Interaction between dipolar forces, such as permanent magnets, generally leads to the formation of one-dimensional chains and rings. We investigated whether it was possible to let dipoles self-assemble into three-dimensional structures by encapsulating them in a shell with a specific shape. We found that the condition for self-assembly of a three-dimensional crystal is satisfied when the energies of dipoles in the parallel and antiparallel states are equal. Our experiments show that the most regular structures are formed using cylinders and cuboids and not by
spheroids. This simple design rule will help the self-assembly community to realize three-dimensional crystals from objects in the micrometer range, which opens up the way toward previously unknown metamaterials.

The extent to which one can use a thermodynamic description of turbulent flow as a source of stochastic kinetic energy for 3D self‐assembly of magnetically interacting macroscopic particles is investigated. It is confirmed that the speed of the objects in the flow field generated in this system obeys the Maxwell–Boltzmann distribution, and their random walk can be defined by a diffusion coefficient following from the Einstein relation. However, it is discovered that the analogy with Brownian dynamics breaks down when considering the directional components of the velocity. For the vectorial components, neither the equipartition theorem nor the Einstein relation is obeyed. Moreover, the kinetic energy estimated from the random walk of individual objects is one order of magnitude higher than the value estimated from Boltzmann statistics on the interaction between two spheres with embedded magnets. These results show that introducing stochastic kinetic energy into a self‐assembly process by means of turbulent flow can to a great extent be described by standard thermodynamic theory, but anisotropies and the specific nature of the interactions need to be taken into account.

Robust and accurate pose estimation of moving systems is a challenging task that is often tackled by combining information from different sensor subsystems in a multi-sensor fusion setup. To obtain robust and accurate estimates, it is crucial to respect the exact time of each measurement. Data fusion is additionally challenged when the sensors are running at different rates and the information is subject to processing- and transmission delays. In this paper, we present an optimization-based moving horizon estimator which allows to estimate and compensate for time-varying measurement delays without the need for any synchronization signals between the sensors. By adopting a direct collocation approach, we find a continuous-time solution for the navigation states which allows us to incorporate the discrete-time sensor measurements in an optimal way despite the presence of unknown time delays. The presented sensor fusion algorithm is applied to the problem of pose estimation by fusing data of a high-rate inertial measurement unit and a low-rate centimeter-accurate global navigation satellite system receiver using simulated and real-data experiments.