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Quantum and quasi-classical effects in the strong field ionization and subsequent excitation of nitrogen molecules
No full textInternational audienceThe processes leading to the N lasing are rather complex and even the population distribution after the pump laser excitation is unknown. In this paper, we study the population distribution at electronic and vibrational levels in N driven by ultra-short laser pulse at the wavelengths of 800 nm and 400 nm by using the quantum-mechanical time-domain incoherent superposition model based on the time-dependent Schrödinger equation and the quasi-classical model assuming instantaneous ionization injection described by density matrix. It is shown that while both models provide qualitatively similar results, the quasi-classical instantaneous ionization injection model underestimates the population inversions corresponding to the optical transitions at 391 nm, 423 nm and 428 nm due to the assumption of quantum mixed states at the ionization time. A fast and accurate correction to this error is proposed. This work solidifies the theoretical models for population at vibrational states in N and paves the way to uncover the mechanism of the N lasing
Resisting the Repugnant Conclusion: The Space Age, Space 2.0, and the History of the Subjects of Astrofuturism
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Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and recovery of the saturation effect
No full textInternational audienceThis article considers the nonlinear dynamics of coupled oscillators featuring strong coupling in 1:2 internal resonance. In forced oscillations, this particular interaction is the source of energy exchange, leading to a particular shape of the response curves, as well as quasi-periodic responses and a saturation phenomenon. These main features are embedded in the simplest system which considers only the two resonant quadratic monomials conveying the 1:2 internal resonance, since they are the proeminent source allowing one to explain these phenomena. However, it has been shown recently that those features can be substantially modified by the presence of non-resonant quadratic terms. The aim of the present study is thus to explain the effect of the non-resonantquadratic terms on the dynamics. To that purpose, the normal form up to the third order is used, since the effect of the non-resonant quadratic terms will be transferred into the resonant cubic terms. Analytical solutions are detailed using a second-order mutliple scale expansion. A thorough investigation of the backbone curves, their stability and bifurcation, and the link to the forced–damped solutions, is detailed, showing in particular interesting features that had not been addressed in earlier studies. Finally, the saturation effect is investigated, and it is shown how to correct the detuning effect of the cubic terms thanks to a specific tuning of non-resonant quadratic terms and resonant cubic terms. This choice, derived analytically, is shown to extend the validity of the saturation effect to larger amplitudes, which can thus be used in all applications where this effect is needed e.g. for control
Comparison of nonlinear methods for reduced-order modeling of geometrically nonlinear structures
No full textInternational audienceThe aim of this contribution is to review and compare three different methods that have been proposed in order to derive reduced-order models for geometrically nonlinear structures, and relying on a nonlinear technique to better take into account the nonlinearities of the initial problem. The three methods are: implicit condensation, quadratic manifold derived with modal derivatives, and projection onto an invariant manifold, tangent at the origin to the linear eigenspace of the master modes. The methods are briefly reviewed theoretically and then compared with dedicated examples
On the approximation of electromagnetic fields by edge finite elements. Part 4: analysis of the model with one sign-changing coefficient
No full textInternational audienceIn electromagnetism, in the presence of a negative material surrounded by a classical material, the electric permittivity, and possibly the magnetic permeability, can exhibit a sign-change at the interface. In this setting, the study of electromagnetic phenomena is a challenging topic. We focus on the time-harmonic Maxwell equations in a bounded set of , and more precisely on the numerical approximation of the electromagnetic fields by edge finite elements. Special attention is paid to low-regularity solutions, in terms of the Sobolev scale . With the help of T-coercivity, we address the case of one sign-changing coefficient, both for the model itself, and for its discrete version. Optimal a priori error estimates are derived
High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point
No full textInternational audienceAbstract This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems in oscillatory form expressed in the physical basis, so that the technique is directly applicable to mechanical problems discretised by the finite element method. Two nonlinear mappings, respectively related to displacement and velocity, are introduced, and the link between the two is made explicit at arbitrary order of expansion, under the assumption that the damping matrix is diagonalised by the conservative linear eigenvectors. The same development is performed on the reduced-order dynamics which is computed at generic order following different styles of parametrisation. More specifically, three different styles are introduced and commented: the graph style, the complex normal form style and the real normal form style. These developments allow making better connections with earlier works using these parametrisation methods. The technique is then applied to three different examples. A clamped-clamped arch with increasing curvature is first used to show an example of a system with a softening behaviour turning to hardening at larger amplitudes, which can be replicated with a single mode reduction. Secondly, the case of a cantilever beam is investigated. It is shown that invariant manifold of the first mode shows a folding point at large amplitudes. This exemplifies the failure of the graph style due to the folding point on a real structure, whereas the normal form style is able to pass over the folding. Finally, a MEMS (Micro Electro Mechanical System) micromirror undergoing large rotations is used to show the importance of using high-order expansions on an industrial example
Experimental investigation of the influence of the panel stiffness on the behaviour of a wedge under slamming
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Interaction cinématique sol-structure d'un massif renforcé par inclusions rigides sous séisme
No full textInternational audienceInteraction cinématique sol-structure d'un massif renforcé par inclusions rigides sous séism
