization. Reionization simulation CoDa I-AMR, by CPU-GPU code EMMA, used (2048)3 particles and (2048)3 initial cells, adaptively refined, while N-body simulation CoDa I-DM2048, by Gadget2, used (2048)3 particles, to find reionization times for all galaxies at z = 0 with masses M(z = 0) ≥ 108 M ⊙. Galaxies with $M(z=0)\gtrsim {10}^{11}\,{M}_{\odot }$ reionized earlier than the universe as a whole, by up to ~500 Myr, with significant scatter. For Milky Way–like galaxies, z R ranged from 8 to 15. Galaxies with $M(z=0)\lesssim {10}^{11}\,{M}_{\odot }$ typically reionized as late or later than globally averaged 50% reionization at $\langle {z}_{R}\rangle =7.8$, in neighborhoods where reionization was completed by external radiation. The spread of reionization times within galaxies was sometimes as large as the galaxy-to-galaxy scatter. The Milky Way and M31 reionized earlier than global reionization but later than typical for their mass, neither dominated by external radiation. Their most-massive progenitors at z > 6 had z R =9.8 (MW) and 11 (M31), while their total masses had z R = 8.2 (both)