Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

Southern Ocean warming and Antarctic ice shelf melting in conditions plausible by late 23rd century in a high-end scenario

How much Antarctic ice shelf basal melt rates can increase in response to global warming remains an open question. Here we describe the response of the Southern Ocean and ice shelf cavities to an abrupt change to high-end atmospheric conditions plausible by the late 23rd century under the SSP5-8.5 scenario. To achieve this objective, we first present and evaluate a new 0.25∘ global configuration of the NEMO (Nucleus for European Modelling of the Ocean NEMO System Team, 2019) ocean and sea ice model. Our present-day simulations demonstrate good agreement with observational data for key variables such as temperature, salinity, and ice shelf melt rates, despite the remaining difficulties to simulate the interannual variability in the Amundsen Sea. The ocean response to the high-end atmospheric perturbation includes a strengthening and extension of the Ross and Weddell gyres and a quasi-disappearance of sea ice, with a subsequent decrease in production of High Salinity Shelf Water and increased intrusion of warmer water onto the continental shelves favoured by changes in baroclinic currents at the shelf break. We propose to classify the perturbed continental shelf as a “warm–fresh shelf”. This induces a substantial increase in ice shelf basal melt rates, particularly in the coldest seas, with a total basal mass loss rising from 1180 to 15 700 Gt yr−1 and an Antarctica averaged melt rate increasing from 0.8 to 10.6 m yr−1. In the perturbed simulation, most ice shelves around Antarctica experience conditions that are currently found in the Amundsen Sea, while the Amundsen Sea warms by 2 ∘C. These idealised projections can be used as a base to calibrate basal melt parameterisations used in long-term ice sheet projections.</p

Age dependence of the Vega Phenomenon: Theory

In a separate paper (Decin et al 2003), we have re-examined the observations of IR excess obtained with the ISO satellite and discussed the ages of stars with excess. The amount of dust (measured by the luminosity fraction \fdust=L_\mathrm{IR}/L_{\star}) seen around main-sequence stars of different ages shows several interesting trends. To discuss these results in the context of a physical model, we develop in this paper an analytical model for the dust production in Vega-type systems. Previously it has been claimed that a powerlaw slope of about -2 in the diagram plotting amount of dust versus time could be explained by a simple collisional cascade. We show that such a cascade in fact results in a powerlaw \fdust\propto t^{-1} if the dust removal processes are dominated by collisions. A powerlaw \fdust\propto t^{-2} only results when the dust removal processes become dominated by Pointing-Robertson drag. This may be the case in the Kuiper Belt of our own solar system, but it is certainly not the case in any of the observed disks. A steeper slope can, however, be created by including continuous stirring into the models. We show that the existence of both young and old Vega-like systems with large amounts of dust (\fdust\simeq 10^{-3}) can be explained qualitatively by Kuiper-Belt-like structures with \emph{delayed stirring}. Finally, the absence of young stars with intermediate amounts of dust may be due to the fact that stirring due to planet formation may not be active in young low-mass disks. The considerations in this paper support the picture of simultaneous stirring and dust production proposed by Kenyon and Bromley (2002).Comment: 26 pages, 3 figures, accepted for Publication in Ap

Sea ice inertial oscillations in the Arctic Basin

International audienceAn original method to quantify the amplitude of inertial motion of oceanic and ice drifters, through the introduction of a non-dimensional parameter M defined from a spectral analysis, is presented. A strong seasonal dependence of the magnitude of sea ice inertial oscillations is revealed, in agreement with the corresponding annual cycles of sea ice extent, concentration, thickness, advection velocity, and deformation rates. The spatial pattern of the magnitude of the sea ice inertial oscillations over the Arctic Basin is also in agreement with the sea ice thickness and concentration patterns. This argues for a strong interaction between the magnitude of inertial motion on one hand, the dissipation of energy through mechanical processes, and the cohesiveness of the cover on the other hand. Finally, a significant multi-annual evolution towards greater magnitudes of inertial oscillations in recent years, in both summer and winter, is reported, thus concomitant with reduced sea ice thickness, concentration and spatial extent

