Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

Anisotropic Galactic Outflows and Enrichment of the Intergalactic Medium. I: Monte Carlo Simulations

We have developed an analytical model to describe the evolution of anisotropic galactic outflows. With it, we investigate the impact of varying opening angle on galaxy formation and the evolution of the IGM. We have implemented this model in a Monte Carlo algorithm to simulate galaxy formation and outflows in a cosmological context. Using this algorithm, we have simulated the evolution of a comoving volume of size [12h^(-1)Mpc]^3 in the LCDM universe. Starting from a Gaussian density field at redshift z=24, we follow the formation of ~20,000 galaxies, and simulate the galactic outflows produced by these galaxies. When these outflows collide with density peaks, ram pressure stripping of the gas inside the peak may result. This occurs in around half the cases and prevents the formation of galaxies. Anisotropic outflows follow the path of least resistance, and thus travel preferentially into low-density regions, away from cosmological structures (filaments and pancakes) where galaxies form. As a result, the number of collisions is reduced, leading to the formation of a larger number of galaxies. Anisotropic outflows can significantly enrich low-density systems with metals. Conversely, the cross-pollution in metals of objects located in a common cosmological structure, like a filament, is significantly reduced. Highly anisotropic outflows can travel across cosmological voids and deposit metals in other, unrelated cosmological structures.Comment: 32 pages, 9 figures (2 color). Revised version accepted in Ap

Giacobini-Zinner comet: Polarimetric and physical observations

The results of observations of the Giacobini-Zinner comet on 25 and 31 October 1959 are presented. The magnitude of the comet was measured photoelectrically in two spectral regions. The radius is on the order of one kilometer. The photoelectric measurements of comets 1959b and 1957c were used to measure the abundances of the CN and C2 radicals and of solid particles in the heads

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

Comment on `Hawking radiation from fluctuating black holes'

Takahashi & Soda (2010 Class. Quantum Grav. v27 p175008, arXiv:1005.0286) have recently considered the effect (at lowest non-trivial order) of dynamical, quantized gravitational fluctuations on the spectrum of scalar Hawking radiation from a collapsing Schwarzschild black hole. However, due to an unfortunate choice of gauge, the dominant (even divergent) contribution to the coefficient of the spectrum correction that they identify is a pure gauge artifact. I summarize the logic of their calculation, comment on the divergences encountered in its course and comment on how they could be eliminated, and thus the calculation be completed.Comment: 12 pages, 1 fig; feynmp, amsref

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

Unexpected Scaling of the Performance of Carbon Nanotube Transistors

We show that carbon nanotube transistors exhibit scaling that is qualitatively different than conventional transistors. The performance depends in an unexpected way on both the thickness and the dielectric constant of the gate oxide. Experimental measurements and theoretical calculations provide a consistent understanding of the scaling, which reflects the very different device physics of a Schottky barrier transistor with a quasi-one-dimensional channel contacting a sharp edge. A simple analytic model gives explicit scaling expressions for key device parameters such as subthreshold slope, turn-on voltage, and transconductance.Comment: 4 pages, 4 figure

Instability of two interacting, quasi-monochromatic waves in shallow water

We study the nonlinear interactions of waves with a doubled-peaked power spectrum in shallow water. The starting point is the prototypical equation for nonlinear uni-directional waves in shallow water, i.e. the Korteweg de Vries equation. Using a multiple-scale technique two defocusing coupled Nonlinear Schr\"odinger equations are derived. We show analytically that plane wave solutions of such a system can be unstable to small perturbations. This surprising result suggests the existence of a new energy exchange mechanism which could influence the behaviour of ocean waves in shallow water.Comment: 4 pages, 2 figure

Evidence of Brillouin scattering in an ytterbium-doped double-clad fiber laser

We have designed and performed an experiment that permitted direct observation of Brillouin backscattering in an Yb-doped double-clad fiber laser. Fifteen Brillouin-shifted frequencies were observed for the first time to our knowledge. We clearly demonstrate that stimulated Brillouin scattering is directly responsible for both fast transient dynamics of the laser and reduction of the laser’s pulse width