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Connected and autonomous vehicles (CAVs) have the potential to disrupt road transportation. CAVs provide several attractive features, such as seamless connectivity and fine-grained control, which can be exploited to improve the efficiency of traffic networks. In this work, the problem of CAV coordination at an unsignalized intersection crossing is considered, aiming to select the CAV trajectories that minimize fuel consumption and/or travel time. Nonetheless, the minimization of travel time implies high fuel consumption and vice-versa. For this reason, this work considers the problem of simultaneously optimizing the fuel consumption-travel time trade-off for a set of CAVs that are expected to arrive at the intersection within a specific time-window. As the resulting problem is non-convex, we construct a Mixed-Integer Programming formulation that provides tight lower and upper bounds. We also develop a heuristic convex-concave procedure that yields fast, highquality solutions. Simulation results validate the effectiveness of the proposed approaches and highlight the importance of optimizing the fuel consumption-travel time trade-off, as small compromises in travel time produce significant fuel savings.

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Bose-Einstein condensates with tunable interatomic interactions have been studied intensely in recent experiments. The investigation of the collapse of a condensate following a sudden change in the nature of the interaction from repulsive to attractive has led to the observation of a remnant condensate that did not undergo further collapse. We suggest that this high-density remnant is in fact the absolute minimum of the energy, if the attractive atomic interactions are nonlocal, and is therefore inherently stable. We show that a variational trial function consisting of a superposition of two distinct gaussians is an accurate representation of the wavefunction of the ground state of the conventional local Gross-Pitaevskii field equation for an attractive condensate and gives correctly the points of emergence of instability. We then use such a superposition of two gaussians as a variational trial function in order to calculate the minima of the energy when it includes a nonlocal interaction term. We use experimental data in order to study the long range of the nonlocal interaction, showing that they agree very well with a dimensionally derived expression for this range.