Two-point correlation function of galaxy distribution shows that the structure in the present Universe is scale-free up to a certain scale (at least several tens Mpc), which suggests that a fractal structure may exist. If small primordial density fluctuations have a fractal structure, the present fractal-like nonlinear structure below the horizon scale could be naturally explained. We analyze a...

We consider an eigenvalue problem for a divergence form elliptic operator Aε with high contrast periodic coefficients with period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of ‘order one’ size. The local perturbation of coefficients for such operator could result in emergence of localised waves eigenfunctions with corresponding eigenva...

We consider an eigenvalue problem for a divergence form elliptic operator Aε with high contrast periodic coefficients with period ε in each coordinate, where ε is a small parameter. The coefficients are perturbed on a bounded domain of ‘order one’ size. The local perturbation of coefficients for such operator could result in emergence of localized waves eigenfunctions with corresponding eigenva...

The problem of controlling force and position of a exible link manipulator in contact with a compliant environment is considered in this paper. Using singular perturbation theory, a slow subsystem associated with rigid motion dynamics and a fast subsystem associated with link exible dynamics are identi ed. Hence a two-time scale control strategy is adopted, consisting in a force and position co...

In this paper, we tackle the problem of nonlinear adaptive hybrid control of constrained robots with flexible links. According t o the physical properties of a flexible manipulator, a two time-scale approach, namely, singular perturbation a p proach, is further utilized for thorough analysis and general controller design. It is shown tha t asymptotic motional tracking can be effectively achieve...