Using high-speed photography, we investigate two distinct regimes of the impact dynamics of granular jets with noncircular cross sections. In the steady-state regime, we observe the formation of thin granular sheets with anisotropic shapes and show that the degree of anisotropy increases with the aspect ratio of the jet's cross section. Our results illustrate the liquidlike behavior of granular...

We show the existence of noncircular, self-similar solutions to the three-dimensional Hele-Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction speed and the surface tension coefficient....

Sensor based planning for rod-shaped robots is necessary for the realistic deployment of noncircular symmetric robots into unknown environments. To this end, the rod hierarchical generalized Voronoi graph (rod-HGVG), introduced in this paper, is a roadmap for rod-like robots. A key feature of this roadmap is that it can be incrementally constructed using distance (range) information. This plann...

The cavity expansion approach has been a popular tool to interpret wide range of geotechnical problems over the last several decades. Most previous research focused on cylindrical and/or spherical cavities, whereas nonstandard cavities have received much less attention. To address this shortcoming, paper presents general theoretical framework for two-dimensional (2D) displacement-controlled und...