Scaling limit of the invasion percolation cluster on a regular tree

We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive stochastic processes. This convergence allows us to recover and make precise certain asymptotic results for the IPC. In particular, we relate the limit of the rescaled level sets of the IPC to the local time of the scaled height function.Comment: Published in at http://dx.doi.org/10.1214/11-AOP731 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

The Thorium Molten Salt Reactor : Moving on from the MSBR

A re-evaluation of the Molten Salt Breeder Reactor concept has revealed problems related to its safety and to the complexity of the reprocessing considered. A reflection is carried out anew in view of finding innovative solutions leading to the Thorium Molten Salt Reactor concept. Several main constraints are established and serve as guides to parametric evaluations. These then give an understanding of the influence of important core parameters on the reactor's operation. The aim of this paper is to discuss this vast research domain and to single out the Molten Salt Reactor configurations that deserve further evaluation.Comment: 11 pages, 8 figures, 6 table

Fast Thorium Molten Salt Reactors started with Plutonium

One of the pending questions concerning Molten Salt Reactors based on the 232Th/233U fuel cycle is the supply of the fissile matter, and as a consequence the deployment possibilities of a fleet of Molten Salt Reactors, since 233U does not exist on earth and is not yet produced in the current operating reactors. A solution may consist in producing 233U in special devices containing Thorium, in Pressurized Water or Fast Neutrons Reactors. Two alternatives to produce 233U are examined here: directly in standard Molten Salt Reactors started with Plutonium as fissile matter and then operated in the Th/233U cycle; or in dedicated Molten Salt Reactors started and fed with Plutonium as fissile matter and Thorium as fertile matter. The idea is to design a critical reactor able to burn the Plutonium and the minor actinides presently produced in PWRs, and consequently to convert this Plutonium into 233U. A particular reactor configuration is used, called unique channel configuration in which there is no moderator in the core, leading to a quasi fast neutron spectrum, allowing Plutonium to be used as fissile matter. The conversion capacities of such Molten Salt Reactors are excellent. For Molten Salt Reactors only started with Plutonium, the assets of the Thorium fuel cycle turn out to be quickly recovered and the reactors characteristics turn out to be equivalent to Molten Salt Reactors operated with 233U only. Using a combination of Molten Salt Reactors started or operated with Plutonium and of Molten Salt Reactors started with 233U, the deployment capabilities of these reactors fully satisfy the condition of sustainability