2,587 research outputs found
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 -supercritical generalized KdV equations
In this paper we consider the slightly -supercritical gKdV equations
, with the nonlinearity
and . We will prove the existence and
stability of a blow-up dynamic with self-similar blow-up rate in the energy
space 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 -critical half-wave equation in one space
dimension where denotes the
first-order fractional derivative. Standard arguments show that there is a
critical threshold such that all solutions with extend globally in time, while solutions with 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 . More precisely, we construct a
family of minimal mass blowup solutions that are parametrized by the energy
and the linear momentum . In particular, our main result
(and its proof) can be seen as a model scenario of minimal mass blowup for
-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page
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