This paper presents SinguLab, a graphical user interface for the singularity analysis of parallel robots. The algorithm is based on Grassmann-Cayley algebra. The proposed tool is interactive and introduces the designer to the singularity analysis performed by this method, showing all the stages along the procedure and eventually showing the solution algebraically and graphically, allowing as we...

We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cos-mologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three ...

We study the properties of a future singularity encountered by a perfect fluid observer in tilting spatially homogeneous Bianchi cos-mologies. We derive the boost formulae for the Weyl tensor to establish that, for two observers that are asymptotically null with respect to each other, their respective Weyl parameters generally both tend to zero, constant, or infinity together. We examine three ...

In their long-term study of the approach to the singularity in generic cosmological spacetimes [1–5], Belinskii, Khalatnikov, and Lifshitz (BKL) concluded that generic cosmological spacetimes approach the singularity as a (different) Mixmaster universe [6] at every spatial point. The Mixmaster universe is characterized by “oscillations” from one Kasner solution [7] to another. When BKL consider...

The parabolic-profile model for the singularity spectrum f(α) of fully-developed turbulence (FDT) is pursued further. This model is shown to provide not only considerable insight into the qualitative aspects of the intermittency problem but also the universal aspects associated with it. The parabolic-profile model also affords, unlike the multi-fractal model, an analytical calculation of probab...