Existence and Stability of standing waves for supercritical NLS with a Partial Confinement

We prove the existence of orbitally stable ground states to NLS with a partial confinement together with qualitative and symmetry properties. This result is obtained for nonlinearities which are $L^2$-supercritical, in particular we cover the physically relevant cubic case. The equation that we consider is the limit case of the cigar-shaped model in BEC.Comment: Revised version, accepted on Comm. Math. Physic

The electron's dance

A joint Fermilab/SLAC publicationParis' Trocadéro science exhibition allows science enthusiasts to see--and even control--a real electron accelerator

On a functional satisfying a weak Palais-Smale condition

In this paper we study a quasilinear elliptic problem whose functional satisfies a weak version of the well known Palais-Smale condition. An existence result is proved under general assumptions on the nonlinearities.Comment: 18 page

Salt shock-inducible Photosystem I cyclic electron transfer in Synechocystis PCC6803 relies on binding of ferredoxin:NADP+ reductase to the thylakoid membranes via its CpcD phycobilisome-linker homologous N-terminal domain

AbstractRelative to ferredoxin:NADP+ reductase (FNR) from chloroplasts, the comparable enzyme in cyanobacteria contains an additional 9 kDa domain at its amino-terminus. The domain is homologous to the phycocyanin associated linker polypeptide CpcD of the light harvesting phycobilisome antennae. The phenotypic consequences of the genetic removal of this domain from the petH gene, which encodes FNR, have been studied in Synechocystis PCC 6803. The in frame deletion of 75 residues at the amino-terminus, rendered chloroplast length FNR enzyme with normal functionality in linear photosynthetic electron transfer. Salt shock correlated with increased abundance of petH mRNA in the wild-type and mutant alike. The truncation stopped salt stress-inducible increase of Photosystem I-dependent cyclic electron flow. Both photoacoustic determination of the storage of energy from Photosystem I specific far-red light, and the re-reduction kinetics of P700+, suggest lack of function of the truncated FNR in the plastoquinone–cytochrome b6f complex reductase step of the PS I-dependent cyclic electron transfer chain. Independent gold-immunodecoration studies and analysis of FNR distribution through activity staining after native polyacrylamide gelelectrophoresis showed that association of FNR with the thylakoid membranes of Synechocystis PCC 6803 requires the presence of the extended amino-terminal domain of the enzyme. The truncated ΔpetH gene was also transformed into a NAD(P)H dehydrogenase (NDH1) deficient mutant of Synechocystis PCC 6803 (strain M55) (T. Ogawa, Proc. Natl. Acad. Sci. USA 88 (1991) 4275–4279). Phenotypic characterisation of the double mutant supported our conclusion that both the NAD(P)H dehydrogenase complex and FNR contribute independently to the quinone cytochrome b6f reductase step in PS I-dependent cyclic electron transfer. The distribution, binding properties and function of FNR in the model cyanobacterium Synechocystis PCC 6803 will be discussed

Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schr\"odinger equation

We study the standing waves for a fourth-order Schr\"odinger equation with mixed dispersion that minimize the associated energy when the $L^2-$norm (the \textit{mass}) } is kept fixed. We need some non-homogeneous Gagliardo-Nirenberg-type inequalities and we develop a method to prove such estimates that should be useful elsewhere. We prove optimal results on the existence of minimizers in the {\it mass-subcritical } and {\it mass-critical } cases. In the { \it mass supercritical} case we show that global minimizers do not exist, and we investigate the existence of local minimizers. If the mass does not exceed some threshold $\mu_0 \in (0,+\infty)$, our results on "best" local minimizers are also optimal.Comment: 46 page

Parallel declines in species and genetic diversity driven by anthropogenic disturbance: a multispecies approach in a French Atlantic dune system.

Numerous studies assess the correlation between genetic and species diversities, but the processes underlying the observed patterns have only received limited attention. For instance, varying levels of habitat disturbance across a region may locally reduce both diversities due to extinctions, and increased genetic drift during population bottlenecks and founder events. We investigated the regional distribution of genetic and species diversities of a coastal sand dune plant community along 240 kilometers of coastline with the aim to test for a correlation between the two diversity levels. We further quantify and tease apart the respective contributions of natural and anthropogenic disturbance factors to the observed patterns. We detected significant positive correlation between both variables. We further revealed a negative impact of urbanization: Sites with a high amount of recreational infrastructure within 10 km coastline had significantly lowered genetic and species diversities. On the other hand, a measure of natural habitat disturbance had no effect. This study shows that parallel variation of genetic and species diversities across a region can be traced back to human landscape alteration, provides arguments for a more resolute dune protection, and may help to design priority conservation areas