Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator

The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical periodic orbits. Because of the three different scenarios depending on the ratio of its frequencies, the two-dimensional harmonic oscillator offers a unique way to explicitly analyze the role of symmetries in classical and quantum mechanics.Comment: 9 pages, 3 figures; to appear in Am. J. Phy

Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.Comment: 10 pages, 4 figures, to appear in j.math.phys

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure

Nonlinear response of dense colloidal suspensions under oscillatory shear: Mode-coupling theory and FT-rheology experiments

Using a combination of theory, experiment and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the non linearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory (LAOS) experiments (with FT-rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disc mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in excellent agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves and large amplitude oscillatory spectroscopy

Étude sur la faune du Bathonien des environs de Mâcon. Première partie

, . Étude sur la faune du Bathonien des environs de Mâcon. Première partie. Lyon : Laboratoire de géologie de la Faculté des sciences de Lyon, 1923 (Travaux du Laboratoire de Géologie de la Faculté des Sciences de Lyon. Ancienne série, 3

EMILIO VILLARI. — Studi acustici sulle flamme (Études acoustiques sur les flammes) ; Nuovo Cimento, 2e série, t. I , mai 1869

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Répertoire alphabétique des Bélemnites jurassiques précédé d’un essai de classification

, . Répertoire alphabétique des Bélemnites jurassiques précédé d'un essai de classification. Lyon : Laboratoire de géologie de la Faculté des sciences de Lyon, 1925 (Travaux du Laboratoire de Géologie de la Faculté des Sciences de Lyon. Ancienne série, 8

Flamme sifflante

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Observations sur la note précédente

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