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

Quantifying and controlling entanglement in the quantum magnet Cs2_2CoCl4_4

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs$_2$CoCl$_4$, a close realization of the $S=1/2$ transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one- and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.Comment: Main text: 7 pages, 4 figures. Supplementary Information: 15 pages, 15 figure

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

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