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

Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability

A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - Bénard convection

GePEToS : A Geant4 Monte Carlo simulation package for Positron Emission Tomography

GePEToS is a simulation framework developed over the last few years for assessing the instrumental performance of future PET scanners. It is based on Geant4, written in Object-Oriented C++ and runs on Linux platforms. The validity of GePEToS has been tested on the well-known Siemens ECAT EXACT HR+ camera. The results of two application examples are presented : the design optimization of a liquid Xe micro-PET camera dedicated to small animal imaging as well as the evaluation of the effect of a strong axial magnetic field on the image resolution of a Concorde P4 micro-PET camera.Comment: 5 pages, 12 figures, submitted to IEEE Transactions on Nuclear Scienc

Experimental study of a liquid Xenon PET prototype module

A detector using liquid Xenon in the scintillation mode is studied for Positron Emission Tomography (PET). The specific design aims at taking full advantage of the liquid Xenon properties. It does feature a promising insensitive to any parallax effect. This work reports on the performances of the first LXe prototype module, equipped with a position sensitive PMT operating in the VUV range (178 nm).Comment: Proc. of the 7th International Workshops on Radiation Imaging Detectors (IWORID-7), Grenoble, France 4-7 July 200

A low power 12-bit and 25-MS/s pipelined ADC for the ILC/Ecal integrated readout

International audienc

Light Propagation in Inhomogeneous Universes. IV. Strong Lensing and Environmental Effects

We study the gravitational lensing of high-redshift sources in a LCDM universe. We have performed a series of ray-tracing experiments, and selected a subsample of cases of strong lensing (multiple images, arcs, and Einstein rings). For each case, we identify a massive galaxy that is primarily responsible for lensing, and studied how the various density inhomogeneities along the line of sight (other galaxies, background matter) affect the properties of the image. The matter located near the lensing galaxy, and physically associated with it, has a small effect. The background matter increases the magnification by a few percents at most, while nearby galaxies can increase it by up to about 10 percent. The effect on the image separation is even smaller. The only significant effect results from the random alignment of physically unassociated galaxies, which can increase the magnification by factors of several, create additional images, and turn arcs into rings. We conclude that the effect of environment on strong lensing in negligible in general, and might be important only in rare cases. We show that our conclusion does not depend on the radial density profile of the galaxies responsible for lensing.Comment: 23 pages, 7 figures (one in color). Accepted for publication in The Astrophysical Journal. Minor typos correcte

Anthropic Explanation of the Dark Matter Abundance

I use Bousso's causal diamond measure to make a statistical prediction for the dark matter abundance, assuming an axion with a large decay constant f_a >> 10^{12} GeV. Using a crude approximation for observer formation, the prediction agrees well with observation: 30% of observers form in regions with less dark matter than we observe, while 70% of observers form in regions with more dark matter. Large values of the dark matter ratio are disfavored by an elementary effect: increasing the amount of dark matter while holding fixed the baryon to photon ratio decreases the number of baryons inside one horizon volume. Thus the prediction is rather insensitive to assumptions about observer formation in universes with much more dark matter than our own. The key assumption is that the number of observers per baryon is roughly independent of the dark matter ratio for ratios near the observed value.Comment: 10 pages; v3: published version, references adde

Altitude Reconstitution of a Small Scientific Satellite using a Limited Set of On-Board Sensors

The ALEXIS spacecraft carries a limited set of attitude instruments on board. The scientific mission of ALEXIS requires after the fact knowledge of the spacecraft attitude at all times. Reconstitution of the attitude is performed as one of the permanent tasks of the microcomputer based ground station. ALEXIS carries a fine sun-sensor, an Infrared horizon crossing indicator and a magnetometer. Because of the orbital and attitude configurations horizon and sun will not be observed during sizable fractions of some orbits. The attitude will be estimated at all times by an extended fitter making use of whatever data is available. The state vector includes disturbance and misalignment terms. Fiber initialization uses the first available set of valid data from sun sensor and magnetometer, for a deterministic fix insuring rapid convergence. Magnetic field measurements provide a ceiling to the possible errors when the optical sensors are not operating, and can be used as back up. Detailed simulations of the filter were run to assess its performance. The simulations include major disturbance torques, misalignments, and earth oblateness effects. They show that the filter maintains knowledge of the attitude well within the mission data requirements. As a result, with a minimal amount of low cost instrumentation, without a star tracker on board, ALEXIS attitude and rates can be reconstituted for all times from a simple microcomputer based ground station. This illustrates a practical trade-off between hardware and software

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page