Free Path Lengths in Quasi Crystals

The Lorentz gas is a model for a cloud of point particles (electrons) in a distribution of scatterers in space. The scatterers are often assumed to be spherical with a fixed diameter d, and the point particles move with constant velocity between the scatterers, and are specularly reflected when hitting a scatterer. There is no interaction between point particles. An interesting question concerns the distribution of free path lengths, i.e. the distance a point particle moves between the scattering events, and how this distribution scales with scatterer diameter, scatterer density and the distribution of the scatterers. It is by now well known that in the so-called Boltzmann–Grad limit, a Poisson distribution of scatterers leads to an exponential distribution of free path lengths, whereas if the scatterer distribution is periodic, the free path length distribution asymptotically behaves as a power law.     

Modelling of inextensible cable dynamics with experiments

The recognition of very stiff axial elastic motion compared to the motion in the transverse direction for cable dynamics motivates separation of the axial and transversal dynamics. For certain applications, e.g. real-time model-based control, fast calculation of the transverse motion may be of high importance, motivating the development of numerically efficient software code. Separation of axial dynamics renders possible neglection or simplification of the axial dynamics if appropriate for the system studied. A model is proposed with the assumption of axial inextensible material and negligible bending, torsion and shear stiffness in the cable. Experiments are carried out to verify the model, and the results are compared with simulations. The comparison between the experiments and numerical simulations showed good agreement up to the second frequency range with resonant behavior and the corresponding motion amplitudes.