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David Chiron

Publications and source records attributed to David Chiron.

8 recordsLinked to original sources
arXiv2025

The Ongoing Decline in Activity of Comet 103P/Hartley 2

We report photometric observations of Comet 103P/Hartley 2 during its 2023 apparition. Our campaign, conducted from August through December 2023, combined data from a global network of citizen astronomers coordinated by Unistellar and the Association Fran\c{c}aise d'Astronomie. Photometry was derived using an automated pipeline for eVscope observations in partnership with the SETI Institute and aperture photometry via AstroLab Stellar. We find that the comet's peak reduced brightness, measured at $G_{\rm min} = 10.24 \pm 0.47$, continues a long-term fading trend since 1991. The decline in activity follows a per-apparition minimum magnitude increase of $\Delta G_{\rm min} = 0.59 \pm 0.11$ mag, corresponding to an approximately $42\%$ reduction in brightness each return. This trend implies that the comet's active fraction has declined by about an order of magnitude since 1991 and may indicate that Hartley 2 is no longer hyperactive by definition. The fading is consistent with progressive volatile depletion rather than orbital effects. These results offer insight into the evolutionary processes shaping Jupiter-family comets.

astro-ph.EP↗
arXiv2021

A uniqueness result for the two vortex travelling wave in the Nonlinear Schrodinger equation

For the Nonlinear Schrodinger equation in dimension 2, the existence of a global minimizer of the energy at fixed momentum has been established by Bethuel-Gravejat-Saut. This minimizer is a travelling wave for the Nonlinear Schrodinger equation. For large momentums, the propagation speed is small and the minimizer behaves like two well separated vortices. In that limit, we show the uniqueness of this minimizer, up to the invariances of the problem, hence proving the orbital stability of this travelling wave. This work is a follow up to two previous papers, where we constructed and studied a particular travelling wave of the equation. We show a uniqueness result on this travelling wave in a class of functions that contains in particular all possible minimizers of the energy.

math.AP↗
arXiv2019

Coercivity for travelling waves in the Gross-Pitaevskii equation in $\mathbb{R}^2$ for small speed

In the previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space. In particular, our result proves the non degeneracy of these travelling waves, which is a key step in the classification of these waves and for the construction of multi-travelling waves.

math.AP↗
arXiv2017

Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity, II

We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schrödinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension $ N \geq 2$. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.

math.AP↗
arXiv2015

From Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck Systems to Incompressible Euler Equations: the case with finite charge

We study the asymptotic regime of strong electric fields that leads from the Vlasov-Poisson system to the Incompressible Euler equations. We also deal with the Vlasov-Poisson-Fokker-Planck system which induces dissipative effects. The originality consists in considering a situation with a finite total charge confined by a strong external field. In turn, the limiting equation is set in a bounded domain, the shape of which is determined by the external confining potential. The analysis extends to the situation where the limiting density is non-homogeneous and where the Euler equation is replaced by the Lake Equation, also called Anelastic Equation.

math.AP↗
arXiv2012

Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit

We investigate the properties of finite energy travelling waves to the nonlinear Schrodinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results generalize an earlier result of F. Bethuel, P. Gravejat and J-C. Saut for the two-dimensional Gross-Pitaevskii equation, and provide a rigorous proof to a conjecture by C. Jones and P. H. Roberts about the existence of an upper branch of travelling waves in dimension three.

math.AP↗
arXiv2012

Stability and instability for subsonic travelling waves of the Nonlinear Schrödinger Equation in dimension one

We study the stability/instability of the subsonic travelling waves of the Nonlinear Schrödinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the Grillakis-Shatah-Strauss theory, proof of existence of an unstable eigenvalue via an Evans function) or stability. For the later, we show how to construct in a systematic way a Liapounov functional for which the travelling wave is a local minimizer. These approaches allow to give a complete stability/instability analysis in the energy space including the critical case of the kink solution. We also treat the case of a cusp in the energy-momentum diagram.

math.AP↗