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.

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

Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations

We consider a family of dispersion generalized Benjamin-Ono equations (dgBO) which are critical with respect to the L2 norm and interpolate between the critical modified (BO) equation and the critical generalized Korteweg-de Vries equation (gKdV). First, we prove local well-posedness in the energy space for these equations, extending results by Kenig, Ponce and Vega concerning the (gKdV) equations. Second, we address the blow up problem in the spirit of works of Martel and Merle on the critical (gKdV) equation, by studying rigidity properties of the (dgBO) flow in a neighborhood of solitons. We prove that when the model is close to critical (gKdV), solutions of negative energy close to solitons blow up in finite or infinite time in the energy space. The blow up proof requires in particular extensions to (dgBO) of monotonicity results for localized versions of L2 norms by pseudo-differential operator tools.Comment: Submitte

Asymptotic stability of solitons for the Benjamin-Ono equation

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of Martel and Merle (arXiv:0706.1174v2). As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.Comment: Submitted for publication on December 26, 200

Fano Resonances in Mid-Infrared Spectra of Single-Walled Carbon Nanotubes

This work revisits the physics giving rise to the carbon nanotubes phonon bands in the mid- infrared. Our measurements of doped and undoped samples of single-walled carbon nanotubes in Fourier transform infrared spectroscopy show that the phonon bands exhibit an asymmetric lineshape and that their effective cross-section is enhanced upon doping. We relate these observations to electron-phonon coupling or, more specifically, to a Fano resonance phenomenon. We note that only the dopant-induced intraband continuum couples to the phonon modes and that defects induced in the sidewall increase the resonance probabilities.Comment: 5 pages, 4 figures and 1 Supplementary Information File (in pdf

Effects of cultivation on the organic matter of grassland soils as determined by fractionation and radiocarbon dating

Includes bibliographical references (pages 425-426).The effects of cultivation on the net mineralization of carbon and nitrogen in a lacustrine Brown clay (Sceptre) and two Orthic Black soils on glacial till (Oxbow) were assessed with the aid of fractionation and radiocarbon dating techniques. Fractionation of the soil organic matter of comparative virgin and cultivated soils by acid hydrolysis and peptization in dilute NaOH showed that the distribution of carbon and nitrogen among fractions of these soils was similar. There was no measurable alteration in the mean residence time (MRT) of the soil during the first 15 to 20 yr of cultivation, during which time the Sceptre soil had lost 19% of its carbon and the Oxbow, 35%. However, the MRT increased from 250 yr before present (BP) to 710 years BP after 60 yr of cultivation of the Oxbow soil. The losses for nitrogen were 10% lower than for carbon in the Oxbow soil due to the recycling of nitrogen in the soil. The rate of loss of carbon from the Oxbow soil during the cultivation period was simulated by expressing it as the sum of two first order reactions using fractionation and carbon dating data as the variables

Analytical Expressions for Radiative Opacities of Low Z Plasmas

In this work we obtain analytical expressions for the radiative opacity of several low Z plasmas (He, Li, Be, and B) in a wide range of temperatures and densities. These formulas are obtained by fitting the proposed expression to mean opacities data calculated by using the code ABAKO/ RAPCAL. This code computes the radiative properties of plasmas, both in LTE and NLTE conditions, under the detailed-level-accounting approach. It has been successfully validated in the range of interest in previous works

Linac modeling for external beam radiotherapy quality assurance using a dedicated 2D pixelated detector

International audienceQuality assurance is a key issue in intensity modulated radiotherapy. Errors can occur in the dose delivery process induces significant differences between the planned treatment and the delivered one. In this context, the Medical Application Physics group of the LPSC is developing TraDeRa (Transparent Detector for Radiotherapy), a 2D pixelated matrix of ionization chambers located upstream to the patient. The signal map obtained with TraDeRa has to be processed to provide medical observables to quantify the quality of the treatment delivery. This relies on accurate Monte Carlo simulations benchmarked with measurements performed under a linear accelerator (Linac).The work described in this paper lies in the optimization of the Linac head simulation and the development of an innovative Monte Carlo/measurements comparison method to perform an accurate enough model of the X-ray production device. An optimized parametrization of the particles transport allowed an increase of the simulation efficiency by a factor 3. The characteristics of an electron beam of a reference Linac were matched with the simulation results by using dose deposition of the created X-ray beam in a water tank. Two parameters are particularly critical: the nominal energy of the electrons and the radial distribution of impact on the target. The innovative method was able to provide within minutes those two parameters for any Linac, achieving, for example, a 10 keV precision on the energy determination for a 6 MV operating Linac

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