Global Behavior Of Finite Energy Solutions To The dd-Dimensional Focusing Nonlinear Schr\"odinger Equation

We study the global behavior of finite energy solutions to the $d$-dimensional focusing nonlinear Schr\"odinger equation (NLS), $i \partial_t u+\Delta u+ |u|^{p-1}u=0,$ with initial data $u_0\in H^1,\; x \in R^n$. The nonlinearity power $p$ and the dimension $d$ are such that the scaling index $s=\frac{d}2-\frac2{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with \ME[u_0]<1 (\ME[u_0] stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient \g_u of a solution $u$ to NLS is initially less than 1, i.e., \g_u(0)<1, then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr\"odinger evolution as $t\to\pm\infty$); if the renormalized gradient \g_u(0)>1, then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle.Comment: 57 pages, 4 figures and updated reference

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

Symbiont diversity is not involved in depth acclimation in the Mediterranean sea whip Eunicella singularis

In symbiotic cnidarians, acclimation to depth and lower irradiance can involve physiological changes in the photosynthetic dinoflagellate endosymbiont, such as increased chlorophyll content, or qualitative modifications in the symbiont population in favour of better adapted strains. It has been argued that a lack of capacity to acquire new symbionts could limit the bathymetric distribution of the host species, or compromise its long-term survival in a changing environment. But is that always true? To address this question, we investigated the symbiont genetic diversity in Eunicella singularis, a Mediterranean sea whip species with a wide bathymetric distribution (10 to 50 m depth), which has recently suffered from mass mortalities after periods of abnormally high sea temperatures. We measured symbiont population densities and chlorophyll content in natural populations, and followed the response of the holobionts after reciprocal transplantations to deep and shallow depths. A total of 161 colonies were sampled at 2 depths (10 and 30 m) at 5 sites in the northwestern Mediterranean. All colonies harboured a single ribosomal Symbiodinium clade (A'), but a relatively high within-clade genetic diversity was found among and within colonies. This diversity was not structured by depth, even though the deeper colonies contained significantly lower population densities of symbionts and less chlorophyll. We did, however, reveal host-symbiont specificity among E. singularis and other Mediterranean cnidarian species. Transplantation experiments revealed a limit of plasticity for symbiont population density and chlorophyll content, which in turn questions the importance of the trophic role of Symbiodinium in E. singularis

RBF neural net based classifier for the AIRIX accelerator fault diagnosis

The AIRIX facility is a high current linear accelerator (2-3.5kA) used for flash-radiography at the CEA of Moronvilliers France. The general background of this study is the diagnosis and the predictive maintenance of AIRIX. We will present a tool for fault diagnosis and monitoring based on pattern recognition using artificial neural network. Parameters extracted from the signals recorded on each shot are used to define a vector to be classified. The principal component analysis permits us to select the most pertinent information and reduce the redundancy. A three layer Radial Basis Function (RBF) neural network is used to classify the states of the accelerator. We initialize the network by applying an unsupervised fuzzy technique to the training base. This allows us to determine the number of clusters and real classes, which define the number of cells on the hidden and output layers of the network. The weights between the hidden and the output layers, realising the non-convex union of the clusters, are determined by a least square method. Membership and ambiguity rejection enable the network to learn unknown failures, and to monitor accelerator operations to predict future failures. We will present the first results obtained on the injector.Comment: 3 pages, 4 figures, LINAC'2000 conferenc

Ultra-low Q values for neutrino mass measurements

We investigate weak nuclear decays with extremely small kinetic energy release (Q value) and thus extremely good sensitivity to the absolute neutrino mass scale. In particular, we consider decays into excited daughter states, and we show that partial ionization of the parent atom can help to tune Q values to << 1 keV. We discuss several candidate isotopes undergoing beta+, beta-, bound state beta, or electron capture decay, and come to the conclusion that a neutrino mass measurement using low-Q decays might only be feasible if no ionization is required, and if future improvements in isotope production technology, nuclear mass spectroscopy, and atomic structure calculations are possible. Experiments using ions, however, are extremely challenging due to the large number of ions that must be stored. New precision data on nuclear excitation levels could help to identify further isotopes with low-Q decay modes and possibly less challenging requirements.Comment: 7 pages, 2 figures; v2: Typos corrected, references adde

Enhancing Dark Matter Annihilation into Neutrinos

We perform a detailed and quasi model-independent analysis of direct annihilation of Dark Matter into neutrinos. Considering different cases for scalar and fermionic Dark Matter, we identify several settings in which this annihilation is enhanced, contrary to some statements in the literature. They key point is that several restrictions of, e.g., a supersymmetric framework do not hold in general. The mass generation mechanism of the neutrinos plays an important role, too. We illustrate our considerations by two examples that are not (as usually) suppressed by the smallness of the neutrino mass, for which we also present a numerical analysis. Our results can be easily used as guidelines for model building.Comment: 33 pages, 2 figure

BCG vaccination and leprosy protection: review of current evidence and status of BCG in leprosy control.

The bacillus Calmette-Guérin (BCG) vaccine, initially developed to provide protection against TB, also protects against leprosy; and the magnitude of this effect varies. Previous meta-analyses did not provide a summary estimate of the efficacy due to the heterogeneity of the results. We conducted a meta-analysis of published data including recently published studies (up to June 2009) to determine the efficacy of BCG protection on leprosy and to investigate whether age at vaccination, clinical form, number of doses, type of study, the latitude of study area and year of publication influence the degree of efficacy and explain the variation. In the light of the results, we argue for more emphasis on the role of BCG vaccination in leprosy control and research

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

Continuations of the nonlinear Schr\"odinger equation beyond the singularity

We present four continuations of the critical nonlinear \schro equation (NLS) beyond the singularity: 1) a sub-threshold power continuation, 2) a shrinking-hole continuation for ring-type solutions, 3) a vanishing nonlinear-damping continuation, and 4) a complex Ginzburg-Landau (CGL) continuation. Using asymptotic analysis, we explicitly calculate the limiting solutions beyond the singularity. These calculations show that for generic initial data that leads to a loglog collapse, the sub-threshold power limit is a Bourgain-Wang solution, both before and after the singularity, and the vanishing nonlinear-damping and CGL limits are a loglog solution before the singularity, and have an infinite-velocity{\rev{expanding core}} after the singularity. Our results suggest that all NLS continuations share the universal feature that after the singularity time $T_c$, the phase of the singular core is only determined up to multiplication by $e^{i\theta}$. As a result, interactions between post-collapse beams (filaments) become chaotic. We also show that when the continuation model leads to a point singularity and preserves the NLS invariance under the transformation $t\rightarrow-t$ and $\psi\rightarrow\psi^\ast$, the singular core of the weak solution is symmetric with respect to $T_c$. Therefore, the sub-threshold power and the{\rev{shrinking}}-hole continuations are symmetric with respect to $T_c$, but continuations which are based on perturbations of the NLS equation are generically asymmetric