Stability of Two-Dimensional Soft Quasicrystals

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.Comment: 11 pages, 7 figure

Dark matter haloes in interacting dark energy models : formation history, density profile, spin, and shape

The interacting dark energy (IDE) model, which considers the interaction between dark energy and dark matter, provides a natural mechanism to alleviate the coincidence problem and can also relieve the observational tensions under the ?CDM model. Previous studies have put constraints on IDE models by observations of cosmic expansion history, cosmic microwave background, and large-scale structures. However, these data are not yet enough to distinguish IDE models from ?CDM effectively. Because the non-linear structure formation contains rich cosmological information, it can provide additional means to differentiate alternative models. In this paper, based on a set of N-body simulations for IDE models, we investigate the formation histories and properties of dark matter haloes and compare with their ?CDM counterparts. For the model with dark matter decaying into dark energy and the parameters being the best-fitting values from previous constraints, the structure formation is markedly slowed down, and the haloes have systematically lower mass, looser internal structure, higher spin, and anisotropy. This is inconsistent with the observed structure formation, and thus this model can be safely ruled out from the perspective of non-linear structure formation. Moreover, we find that the ratio of halo concentrations between IDE and ?CDM counterparts depends sensitively on the interaction parameter and is independent of halo mass. This can act as a powerful probe to constrain IDE models. Our results concretely demonstrate that the interaction of the two dark components can affect the halo formation considerably, and therefore the constraints from non-linear structures are indispensable.Peer reviewe

Towards Safe Landing of Falling Quadruped Robots Using a 3-DoF Morphable Inertial Tail

Falling cat problem is well-known where cats show their super aerial reorientation capability and can land safely. For their robotic counterparts, a similar falling quadruped robot problem, has not been fully addressed, although achieving safe landing as the cats has been increasingly investigated. Unlike imposing the burden on landing control, we approach to safe landing of falling quadruped robots by effective flight phase control. Different from existing work like swinging legs and attaching reaction wheels or simple tails, we propose to deploy a 3-DoF morphable inertial tail on a medium-size quadruped robot. In the flight phase, the tail with its maximum length can self-right the body orientation in 3D effectively; before touch-down, the tail length can be retracted to about 1/4 of its maximum for impressing the tail's side-effect on landing. To enable aerial reorientation for safe landing in the quadruped robots, we design a control architecture, which has been verified in a high-fidelity physics simulation environment with different initial conditions. Experimental results on a customized flight-phase test platform with comparable inertial properties are provided and show the tail's effectiveness on 3D body reorientation and its fast retractability before touch-down. An initial falling quadruped robot experiment is shown, where the robot Unitree A1 with the 3-DoF tail can land safely subject to non-negligible initial body angles.Comment: 7 pages, 8 figures, submit to ICRA202