Time-periodic corner states from Floquet higher-order topology

The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.

Generalized Quantitative Stability Analysis of Time-Dependent Comprehensive Rotorcraft Systems

Rotorcraft stability is an inherently multidisciplinary area, including aerodynamics of rotor and fuselage, structural dynamics of flexible structures, actuator dynamics, control, and stability augmentation systems. The related engineering models can be formulated with increasing complexity due to the asymmetric nature of rotorcraft and the airflow on the rotors in forward flight conditions. As a result, linear time-invariant (LTI) models are drastic simplifications of the real problem, which can significantly affect the evaluation of the stability. This usually reveals itself in form of periodic governing equations and is solved using Floquet’s method. However, in more general cases, the resulting models could be non-periodic, as well, which requires a more versatile approach. Lyapunov Characteristic Exponents (LCEs), as a quantitative method, can represent a solution to this problem. LCEs generalize the stability solutions of the linear models, i.e., eigenvalues of LTI systems and Floquet multipliers of linear time-periodic (LTP) systems, to the case of non-linear, time-dependent systems. Motivated by the need for a generic tool for rotorcraft stability analysis, this work investigates the use of LCEs and their sensitivity in the stability analysis of time-dependent, comprehensive rotorcraft models. The stability of a rotorcraft modeled using mid-fidelity tools is considered to illustrate the equivalence of LCEs and Floquet’s characteristic coefficients for linear time-periodic problems.