Admissibility of linear predictor in the extended growth curve model

In the present paper, we first give the definition of the extended growth curve model, then according to the definition of admissible linear predictor and some matrix properties, obtain the necessary and sufficient conditions for a linear predictor to be admissible in the classes of homogenous and inhomogeneous linear predictors, respectively

Passive flexibility effect on oscillating foil energy harvester

It is well-known that structural flexibility enhances the performance of flapping foil propellers. There is, however, much less knowledge about the effect of deformability on the flow energy extraction capacity of flapping foils. Following our recent work on an oscillating foil energy harvesting device with prescribed foil deformations1, we investigate the fully-coupled dynamics of a flapping foil energy harvester with a passively deformable foil. Towards this end, we computationally study the dynamics of a foil with realistic internal structure (containing a rigid leading edge and a flexible trailing edge with a stiffener) in energy harvesting regime through a fluid-structure interaction scheme. To examine the effect of different levels of flexibility, various materials (ranging from metals such as copper to virtual materials with arbitrary elasticity and density) for the stiffener have been tested. With the virtual materials, the effects of Young’s modulus coefficient and density ratio have been studied. Our simulation results show that flexibility around the trailing edge could enhance the overall energy extraction performance. For example, with a copper stiffener, an increase of 32.2% in efficiency can be reached at high reduced frequency. The performance enhancement is achieved mostly in cases with low Young’s modulus coefficient and density ratio. A possible underlying mechanism is that the specific foil deformations in these cases encourage the generation and shedding of vortices from the foil leading edge, which is known to be beneficial to flow energy extraction

Optical interface states protected by synthetic Weyl points

Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points and the trajectories of these states in the parameter space resembles those of Weyl semimetal "Fermi arcs surface states" in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.Comment: 36 pages, 9 figures. arXiv admin note: text overlap with arXiv:1610.0434

Fluid-structure interaction modeling on a 3D ray-strengthened caudal fin

In this paper, we present a numerical model capable of solving the fluid-structure interaction problems involved in the dynamics of skeleton-reinforced fish fins. In this model, the fluid dynamics is simulated by solving the Navier-Stokes equations using a finite-volume method based on an overset, multi-block structured grid system. The bony rays embedded in the fin are modeled as nonlinear Euler-Bernoulli beams. To demonstrate the capability of this model, we numerically investigate the effect of various ray stiffness distributions on the deformation and propulsion performance of a 3D caudal fin. Our numerical results show that with specific ray stiffness distributions, certain caudal fin deformation patterns observed in real fish (e.g. the cupping deformation) can be reproduced through passive structural deformations. Among the four different stiffness distributions (uniform, cupping, W-shape and heterocercal) considered here, we find that the cupping distribution requires the least power expenditure. The uniform distribution, on the other hand, performs the best in terms of thrust generation and efficiency. The uniform stiffness distribution, per se, also leads to 'cupping' deformation patterns with relatively smaller phase differences between various rays. The present model paves the way for future work on dynamics of skeleton-reinforced membranes

Dynamics of seaweed-inspired piezoelectric plates for energy harvesting from oscillatory cross flow

Inspired by the vibrations of aquatic plants such as seaweed in the unsteady flow fields generated by free-surface waves, we investigate a novel device based on piezoelectric plates to harvest energy from oscillatory cross flows. Towards this end, numerical studies are conducted using a flow-structure-electric interaction model to understand the underlying physical mechanisms involved in the dynamics and energy harvesting performance of one or a pair of piezoelectric plates in an oscillatory cross flow. In a single-plate configuration, both periodic and irregular responses have been observed depending on parameters such as normalized plate stiffness and Keulegan-Carpenter number. Large power harvesting is achieved with the excitation of natural modes. Besides, when the time scale of the motion and the intrinsic time scale of the circuit are close to each other the power extraction is enhanced. In a two-plate configuration with tandem formation, the hydrodynamic interaction between the two plates can induce irregularity in the response. In terms of energy harvesting, two counteracting mechanisms have been identified, shielding and energy recovery. The shielding effect reduces plate motion and energy harvesting, whereas with the energy recovery effect one plate is able to recovery energy from the wake of another for performance enhancement. The competition between these mechanisms leads to constructive or destructive interactions between the two plates. These results suggest that for better performance the system should be excited at its natural period, which should be close to the intrinsic time scale of the circuit. Moreover, using a pair of plates in a tandem formation can further improve the energy harvesting capacity when conditions for constructive interaction are satisfied