Existence and multiplicity for elliptic problems with quadratic growth in the gradient

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.Comment: To appear in Comm. PD

Global bifurcation for asymptotically linear Schr\"odinger equations

We prove global asymptotic bifurcation for a very general class of asymptotically linear Schr\"odinger equations \begin{equation}\label{1} \{{array}{lr} \D u + f(x,u)u = \lam u \quad \text{in} \ {\mathbb R}^N, u \in H^1({\mathbb R}^N)\setmimus\{0\}, \quad N \ge 1. {array}. \end{equation} The method is topological, based on recent developments of degree theory. We use the inversion $u\to v:= u/\Vert u\Vert_X^2$ in an appropriate Sobolev space $X=W^{2,p}({\mathbb R}^N)$, and we first obtain bifurcation from the line of trivial solutions for an auxiliary problem in the variables (\lambda,v) \in {\mathbb R} \x X. This problem has a lack of compactness and of regularity, requiring a truncation procedure. Going back to the original problem, we obtain global branches of positive/negative solutions 'bifurcating from infinity'. We believe that, for the values of $\lambda$ covered by our bifurcation approach, the existence result we obtain for positive solutions of \eqref{1} is the most general so fa

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

Long time dynamics and coherent states in nonlinear wave equations

We discuss recent progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.Comment: bases on the authors presentation at 2015 AMMCS-CAIMS Congress, to appear in Fields Institute Communications: Advances in Applied Mathematics, Modeling, and Computational Science 201

CH4 emission estimates from an active landfill site inferred from a combined approach of CFD modelling and in situ FTIR measurements

Globally, the waste sector contributes to nearly a fifth of anthropogenic methane emitted to the atmosphere and is the second largest source of methane in the UK. In recent years great improvements to reduce those emissions have been achieved by installation of methane recovery systems at landfill sites and subsequently methane emissions reported in national emission inventories have been reduced. Nevertheless, methane emissions of landfills remain uncertain and quantification of emission fluxes is essential to verify reported emission inventories and to monitor changes in emissions. Here we present a new approach for methane emission quantification from a complex source like a landfill site by applying a Computational Fluid Dynamics (CFD) model to calibrated in situ measurements of methane as part of a field campaign at a landfill site near Ipswich, UK, in August 2014. The methane distribution for different meteorological scenarios is calculated with the CFD model and compared to methane mole fractions measured by an in situ Fourier Transform Infrared (FTIR) spectrometer downwind of the prevailing wind direction. Assuming emissions only from the active site, a mean daytime flux of 0.83 mg m−2 s−1, corresponding to 53.26 kg h−1, was estimated. The addition of a secondary source area adjacent to the active site, where some methane hotspots were observed, improved the agreement between the simulated and measured methane distribution. As a result, the flux from the active site was reduced slightly to 0.71 mg m−2 s−1 (45.56 kg h−1), at the same time an additional flux of 0.32 mg m−2 s−1 (30.41 kg h−1) was found from the secondary source area. This highlights the capability of our method to distinguish between different emission areas of the landfill site, which can provide more detailed information about emission source apportionment compared to other methods deriving bulk emissions

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Results of final focus test beam

International audienceThe beam experiments of Final Focus Test Beam (FFTB) started in September 1993 at SLAC, and have produced a 1.7 μm×75 nm spot of 46 GeV electron beam. A number of new techniques involving two nanometer spot-size monitors have been developed. Several beam diagnostic/tuning schemes are applied to achieve and maintain the small spot. This experiment opens the way toward the nanometer world for future linear collider

Pathogenic NR2F1 variants cause a developmental ocular phenotype recapitulated in a mutant mouse model

Pathogenic NR2F1 variants cause a rare autosomal dominant neurodevelopmental disorder referred to as the Bosch-Boonstra-Schaaf Optic Atrophy Syndrome. Although visual loss is a prominent feature seen in affected individuals, the molecular and cellular mechanisms contributing to visual impairment are still poorly characterized. We conducted a deep phenotyping study on a cohort of 22 individuals carrying pathogenic NR2F1 variants to document the neurodevelopmental and ophthalmological manifestations, in particular the structural and functional changes within the retina and the optic nerve, which have not been detailed previously. The visual impairment became apparent in early childhood with small and/or tilted hypoplastic optic nerves observed in 10 cases. High-resolution optical coherence tomography imaging confirmed significant loss of retinal ganglion cells with thinning of the ganglion cell layer, consistent with electrophysiological evidence of retinal ganglion cells dysfunction. Interestingly, for those individuals with available longitudinal ophthalmological data, there was no significant deterioration in visual function during the period of follow-up. Diffusion tensor imaging tractography studies showed defective connections and disorganization of the extracortical visual pathways. To further investigate how pathogenic NR2F1 variants impact on retinal and optic nerve development, we took advantage of an Nr2f1 mutant mouse disease model. Abnormal retinogenesis in early stages of development was observed in Nr2f1 mutant mice with decreased retinal ganglion cell density and disruption of retinal ganglion cell axonal guidance from the neural retina into the optic stalk, accounting for the development of optic nerve hypoplasia. The mutant mice showed significantly reduced visual acuity based on electrophysiological parameters with marked conduction delay and decreased amplitude of the recordings in the superficial layers of the visual cortex. The clinical observations in our study cohort, supported by the mouse data, suggest an early neurodevelopmental origin for the retinal and optic nerve head defects caused by NR2F1 pathogenic variants, resulting in congenital vision loss that seems to be non-progressive. We propose NR2F1 as a major gene that orchestrates early retinal and optic nerve head development, playing a key role in the maturation of the visual system