Topological equivalence of crystal and quasicrystal band structures

A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an explicit construction, we here argue that the end states have precisely the same origin as their counterparts in commensurate models and that incommensurability does not in fact provide a meaningful connection to the topological classification of systems in higher dimensions. In particular, we show that it is possible to smoothly interpolate between states with commensurate and incommensurate modulation parameters without closing the band gap and without states crossing the band gap.Comment: 7 pages, 9 figures. Editors' Suggestio

Joint Dynamics and Adaptive Feedforward Control of Lightweight Industrial Robots

The use of lightweight strain-wave transmissions in collaborative industrial robots leads to structural compliance and a complex nonlinear behavior of the robot joints. Furthermore, wear and temperature changes lead to variations in the joint dynamics behavior over time. The immediate negative consequences are related to the performance of motion and force control, safety, and lead-through programming.This thesis introduces and investigates new methods to further increase the performance of collaborative industrial robots subject to complex nonlinear and time-varying joint dynamics behavior. Within this context, the techniques of mathematical modeling, system identification, and adaptive estimation and control are applied. The methods are experimentally validated using the collaborative industrial robots by Universal Robots.Mathematically, the robot and joint dynamics are considered as two coupled subsystems. The robot dynamics are derived and linearly parametrized to facilitate identification of the inertial parameters. Calibrating these parameters leads to improvements in torque prediction accuracy of 16.5 %-28.5 % depending on the motion.The joint dynamics are thoroughly analyzed and characterized. Based on a series of experiments, a comprehensive model of the robot joint is established taking into account the complex nonlinear dynamics of the strain-wave transmission, that is the nonlinear compliance, hysteresis, kinematic error, and friction. The steady-state friction is considered to depend on angular velocity, load torque, and temperature. The dynamic friction characteristics are described by an Extended Generalized Maxwell-Slip (E-GMS) model which describes in a combined framework; hysteresis characteristics that depend on angular position and Coulomb friction that depend on load torque. E-GMS model-based feedforward control improves the torque prediction accuracy by a factor 2.1 and improve the tracking error by a factor 1.5.An E-GMS model-based adaptive feedforward controller is developed to address the issue of friction changing with wear and temperature. The adaptive control strategy leads to improvements in torque prediction of 84 % and tracking error of 20 %

Josephson effect in a Weyl SNS junction

We calculate the Josephson current density j(ϕ) for a Weyl superconductor–normal-metal–superconductor junction for which the outer terminals are superconducting Weyl metals and the normal layer is a Weyl (semi)metal. We describe the Weyl (semi)metal using a simple model with two Weyl points. The model has broken time-reversal symmetry, but inversion symmetry is present. We calculate the Josephson current for both zero and finite temperature for the two pairing mechanisms inside the superconductors that have been proposed in the literature, zero-momentum BCS-like pairing and finite-momentum FFLO-like pairing, and assuming the short-junction limit. For both pairing types we find that the current is proportional to the normal-state junction conductivity, with a proportionality coefficient that shows quantitative differences between the two pairing mechanisms. The current for the BCS-like pairing is found to be independent of the chemical potential, whereas the current for the FFLO-like pairing is not