Stable self similar blow up dynamics for slightly L^2 supercritical NLS equations

We consider the focusing nonlinear Schr\"odinger equations $i\partial_t u+\Delta u +u|u|^{p-1}=0$ in dimension $1\leq N\leq 5$ and for slightly $L^2$ supercritical nonlinearities p_c with $p_c=1+\frac{4}{N}$ and 0<\e\ll 1. We prove the existence and stability in the energy space $H^1$ of a self similar finite time blow up dynamics and provide a qualitative description of the singularity formation near the blow up tim

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop Level

In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, interactions involving electrically neutral and doubly charged bosons are investigated. We also investigate flavour changes at 1-loop level. In all cases we find that the essential theoretical requirements can be reduced to a few basic conditions on the particle content and the coupling matrices. For 1-loop diagrams, we also investigate how exactly a GIM-suppression can occur that will strongly reduce the rates of lepton flavour violating effects even if they are in principle present in a certain theory. In all chapters, we apply our criteria to several models which can in general induce lepton flavour violation, e.g. LR-symmetric models or the MSSM. In the end we give a summarizing table of the obtained results, thereby demonstrating the applicability of our criteria to a large class of models beyond the Standard Model.Comment: 31 pages, 2 figure

Spectroscopic binaries among AGB stars from HERMES/Mercator: the case of V Hya

We report on our search for spectroscopic binaries among a sample of AGB stars. Observations were carried out in the framework of the monitoring of radial velocities of (candidate) binary stars performed at the Mercator 1.2m telescope, using the HERMES spectrograph. We found evidence for duplicity in UV Cam, TU Tau, BL Ori, VZ Per, T Dra, and V Hya. This short communication focus on V Hya, found to behave like RV Tau of the b subtype, which are binaries surrounded by a disc.Comment: Poster presented at IAU Symp. 343 "Why Galaxies Care About AGB Stars", Vienna, august 201

Potassium: a new actor on the globular cluster chemical evolution stage. The case of NGC 2808

We derive [K/Fe] abundance ratios for 119 stars in the globular cluster NGC 2808, all of them having O, Na, Mg and Al abundances homogeneously measured in previous works. We detect an intrinsic star-to-star spread in the Potassium abundance. Moreover [K/Fe] abundance ratios display statistically significant correlations with [Na/Fe] and [Al/Fe], and anti-correlations with [O/Fe] and [Mg/Fe]. All the four Mg deficient stars ([Mg/Fe]<0.0) discovered so far in NGC 2808 are enriched in K by ~0.3 dex with respect to those with normal [Mg/Fe]. NGC 2808 is the second globular cluster, after NGC 2419, where a clear Mg-K anti-correlation is detected, albeit of weaker amplitude. The simultaneous correlation/anti-correlation of [K/Fe] with all the light elements usually involved in the chemical anomalies observed in globular cluster stars, strongly support the idea that these abundance patterns are due to the same self-enrichment mechanism that produces Na-O and Mg-Al anti-correlations. This finding suggests that detectable spreads in K abundances may be typical in the massive globular clusters where the self-enrichment processes are observed to produce their most extreme manifestations.Comment: Accepted for publication by ApJ, 5 pages, 3 figure

Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Improved Limit on theta_{13} and Implications for Neutrino Masses in Neutrino-less Double Beta Decay and Cosmology

We analyze the impact of a measurement, or of an improved bound, on theta_{13} for the determination of the effective neutrino mass in neutrino-less double beta decay and cosmology. In particular, we discuss how an improved limit on (or a specific value of) theta_{13} can influence the determination of the neutrino mass spectrum via neutrino-less double beta decay. We also discuss the interplay with improved cosmological neutrino mass searches.Comment: 22 pages, 5 figures. Minor corrections, matches version in PR

Stable self-similar blow-up dynamics for slightly L2L^2-supercritical generalized KdV equations

In this paper we consider the slightly $L^2$-supercritical gKdV equations $\partial_t u+(u_{xx}+u|u|^{p-1})_x=0$, with the nonlinearity $5<p<5+\varepsilon$ and $0<\varepsilon\ll 1$ . We will prove the existence and stability of a blow-up dynamic with self-similar blow-up rate in the energy space $H^1$ and give a specific description of the formation of the singularity near the blow-up time.Comment: 38 page

Soft L_e-L_mu-L_tau flavour symmetry breaking and sterile neutrino keV Dark Matter

We discuss how a $L_e-L_\mu-L_\tau$ flavour symmetry that is softly broken leads to keV sterile neutrinos, which are a prime candidate for Warm Dark Matter. This is to our knowledge the first model where flavour symmetries are applied simultaneously to active and sterile neutrinos explaining at the same time active neutrino properties and this peculiar Dark Matter scenario. The essential point is that different scales of the symmetry breaking and the symmetry preserving entries in the mass matrix lead to one right-handed neutrino which is nearly massless compared to the other two. Furthermore, we naturally predict vanishing $\theta_{13}$ and maximal $\theta_{23}$, while the correct value of $\theta_{12}$ must come from the mixing of the charged leptons. We can furthermore predict an exact mass spectrum for the light neutrinos, which will be testable in the very near future.Comment: 14 page

A Study of a Fused Course in Physics and Chemistry for Watertown High School

The writers had in mind the modification of the present science curriculum in the Watertown High School. In doing this, they sought the answers to the following questions: Can physics and chemistry be fused into a one-year course for pupils who do not enroll in the conventional physics and chemistry classes? Will such a course be feasible and workable? What content will be included? How will it be taught? How will the laboratory work be handled? Can it be adapted to the interests and ability levels of the pupils? Will the achievement of the pupils in this fused course be comparable to the achievement of the pupils in the other physical science courses? In attempting to find the answers to· these questions, a review of the work which had already been done along the line of fusing physics and chemistry was made. Objectives for science teaching in high school were sought. An outline of content for the fused physics and chemistry course was developed and revised. The course was taught by the writers, each having a section, for a period of one year, and the achievement of the pupils in the fused course compared to those in the conventional physics and chemistry classes. The detailed procedure for these are to be found in the following sections of this study