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