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

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

Why a splitting in the final state cannot explain the GSI-Oscillations

In this paper, I give a pedagogical discussion of the GSI anomaly. Using two different formulations, namely the intuitive Quantum Field Theory language of the second quantized picture as well as the language of amplitudes, I clear up the analogies and differences between the GSI anomaly and other processes (the Double Slit experiment using photons, $e^+ e^- \to \mu^+ \mu^-$ scattering, and charged pion decay). In both formulations, the conclusion is reached that the decay rate measured at GSI cannot oscillate if only Standard Model physics is involved and the initial hydrogen-like ion is no coherent superposition of more than one state (in case there is no new, yet unknown, mechanism at work). Furthermore, a discussion of the Quantum Beat phenomenon will be given, which is often assumed to be able to cause the observed oscillations. This is, however, not possible for a splitting in the final state only.Comment: 10 pages, 3 figures; matches published version (except for some stylistic ambiguities

Physics and engineering of nuclear reactors at the "Ecole Nationale Supérieure de Physique de Grenoble" of the "Institut National Polytechnique de Grenoble"

International audienceIf the use of fossil fuels is to be limited to curtail greenhouse gas emissions, fission nuclear energy is, along with new renewable energies, one of the primary energy sources able to respond significantly to the increasing worldwide demand. In this context, it is necessary to design and evaluate new generations of nuclear reactors as defined by the Gen IV International Forum. The Energy and Nuclear Engineering (GEN) curriculum of the Ecole Nationale Supérieure de Physique de Grenoble (ENSPG), one of the nine engineering schools of the Grenoble Institute of Technology (INPG), includes a balanced blend of basic courses in energy, nuclear and thermal hydraulic engineering, together with the corresponding engineering sciences to cover the technological aspects. The objective is to train engineers who shall master not only nuclear engineering for the production of electricity but, more broadly, energy and nuclear technologies and their various application fields

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

Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system

We describe the asymptotic behavior as time goes to infinity of solutions of the 2 dimensional corotational wave map system and of solutions to the 4 dimensional, radially symmetric Yang-Mills equation, in the critical energy space, with data of energy smaller than or equal to a harmonic map of minimal energy. An alternative holds: either the data is the harmonic map and the soltuion is constant in time, or the solution scatters in infinite time

Plasmonic Resonances and Electromagnetic Forces Between Coupled Silver Nanowires

We compute the electromagnetic response and corresponding forces between two silver nanowires. The wires are illuminated by a plane wave which has the electric field vector perpendicular to the axis of the wires, insuring that plasmonic resonances can be excited. We consider a nontrivial square cross section geometry that has dimensions on the order of $0.1 \lambda$, where $\lambda$ is the wavelength of the incident electromagnetic field. We find that due to the plasmonic resonance, there occurs great enhancement of the direct and mutual electromagnetic forces that are exerted on the nanowires. The Lippman-Schwinger volume integral equation is implemented to obtain solutions to Maxwell's equations for various $\lambda$ and separation distances between wires. The forces are computed using Maxwell's stress tensor and numerical results are shown for both on and off resonant conditions

A hemorrhagic factor in moldy lespedeza hay

Digitized 2007 AES.Includes bibliographical references (page 11)