Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a Navier-Stokes flow in $\Omega \cup \partial \Omega \cup \Sigma \epsilon$ with Reynolds' number of order 1/$\epsilon$ in $\Sigma \epsilon$. Using $\Gamma$-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface $\Gamma$2. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context

Ultra-High-Energy Cosmic Ray Acceleration by Magnetic Reconnection in Newborn Accretion Induced Collapse Pulsars

We here investigate the possibility that the ultra-high energy cosmic ray (UHECR) events observed above the GZK limit are mostly protons accelerated in reconnection sites just above the magnetosphere of newborn millisecond pulsars which are originated by accretion induced collapse (AIC). We show that AIC-pulsars with surface magnetic fields $10^{12} G < B_{\star} \lesssim 10^{15}$ G and spin periods $1 ms \lesssim P_{\star} < 60 ms$, are able to accelerate particles to energies $\geq 10^{20}$ eV. Because the expected rate of AIC sources in our Galaxy is very small (\sim 10^{-5} yr^{-1}), the corresponding contribution to the flux of UHECRs is neglegible, and the total flux is given by the integrated contribution from AIC sources produced by the distribution of galaxies located within the distance which is unaffected by the GZK cutoff ($\sim 50$ Mpc). We find that the reconnection efficiency factor needs to be $\xi \gtrsim 0.1$ in order to reproduce the observed flux of UHECRs.Comment: Latex file, 16 pages, 2 figures, replaced with revised version accepted for publication in the ApJ letter

Synthetic approaches to break the chemical shift degeneracy of glycans

NMR spectroscopy is the leading technique for determining glycans’ three-dimensional structure and dynamic in solution as well as a fundamental tool to study protein-glycan interactions. To overcome the severe chemical shift degeneracy of these compounds, synthetic probes carrying NMR-active nuclei (e.g., 13 C or 19 F) or lanthanide tags have been proposed. These elegant strategies permitted to simplify the complex NMR analysis of unlabeled analogues, shining light on glycans’ conformational aspects and interaction with proteins. Here, we highlight some key achievements in the synthesis of specifically labeled glycan probes and their contribution towards the fundamental understanding of glycans