Models for application of radiation boundary condition for MHD waves in collapse calculations

The problem of reflection of magnetohydrodynamic (MHD) waves at the boundary of a numerical grid has to be resolved in order to obtain reliable results for the end state of the (isothermal) collapse of a rotating, magnetic protostellar cloud. Since the goal of investigating magnetic braking in collapse simulations is to see if the transport of angular momentum via alfven waves is large enough to solve the angular momentum problem an approximation that artificially suppresses large amplitudes in the MHD waves can be self-defeating. For this reason, four alternate methods of handling reflected waves where no assumptions are made regarding the amplitudes of the waves were investigated. In order to study this problem (of reflection) without interference from other effects these methods were tried on two simpler cases. The four methods are discussed

Multi-vehicle planning using RRT-connect

The problem of planning multiple vehicles deals with the design of an effective algorithm that can cause multiple autonomous vehicles on the road to communicate and generate a collaborative optimal travel plan. Our modelling of the problem considers vehicles to vary greatly in terms of both size and speed, which makes it suboptimal to have a faster vehicle follow a slower vehicle or for vehicles to drive with predefined speed lanes. It is essential to have a fast planning algorithm whilst still being probabilistically complete. The Rapidly Exploring Random Trees (RRT) algorithm developed and reported on here uses a problem specific coordination axis, a local optimization algorithm, priority based coordination, and a module for deciding travel speeds. Vehicles are assumed to remain in their current relative position laterally on the road unless otherwise instructed. Experimental results presented here show regular driving behaviours, namely vehicle following, overtaking, and complex obstacle avoidance. The ability to showcase complex behaviours in the absence of speed lanes is characteristic of the solution developed