Classical particle scattering for power-law two-body potentials

We present a rigorous study of the classical scattering for anytwo-body inter-particle potential of the form $v(r)=g/r^\gamma$, with\gamma\textgreater{}0, for repulsive (g\textgreater{}0) and attractive (g\textless{}0)interactions. We give a derivation of the complete power series of thedeflection angle in terms of the impact factor for the weak scatteringregime (large impact factors) as well as the asymptotic expressionsfor the hard scattering regime (small impact factors). We see a verydifferent qualitative and quantitative behavior depending whether theinteraction is repulsive or attractive. In the latter case, thefamilies of trajectories depend also strongly on the value of$\gamma$. We also study carefully the modifications of the resultswhen a regularization is introduced in the potential at small scales.We check and illustrate all the results with the exact integration ofthe equations of motion.Comment: 23 pages, 17 figure

Geometric optics and boundary layers for Nonlinear Schrodinger equations

We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrodinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary condition is also studied.Comment: 44 page

Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity, II

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schr\"odinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension $N \geq 2$. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.Comment: Final version, accepted for publication in the {\it Archive for Rational Mechanics and Analysis.} The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-017-1131-

Successful private–public funding of paediatric medicines research: lessons from the EU programme to fund research into off-patent medicines

The European Paediatric Regulation mandated the European Commission to fund research on off-patent medicines with demonstrated therapeutic interest for children. Responding to this mandate, five FP7 project calls were launched and 20 projects were granted. This paper aims to detail the funded projects and their preliminary results. Publicly available sources have been consulted and a descriptive analysis has been performed. Twenty Research Consortia including 246 partners in 29 European and non-European countries were created (involving 129 universities or public funded research organisations, 51 private companies with 40 SMEs, 7 patient associations). The funded projects investigate 24 medicines, covering 10 therapeutic areas in all paediatric age groups. In response to the Paediatric Regulation and to apply for a Paediatric Use Marketing Authorisation, 15 Paediatric Investigation Plans have been granted by the EMAPaediatric Committee, including 71 studies of whom 29 paediatric clinical trials, leading to a total of 7,300 children to be recruited in more than 380 investigational centres. Conclusion: Notwithstanding the EU contribution for each study is lower than similar publicly funded projects, and also considering the complexity of paediatric research, these projects are performing high-quality research and are progressing towards the increase of new paediatric medicines on the market. Private–public partnerships have been effectively implemented, providing a good example for future collaborative actions. Since these projects cover a limited number of offpatent drugs and many unmet therapeutic needs in paediatrics remain, it is crucial foreseeing new similar initiatives in forthcoming European funding programmes

Travelling waves for the Gross-Pitaevskii equation II

The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built. In dimension three, we also show that there are no travelling wave solutions of small energy.Comment: Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remark

Convergence of Ginzburg-Landau functionals in 3-d superconductivity

In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.Comment: 45 page

Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hölder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs

Incidence and phenotypes of childhood-onset genetic epilepsies:a prospective population-based national cohort

Epilepsy is common in early childhood. In this age group it is associated with high rates of therapy-resistance, and with cognitive, motor, and behavioural comorbidity. A large number of genes, with wide ranging functions, are implicated in its aetiology, especially in those with therapy-resistant seizures. Identifying the more common single-gene epilepsies will aid in targeting resources, the prioritization of diagnostic testing and development of precision therapy. Previous studies of genetic testing in epilepsy have not been prospective and population-based. Therefore, the population-incidence of common genetic epilepsies remains unknown. The objective of this study was to describe the incidence and phenotypic spectrum of the most common single-gene epilepsies in young children, and to calculate what proportion are amenable to precision therapy. This was a prospective national epidemiological cohort study. All children presenting with epilepsy before 36 months of age were eligible. Children presenting with recurrent prolonged (>10 min) febrile seizures; febrile or afebrile status epilepticus (>30 min); or with clusters of two or more febrile or afebrile seizures within a 24-h period were also eligible. Participants were recruited from all 20 regional paediatric departments and four tertiary children’s hospitals in Scotland over a 3-year period. DNA samples were tested on a custom-designed 104-gene epilepsy panel. Detailed clinical information was systematically gathered at initial presentation and during follow-up. Clinical and genetic data were reviewed by a multidisciplinary team of clinicians and genetic scientists. The pathogenic significance of the genetic variants was assessed in accordance with the guidelines of UK Association of Clinical Genetic Science (ACGS). Of the 343 patients who met inclusion criteria, 333 completed genetic testing, and 80/333 (24%) had a diagnostic genetic finding. The overall estimated annual incidence of single-gene epilepsies in this well-defined population was 1 per 2120 live births (47.2/100 000; 95% confidence interval 36.9–57.5). PRRT2 was the most common single-gene epilepsy with an incidence of 1 per 9970 live births (10.0/100 000; 95% confidence interval 5.26–14.8) followed by SCN1A: 1 per 12 200 (8.26/100 000; 95% confidence interval 3.93–12.6); KCNQ2: 1 per 17 000 (5.89/100 000; 95% confidence interval 2.24–9.56) and SLC2A1: 1 per 24 300 (4.13/100 000; 95% confidence interval 1.07–7.19). Presentation before the age of 6 months, and presentation with afebrile focal seizures were significantly associated with genetic diagnosis. Single-gene disorders accounted for a quarter of the seizure disorders in this cohort. Genetic testing is recommended to identify children who may benefit from precision treatment and should be mainstream practice in early childhood onset epilepsy