Inclusive 2H(3He,t) reaction at 2 GeV

The inclusive 2H(3He,t) reaction has been studied at 2 GeV for energy transfers up to 500 MeV and scattering angles from 0.25 up to 4 degrees. Data are well reproduced by a model based on a coupled-channel approach for describing the NN and N Delta systems. The effect of final state interaction is important in the low energy part of the spectra. In the delta region, the cross-section is very sensitive to the effects of Delta-N interaction and Delta N - NN process. The latter has also a large influence well below the pion threshold. The calculation underestimates the experimental cross-section between the quasi-elastic and the delta peaks; this is possibly due to projectile excitation or purely mesonic exchange currents.Comment: 9 pages, 9 figures, accepted for publication in EPJ

Reducing the debt : is it optimal to outsource an investment?

International audienceWe deal with the problem of outsourcing the debt for a big investment, according two situations: either the firm outsources both the investment (and the associated debt) and the exploitation to a private consortium, or the firm supports the debt and the investment but outsources the exploitation. We prove the existence of Stackelberg and Nash equilibria between the firm and the private consortium, in both situations. We compare the benefits of these contracts. We conclude with a study of what happens in case of incomplete information, in the sense that the risk aversion coefficient of each partner may be unknown by the other partner

Technical Note: Impact of nonlinearity on changing the a priori of trace gas profiles estimates from the Tropospheric Emission Spectrometer (TES)

International audienceNon-linear optimal estimates of atmospheric profiles from the Tropospheric Emission Spectrometer (TES) may contain a priori information that varies geographically, which is a confounding factor in the analysis and physical interpretation of an ensemble of profiles. A common strategy is to transform these profile estimates to a common prior using a linear operation thereby facilitating the interpretation of profile variability. However, this operation is dependent on the assumption of not worse than moderate non-linearity near the solution of the non-linear estimate. We examines the robustness of this assumption when exchanging the prior by comparing atmospheric retrievals from the Tropospheric Emission Spectrometer processed with a uniform prior with those processed with a variable prior and converted to a uniform prior following the non-linear retrieval. We find that linearly converting the prior following a non-linear retrieval is shown to have a minor effect on the results as compared to a non-linear retrieval using a uniform prior when compared to the expected total error, with less than 10% of the change in the prior ending up as unbiased fluctuations in the profile estimate results

Evaluation of monsoon seasonality and the tropospheric biennial oscillation transitions in the CMIP models

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 39 (2012): L20713, doi:10.1029/2012GL053322.Characteristics of the Indian and Australian summer monsoon systems, their seasonality and interactions are examined in a variety of observational datasets and in the Coupled Model Intercomparison Project Phase 3 and 5 (CMIP3 and CMIP5) climate models. In particular, it is examined whether preferred monsoon transitions between the two regions and from one year to another, that form parts of the Tropospheric Biennial Oscillation, can lead to improved predictive skill. An overall improvement in simulation of seasonality for both monsoons is seen in CMIP5 over CMIP3, with most CMIP5 models correctly simulating very low rainfall rates outside of the monsoon season. The predictability resulting from each transition is quantified using a Monte Carlo technique. The transition from strong/weak Indian monsoon to strong/weak Australian monsoon shows ∼15% enhanced predictability in the observations, in estimating whether the following monsoon will be stronger/weaker than the climatology. Most models also successfully simulate this transition. However, enhanced predictability for other transitions is less clear.This project was supported by funding from the Australian Research Council (DP110100601) and the Centre of Excellence for Climate System Science. This work was also supported by an award under the Merit Allocation Scheme on the NCI National Facility at the ANU2013-04-2

Meso-macro numerical approach to macroscopic permeability of fractured concrete – COMPLAS XI

In this paper, a sequential multi-scale framework to solve mass (air or water) transfer problems is described. Numerical results are checked against mechanical and permeation experimental datas from a reinforced concrete specimen under tensile load designed by C. Desmettre and J.P. Charron [2