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

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

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

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Observations sur la note précédente

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Méthode pour étudier la propagation des ondes

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Dentin bond durability after three years using a dentin bonding agent with and without priming.

OBJECTIVES: This three-year study was conducted to evaluate the tensile bond strengths of a dual-cured bonding resin, with and without priming, to bovine dentin. METHODS: Superficial bovine dentin was conditioned with 37% phosphoric acid and left unprimed (control) or was primed with 5-NMSA. Clearfil Photobond (Kuraray Co., Japan) was placed and light-cured, a layer of Protect Liner (Kuraray Co.) was applied, cured, then covered with Photo Clearfil Bright (Kurary Co.) resin composite and cured. Bonds were stressed in tension to failure at 1 d, 1 mon, 3 mon, 6 mon, 1 y and 3 y after preparation. Ten specimens were made for each group. Results were analyzed using one-way ANOVA and Duncan's multiple range test. Visual and SEM observations determined mode of failure and were analyzed using the Mann-Whitney U-test. Separate 1 d and 3 y specimens were fractured across the bonded interface and observed using a Field Emission SEM. After observation, the photomicrographs were compared for visual qualitative changes between the two time periods. RESULTS: The control (non-primed) group showed only a small decrease in bond strengths over 3 y, but in the primed group, a significant decrease was observed (p < 0.05). The bond strength of the non-primed group (5.2 MPa) was less than the primed group (10.6 MPa) at 1 d (p < 0.01), but by 3 y, the bonds of both groups were similar, 4.3 MPa and 5.5 MPa, respectively. Fractography indicated that only adhesive failure occurred in the control group. Failure in the primed group was cohesive in dentin initially, but shifted to the base or top of the hybrid layer after 1 y. Field Emission SEM observations showed hybrid layer formation in the primed group, but minimal resin infiltration in the control group. SIGNIFICANCE: Initially greater bond strengths were obtained for the primed group compared to the unprimed group (p < 0.01). However, by 3 y, the bond strength had decreased markedly in the primed group (p < 0.01), being almost the same for both groups. It was concluded that priming may only be useful to achieve strong bonding in the short term. These results may have significant implications related to clinical longevity of restorations.link_to_subscribed_fulltex