Examples of sharp asymptotic profiles of singular solutions to an elliptic equation with a sign-changing non-linearity

The first two authors [Proc. Lond. Math. Soc. (3) {\bf 114}(1):1--34, 2017] classified the behaviour near zero for all positive solutions of the perturbed elliptic equation with a critical Hardy--Sobolev growth $$-\Delta u=|x|^{-s} u^{2^\star(s)-1} -\mu u^q \hbox{ in }B\setminus\{0\},$$ where $B$ denotes the open unit ball centred at $0$ in $\mathbb{R}^n$ for $n\geq 3$, $s\in (0,2)$, $2^\star(s):=2(n-s)/(n-2)$, $\mu>0$ and $q>1$. For $q\in (1,2^\star-1)$ with $2^\star=2n/(n-2)$, it was shown in the op. cit. that the positive solutions with a non-removable singularity at $0$ could exhibit up to three different singular profiles, although their existence was left open. In the present paper, we settle this question for all three singular profiles in the maximal possible range. As an important novelty for $\mu>0$, we prove that for every $q\in (2^\star(s) -1,2^\star-1)$ there exist infinitely many positive solutions satisfying $|x|^{s/(q-2^\star(s)+1)}u(x)\to \mu^{-1/(q-2^\star(s)+1)}$ as $|x|\to 0$, using a dynamical system approach. Moreover, we show that there exists a positive singular solution with $\liminf_{|x|\to 0} |x|^{(n-2)/2} u(x)=0$ and $\limsup_{|x|\to 0} |x|^{(n-2)/2} u(x)\in (0,\infty)$ if (and only if) $q\in (2^\star-2,2^\star-1)$.Comment: Mathematische Annalen, to appea

Random walks with imperfect trapping in the decoupled-ring approximation

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model, where for sufficiently large transverse diffusion the system is described by the mean-field kinetics. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics.Comment: 10 page

Magnetic reconnection at the termination shock in a striped pulsar wind

Most of the rotational luminosity of a pulsar is carried away by a relativistic magnetised wind in which the matter energy flux is negligible compared to the Poynting flux. Near the equatorial plane of an obliquely rotating pulsar magnetosphere, the magnetic field reverses polarity with the pulsar period, forming a wind with oppositely directed field lines. This structure is called a striped wind; dissipation of alternating fields in the striped wind is the object of our study. The aim of this paper is to study the conditions required for magnetic energy release at the termination shock of the striped pulsar wind. Magnetic reconnection is considered via analytical methods and 1D relativistic PIC simulations. An analytical condition on the upstream parameters for partial and full magnetic reconnection is derived from the conservation laws of energy, momentum and particle number density across the relativistic shock. Furthermore, by using a 1D relativistic PIC code, we study in detail the reconnection process at the termination shock. We found a very simple criterion for dissipation of alternating fields at the termination shock, depending on the upstream parameters of the flow. 1D relativistic PIC simulations are in agreement with our criterion. Thus, alternating magnetic fields annihilate easily at relativistic highly magnetised shocks.Comment: Accepted by A&

Sensitivity of freshwater periphytic diatoms to agricultural herbicides

The biomonitoring of pesticide pollution in streams and rivers using algae such as diatoms remains difficult. The responses of diatomcommunities to toxic stress in streamwater are disturbed by the variations of environmental parameters. In this study, periphytic algae collected in situwere exposed under controlled conditions to two major herbicides used in French agriculture (isoproturon and s-metolachlor). Three exposure regimes were tested: 5 and 30gL−1 for 6 days and 30gL−1 for 3 days followed by a recovery period of 3 days. The algal biomasses were assessed from pigment concentrations (chlorophyll a and c) and from live cell density. The highest concentration (30gL−1) of isoproturon inhibited the biomass increase statistically significantly. In periphyton exposed to 5 and 30gL−1 of s-metolachlor, chlorophyll c concentration and live cell densitywere also statistically significantly lower than in the control. Periphyton left to recover after reduced exposure duration (3 days) showed higher growth rates after treatment with s-metolachlor than with isoproturon. Taxonomic identifications showed that species like Melosira varians, Nitzschia dissipata and Cocconeis placentula were not affected by the herbicide exposure. Other species like Eolimna minima and Navicula reichardtiana were more sensitive. Studying diatoms according to their trophic mode showed that facultative heterotroph specieswere statistically significantly favoured by isoproturon exposure at the highest concentration. Results obtained with s-metolachlor exposure showed a disturbance of cell multiplication rather than that of photosynthesis. These results suggest that photosynthesis inhibitors like isoproturon favour species able to survive when the autotroph mode is inhibited

Damage-cluster distributions and size effect on strength in compressive failure

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments

Central bank intervention and exchange rate volatility, its continuous and jump components

We analyze the relationship between interventions and volatility at daily and intra-daily frequencies for the two major exchange rate markets. Using recent econometric methods to estimate realized volatility, we employ bipower variation to decompose this volatility into a continuously varying and jump component. Analysis of the timing and direction of jumps and interventions imply that coordinated interventions tend to cause few, but large jumps. Most coordinated operations explain, statistically, an increase in the persistent (continuous) part of exchange rate volatility. This correlation is even stronger on days with jumps.

A dynamical collective calculation of supernova neutrino signals

We present the first calculations with three flavors of collective and shock wave effects for neutrino propagation in core-collapse supernovae using hydroynamical density profiles and the S matrix formalism. We explore the interplay between the neutrino-neutrino interaction and the effects of multiple resonances upon the time signal of positrons in supernova observatories. A specific signature is found for the inverted hierarchy and a large third neutrino mixing angle and we predict, in this case, a dearth of lower energy positrons in Cherenkov detectors midway through the neutrino signal and the simultaneous revelation of valuable information about the original fluxes. We show that this feature is also observable with current generation neutrino detectors at the level of several sigmas.Comment: 4 pages, 5 figure

Exact solution of the anisotropic special transition in the O(n) model in 2D

The effect of surface exchange anisotropies is known to play a important role in magnetic critical and multicritical behavior at surfaces. We give an exact analysis of this problem in d=2 for the O(n) model by using Coulomb gas, conformal invariance and integrability techniques. We obtain the full set of critical exponents at the anisotropic special transition--where the symmetry on the boundary is broken down to O(n_1)xO(n-n_1)--as a function of n_1. We also obtain the full phase diagram and crossover exponents. Crucial in this analysis is a new solution of the boundary Yang-Baxter equations for loop models. The appearance of the generalization of Schramm-Loewner Evolution SLE_{\kappa,\rho} is also discussed.Comment: 4 pages, 2 figure

Delay interferometric single-shot measurement of a petawatt-class laser longitudinal chromatism corrector

International audienceIn this paper we present a self-referenced interferometric single-shot measurement technique that we use to evaluate the longitudinal chromatism compensation made by a diffractive lens corrector. A diffractive lens with a delay of 1 ps is qualified for a 60 mm beam aperture. This corrector was implemented on the Alisé Nd:glass power chain. We qualify the corrector and the Alisé power chain chromatism, demonstrating the potential of this measuring principle as well as the interest of diffractive lenses to correct longitudinal chromatism of petawatt-class lasers

The ruminal level of trans-10 fatty acids of dairy cows is linked to the composition of bacterial community

The ruminal level of trans-10 fatty acids of dairy cows is linked to the composition of bacterial communit