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-

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

Cold tongue and warm pool ENSO events in CMIP5 : mean state and future projections

Author Posting. © American Meteorological Society, 2014. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 27 (2014): 2861–2885, doi:10.1175/JCLI-D-13-00437.1.The representation of the El Niño–Southern Oscillation (ENSO) under historical forcing and future projections is analyzed in 34 models from the Coupled Model Intercomparison Project phase 5 (CMIP5). Most models realistically simulate the observed intensity and location of maximum sea surface temperature (SST) anomalies during ENSO events. However, there exist systematic biases in the westward extent of ENSO-related SST anomalies, driven by unrealistic westward displacement and enhancement of the equatorial wind stress in the western Pacific. Almost all CMIP5 models capture the observed asymmetry in magnitude between the warm and cold events (i.e., El Niños are stronger than La Niñas) and between the two types of El Niños: that is, cold tongue (CT) El Niños are stronger than warm pool (WP) El Niños. However, most models fail to reproduce the asymmetry between the two types of La Niñas, with CT stronger than WP events, which is opposite to observations. Most models capture the observed peak in ENSO amplitude around December; however, the seasonal evolution of ENSO has a large range of behavior across the models. The CMIP5 models generally reproduce the duration of CT El Niños but have biases in the evolution of the other types of events. The evolution of WP El Niños suggests that the decay of this event occurs through heat content discharge in the models rather than the advection of SST via anomalous zonal currents, as seems to occur in observations. No consistent changes are seen across the models in the location and magnitude of maximum SST anomalies, frequency, or temporal evolution of these events in a warmer world.2014-10-1

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