Effective non-linear dynamics of binary condensates and open problems

We report on a recent result concerning the effective dynamics for a mixture of Bose-Einstein condensates, a class of systems much studied in physics and receiving a large amount of attention in the recent literature in mathematical physics; for such models, the effective dynamics is described by a coupled system of non-linear Sch\"odinger equations. After reviewing and commenting our proof in the mean field regime from a previous paper, we collect the main details needed to obtain the rigorous derivation of the effective dynamics in the Gross-Pitaevskii scaling limit.Comment: Corrected typos, updated reference

Nonstationary probabilistic downscaling of extreme precipitation

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On Singularity formation for the L^2-critical Boson star equation

We prove a general, non-perturbative result about finite-time blowup solutions for the $L^2$-critical boson star equation $i\partial_t u = \sqrt{-\Delta+m^2} \, u - (|x|^{-1} \ast |u|^2) u$ in 3 space dimensions. Under the sole assumption that the solution blows up in $H^{1/2}$ at finite time, we show that $u(t)$ has a unique weak limit in $L^2$ and that $|u(t)|^2$ has a unique weak limit in the sense of measures. Moreover, we prove that the limiting measure exhibits minimal mass concentration. A central ingredient used in the proof is a "finite speed of propagation" property, which puts a strong rigidity on the blowup behavior of $u$. As the second main result, we prove that any radial finite-time blowup solution $u$ converges strongly in $L^2$ away from the origin. For radial solutions, this result establishes a large data blowup conjecture for the $L^2$-critical boson star equation, similar to a conjecture which was originally formulated by F. Merle and P. Raphael for the $L^2$-critical nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704]. We also discuss some extensions of our results to other $L^2$-critical theories of gravitational collapse, in particular to critical Hartree-type equations.Comment: 24 pages. Accepted in Nonlinearit

Rate of Convergence Towards Semi-Relativistic Hartree Dynamics

We consider the semi-relativistic system of $N$ gravitating Bosons with gravitation constant $G$. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where $N \to \infty$ and $G \to 0$ while $GN = \lambda$ fixed. In the super-critical regime of large $\lambda$, we introduce the regularized interaction where the cutoff vanishes as $N \to \infty$. We show that the difference between the many-body semi-relativistic Schr\"{o}dinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order $N^{-1}$ for all $\lambda$, i.e., the result covers the sub-critical regime and the super-critical regime. The $N$ dependence of the bound is optimal.Comment: 29 page

Characterizing, modelling and understanding the climate variability of the deep water formation in the North-Western Mediterranean Sea

Observing, modelling and understanding the climate-scale variability of the deep water formation (DWF) in the North-Western Mediterranean Sea remains today very challenging. In this study, we first characterize the interannual variability of this phenomenon by a thorough reanalysis of observations in order to establish reference time series. These quantitative indicators include 31 observed years for the yearly maximum mixed layer depth over the period 1980–2013 and a detailed multi-indicator description of the period 2007–2013. Then a 1980–2013 hindcast simulation is performed with a fully-coupled regional climate system model including the high-resolution representation of the regional atmosphere, ocean, land-surface and rivers. The simulation reproduces quantitatively well the mean behaviour and the large interannual variability of the DWF phenomenon. The model shows convection deeper than 1000 m in 2/3 of the modelled winters, a mean DWF rate equal to 0.35 Sv with maximum values of 1.7 (resp. 1.6) Sv in 2013 (resp. 2005). Using the model results, the winter-integrated buoyancy loss over the Gulf of Lions is identified as the primary driving factor of the DWF interannual variability and explains, alone, around 50 % of its variance. It is itself explained by the occurrence of few stormy days during winter. At daily scale, the Atlantic ridge weather regime is identified as favourable to strong buoyancy losses and therefore DWF, whereas the positive phase of the North Atlantic oscillation is unfavourable. The driving role of the vertical stratification in autumn, a measure of the water column inhibition to mixing, has also been analyzed. Combining both driving factors allows to explain more than 70 % of the interannual variance of the phenomenon and in particular the occurrence of the five strongest convective years of the model (1981, 1999, 2005, 2009, 2013). The model simulates qualitatively well the trends in the deep waters (warming, saltening, increase in the dense water volume, increase in the bottom water density) despite an underestimation of the salinity and density trends. These deep trends come from a heat and salt accumulation during the 1980s and the 1990s in the surface and intermediate layers of the Gulf of Lions before being transferred stepwise towards the deep layers when very convective years occur in 1999 and later. The salinity increase in the near Atlantic Ocean surface layers seems to be the external forcing that finally leads to these deep trends. In the future, our results may allow to better understand the behaviour of the DWF phenomenon in Mediterranean Sea simulations in hindcast, forecast, reanalysis or future climate change scenario modes. The robustness of the obtained results must be however confirmed in multi-model studies

An Environmental and Climate History of the Roman Expansion in Italy

A first synthesis of available data for the period of Rome’s expansion in Italy (about 400–29 b.c.e.) shows the role of climate and environment in early Roman imperialism. Although global indices suggest a warmer phase with relatively few short-term climate events occuring around the same time as the expansion, local data emphasize the highly variable timing and expression of these trends. This variability casts doubt on ideas of a unitary, historically consequential “Roman Warm Period.” The historical importance of climate and environment to socioeconomic development merits emphasis, but should be understood in terms of evolving, contingent forms of resilience and risk-mitigating behavior by Italian communities during Roman expansion

Disequilibrium Carbon, Oxygen, and Nitrogen Chemistry in the Atmospheres of HD 189733b and HD 209458b

We have developed 1-D photochemical and thermochemical kinetics and diffusion models for the transiting exoplanets HD 189733b and HD 209458b to study the effects of disequilibrium chemistry on the atmospheric composition of "hot Jupiters." Here we investigate the coupled chemistry of neutral carbon, hydrogen, oxygen, and nitrogen species, and we compare the model results with existing transit and eclipse observations. We find that the vertical profiles of molecular constituents are significantly affected by transport-induced quenching and photochemistry, particularly on cooler HD 189733b; however, the warmer stratospheric temperatures on HD 209458b can help maintain thermochemical equilibrium and reduce the effects of disequilibrium chemistry. For both planets, the methane and ammonia mole fractions are found to be enhanced over their equilibrium values at pressures of a few bar to less than a mbar due to transport-induced quenching, but CH4 and NH3 are photochemically removed at higher altitudes. Atomic species, unsaturated hydrocarbons (particularly C2H2), some nitriles (particularly HCN), and radicals like OH, CH3, and NH2 are enhanced overequilibrium predictions because of quenching and photochemistry. In contrast, CO, H2O, N2, and CO2 more closely follow their equilibrium profiles, except at pressures < 1 microbar, where CO, H2O, and N2 are photochemically destroyed and CO2 is produced before its eventual high-altitude destruction. The enhanced abundances of HCN, CH4, and NH3 in particular are expected to affect the spectral signatures and thermal profiles HD 189733b and other, relatively cool, close-in transiting exoplanets. We examine the sensitivity of our results to the assumed temperature structure and eddy diffusion coefficientss and discuss further observational consequences of these models.Comment: 40 pages, 16 figures, accepted for publication in Astrophysical Journa

Perspectives Pathways to clean hands: highlights of successful hand hygiene implementation

infections and estimates of vaccine effectiveness i