The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Transport of volatile chlorinated hydrocarbons in unsaturated aggregated media

Transport of volatile hydrocarbons in soils is largely controlled by interactions of vapours with the liquid and solid phase. Sorption on solids of gaseous or dissolved comPounds may be important. Since the contact time between a chemical and a specific sorption site can be rather short, kinetic or mass-transfer resistance effects may be relevant. An existing mathematical model describing advection and diffusion in the gas phase and diffusional transport from the gaseous phase into an intra-aggregate water phase is modified to include linear kinetic sorption on ps-solid and water-solid interfaces. The model accounts for kinetic mass transfer between all three phases in a soil. The solution of the Laplace-transformed equations is inverted numerically. We performed transient column experiments with 1,1,2-Trichloroethane, Trichloroethylene, and Tetrachloroethylene using air-dry solid and water-saturated porous glass beads. The breakthrough curves were calculated based on independently estimated parameters. The model calculations agree well with experimental data. The different transport behaviour of the three compounds in our system primarily depends on Henry's constants.

On the evolution of the oceanic component of the IPSL climate models from CMIP3 to CMIP5: A mean state comparison

This study analyses the impact on the oceanic mean state of the evolution of the oceanic component (NEMO) of the climate model developed at Institut Pierre Simon Laplace (IPSL-CM), from the version IPSL-CM4, used for third phase of the Coupled Model Intercomparison Project (CMIP3), to IPSL-CM5A, used for CMIP5. Several modifications have been implemented between these two versions, in particular an interactive coupling with a biogeochemical module, a 3-band model for the penetration of the solar radiation, partial steps at the bottom of the ocean and a set of physical parameterisations to improve the representation of the impact of turbulent and tidal mixing. A set of forced and coupled experiments is used to single out the effect of each of these modifications and more generally the evolution of the oceanic component on the IPSL coupled models family. Major improvements are located in the Southern Ocean, where physical parameterisations such as partial steps and tidal mixing reinforce the barotropic transport of water mass, in particular in the Antarctic Circumpolar Current) and ensure a better representation of Antarctic bottom water masses. However, our analysis highlights that modifications, which substantially improve ocean dynamics in forced configuration, can yield or amplify biases in coupled configuration. In particular, the activation of radiative biophysical coupling between biogeochemical cycle and ocean dynamics results in a cooling of the ocean mean state. This illustrates the difficulty to improve and tune coupled climate models, given the large number of degrees of freedom and the potential compensating effects masking some biases.

Reconciling two alternative mechanisms behind bi-decadal variability in the North Atlantic

Understanding the preferential timescales of variability in the North Atlantic, usually associated with the Atlantic meridional overturning circulation (AMOC), is essential for the prospects for decadal prediction. However, the wide variety of mechanisms proposed from the analysis of climate simulations, potentially dependent on the models themselves, has stimulated the debate of which processes take place in reality. One mechanism receiving increasing attention, identified both in idealized models and observations, is a westward propagation of subsurface buoyancy anomalies that impact the AMOC through a basin-scale intensification of the zonal density gradient, enhancing the northward transport via thermal wind balance. In this study, we revisit a control simulation from the Institut Pierre-Simon Laplace Coupled Model 5A (IPSL-CM5A), characterized by a strong AMOC periodicity at 20 years, previously explained by an upper ocean–atmosphere–sea ice coupled mode driving convection activity south of Iceland. Our study shows that this mechanism interacts constructively with the basin-wide propagation in the subsurface. This constructive feedback may explain why bi-decadal variability is so intense in this coupled model as compared to others.

Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.