Minimum energy configurations of classical charges: Large N asymptotics

We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron distribution explicitly, showing in particular that the number of electrons surrounding each nucleus is asymptotic to the nuclear charge ("screening"). The proof proceeds by establishing, via Gamma-convergence, a coarse-grained variational principle for the limit distribution, which can be solved explicitly.Comment: To appear in Applied Mathematics Research Expres

Antenna Gain and Link Budget for Waves Carrying Orbital Angular Momentum (OAM)

This paper addresses the RF link budget of a communication system using unusual waves carrying an orbital angular momentum (OAM) in order to clearly analyse the fundamental changes for telecommunication applications. The study is based on a typical configuration using circular array antennas to transmit and receive OAM waves. For any value of the OAM mode order, an original asymptotic formulation of the link budget is proposed in which equivalent antenna gains and free-space losses appear. The formulations are then validated with the results of a commercial electromagnetic simulation software. By this way, we also show how our formula can help to design a system capable of superimposing several channels on the same bandwidth and the same polarisation, based on the orthogonality of the OAM. Additional losses due to the use of this degree of freedom are notably clearly calculated to quantify the benefit and drawback according to the case.Comment: 33 pages, 11 figure

Dissipation of the energy imparted by mid-latitude storms in the Southern Ocean

The aim of this study is to clarify the role of the Southern Ocean storms on interior mixing and meridional overturning circulation. A periodic and idealized numerical model has been designed to represent the key physical processes of a zonal portion of the Southern Ocean located between 70 and 40°?S. It incorporates physical ingredients deemed essential for Southern Ocean functioning: rough topography, seasonally varying air–sea fluxes, and high-latitude storms with analytical form. The forcing strategy ensures that the time mean wind stress is the same between the different simulations, so the effect of the storms on the mean wind stress and resulting impacts on the Southern Ocean dynamics are not considered in this study. Level and distribution of mixing attributable to high-frequency winds are quantified and compared to those generated by eddy–topography interactions and dissipation of the balanced flow. Results suggest that (1) the synoptic atmospheric variability alone can generate the levels of mid-depth dissipation frequently observed in the Southern Ocean (10?10–10?9?W?kg?1) and (2) the storms strengthen the overturning, primarily through enhanced mixing in the upper 300?m, whereas deeper mixing has a minor effect. The sensitivity of the results to horizontal resolution (20, 5, 2 and 1?km), vertical resolution and numerical choices is evaluated. Challenging issues concerning how numerical models are able to represent interior mixing forced by high-frequency winds are exposed and discussed, particularly in the context of the overturning circulation. Overall, submesoscale-permitting ocean modeling exhibits important delicacies owing to a lack of convergence of key components of its energetics even when reaching ?x?=??1?km

DEMONSTRATION OF HETEROARYLMETHANE OXIDATION IN A BENZIMIDAZOLE DERIVATIVE WITH THE USE OF UV SPECTROPHOTOMETRY AND X-RAY DIFFRACTION

In this work, we present the synthesis of a copper complex of 1-benzyl-2-[(5-methyl-isoxazol-3-yl)methyl]-benzimidazole, by using simultaneously UV spectrophotometry and X-ray diffraction. It has been possible for us to highlight an original oxidation of benzylbenzimidazole group in such complex leading to ketone. A kinetic study carried out by UV spectrophotometry shows well that the oxidation reaction proceeds according to the first-order kinetic law: K = 9.4×10-4 s-1 and t½ = 12.4 min

Application of two way nesting model to upscale sediment processes of the Southern Bight of the North Sea: full model validation

The BRAIN project FaCE-iT (Functional biodiversity in a Changing sedimentary Environment: Implications for biogeochemistry and food webs in a managerial setting) funded by BELSPO aims at evaluating the influence of offshore wind farms settlements and dredging activities on the distribution of sediment grain size over the Southern Bight of the North Sea (SBNS) and the Belgian Coastal Zone (BCZ), as well as associated impacts on biodiversity and biogeochemistry.In this framework an implementation of the tri-dimensional hydrodynamical and sediment transport model ROMS-COAWST was set-up to conduct scenario experiment relating offshore activities to resulting alteration of the seafloor structure. This implementation combines high resolution nested grids covering the Belgian Coastal Zone, embedded into a coarser grid covering the Southern Bight of the North Sea and is forced by ECMWF ERA-Interim data at the air-sea interface, CMEMS data at the open boundaries, TPXO data to introduce/force the tidal impact, and consider the discharge of four main rivers. Currently, the work focuses on assessing the skills of this modelling system to resolve the dynamics of the complex shallow and highly tidal region. The 3-year climatological run for 2006-2009 was performed to test the model ability to simulate the interannual dynamics. The model skills were evaluated by validation against remote-sensing temperature fields, tidal elevations and currents at the Meetnet pylons, and in situ temperature and salinity data provided by the Lifewatch network. We evaluate how grid refinement and different set-up of the nesting strategy enhance essential model skills in relation with sediment transport The further step will be to confront the sediment transport dynamics stemming from the nested system to that resolved from the coarser parent alone. A diagenetic model developed in the frame of FaCE-iT will be joint with the sediment model in order to upscale locally derived alteration of the biogeochemistry and benthic functionality stemming from seafloor texture alteration.Functional biodiversity in a Changing sedimentary Environment: Implications for biogeochemistry and food webs in a managerial setting (FaCE-It

Insight from PREFACE & AWA on Tropical Atlantic Tuna ecology and effects on western African fisheries economies

International audienc

Turbulent mixing, restratification, and phytoplankton growth at a submesoscale eddy

High-resolution large-eddy simulations are used to study the influence of submesoscale mixed layer instability and small-scale turbulence on phytoplankton growth in light-limited conditions. Four simulations are considered with small-scale turbulence driven by varying levels of surface cooling. Significant small-scale turbulence is seen even without surface forcing, and the downward mixing of phytoplankton is sufficient to briefly delay the developing bloom. Moderate and strong values of the constant surface heat flux (Q =− 10,−100 W/m2) are sufficient to prevent a bloom. In contrast to the critical depth hypothesis, the growth rate for phytoplankton does not appear to be controlled by the mixed layer depth. Instead, a comparison between the turbulent diffusivity above the compensation depth and a critical value predicted by the critical turbulence hypothesis closely matches the timing and magnitude of phytoplankton growth.J.R.T. was supported by a grant from the Natural Environment Research Council, award NE/J010472/1.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1002/2016GL06910

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to anotherComment: 16 pages, talk delivered at the Geilo Winter School 201