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Fractures are ubiquitous and can lead to the catastrophic material failure of materials. Although fracturing in a two-dimensional plane is well understood, all fractures are extended in and propagate through three-dimensional space. Moreover, their behaviour is complex. Here we show that the forward propagation of a fracture front occurs through an initial rupture, nucleated at some localized position, followed by a very rapid transverse expansion at velocities as high as the Rayleigh-wave speed. We study fracturing in a circular geometry that achieves an uninterrupted extended fracture front and use a fluid to control the loading conditions that determine the amplitude of the forward jump. We find that this amplitude correlates with the transverse velocity. Dynamic rupture simulations capture the observations for only a high transverse velocity. These results highlight the importance of transverse dynamics in the forward propagation of an extended fracture.

 

This article proposes the application of a distributed containment control algorithm to a team of mobile robots. This paper builds on the containment controller developed by Yuan et al. (2019) for generic linear multi-agent system and tested in simulation only. In this article, we particularize the controller for the case of multiple mobile robots by including it into a two-layer control scheme. The high-level controller computes a desired position for the mobile robots, that is then used as reference trajectory for the low-level controller. The resulting control system is implemented as a fully distributed system on a team of mobile robots and validated in simulations and experiments.