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Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits
2015
International audience; The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using the standard tools of Riemannian geometry (curvature computations, geodesic convexity), the time minimal case is associated to a Finsler metric which is not smooth. Nevertheless a qualitative analysis of the geodesic flow is given in this article to describe the optimal transfers. In particular we prove geodesic convexity of the elliptic domain.
Computation of conjugate times in smooth optimal control: the COTCOT algorithm
2006
Conjugate point type second order optimality conditions for extremals associated to smooth Hamiltonians are evaluated by means of a new algorithm. Two kinds of standard control problems fit in this setting: the so-called regular ones, and the minimum time singular single-input affine systems. Conjugate point theory is recalled in these two cases, and two applications are presented: the minimum time control of the Kepler and Euler equations.
On some Riemannian aspects of two and three-body controlled problems
2009
The flow of the Kepler problem (motion of two mutually attracting bodies) is known to be geodesic after the work of Moser [20], extended by Belbruno and Osipov [2, 21]: Trajectories are reparameterizations of minimum length curves for some Riemannian metric. This is not true anymore in the case of the three-body problem, and there are topological obstructions as observed by McCord et al. [19]. The controlled formulations of these two problems are considered so as to model the motion of a spacecraft within the influence of one or two planets. The averaged flow of the (energy minimum) controlled Kepler problem with two controls is shown to remain geodesic. The same holds true in the case of o…
Investigation of the vibrational dynamics of the HCN/CNH isomers through high order canonical perturbation theory
2000
International audience; Molecular vibrations of the molecule HCN/CNH are examined using a combination of a minimum energy path Hamiltonian and high order canonical perturbation theory , as suggested in a recent work [D. Sugny and M. Joyeux, J. Chem. Phys. 112, 31 (2000)]. In addition, the quantum analog of the classical CPT is presented and results obtained therefrom are compared to the classical ones. The MEP Hamiltonian is shown to provide an accurate representation of the original potential energy surface and a convenient starting point for the CPT. The CPT results are subsequently used to elucidate the molecular dynamics: It appears that the isomerization dynamics of HCN/CNH is very tri…
On the high resolution spectroscopy and intramolecular potential function of SO2
2009
Abstract Two weak stretching bands, ν 1 + 3 ν 3 and 3 ν 1 + ν 3 , of the sulfur dioxide molecule have been recorded at high resolution and analyzed for the first time with using a Fourier transform Bruker IFS-120 HR interferometer. About 1000 transitions with J max . = 51, K a max . = 16 , and 900 transitions with J max . = 53, K a max . = 16 have been assigned to the bands ν 1 + 3 ν 3 and 3 ν 1 + ν 3 , respectively. Analysis of the recorded spectra was made using the model of isolated vibrational states. Parameters obtained from the fit reproduce the initial experimental ro-vibrational energies with the rms deviation of 0.0006 and 0.0012 cm −1 for the bands, 3 ν 1 + ν 3 and ν 1 …
Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses
2009
We present a general and versatile technique of population transfer based on {\it parallel adiabatic passage} by femtosecond shaped pulses. Their amplitude and phase are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times. We show that this technique allows the robust adiabatic population transfer in a Raman system with the total pulse area as low as 3 $\pi$, corresponding to a fluence of one order of magnitude below the conventional stimulated Raman adiabatic passage process. This process of short duration, typically pico- and subpicosecond, is easily implementable with the modern pulse shaper technology and opens the possibility of ul…
A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families
2013
Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.
Straightforward access to water-soluble unsymmetrical sulfoxanthene dyes: application to the preparation of far-red fluorescent dyes with large stoke…
2014
An efficient synthesis of water-soluble unsymmetrical sulforhodamine/sulforhodol fluorophores containing a single julolidine fragment is presented. Owing to their valuable spectral properties in aqueous buffers, these dyes, especially those bearing a free aniline or phenol moiety, are valuable components of fluorogenic probes for a variety of biosensing applications. A further extension of this synthetic methodology to unusual phenols, namely 7-N,N-dialkylamino-4-hydroxy coumarins has enabled us to provide a new family water-soluble dyes of large Stokes’ shift with far-red spectral features.
Statistics of transitions for Markov chains with periodic forcing
2013
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.
Integrable Systems and Factorization Problems
2002
The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is…