Wireless sensor networks play a very important role in environmental monitoring, structural health monitoring, smart city construction, smart grid, and ecological agriculture. The wireless sensor nodes powered by a battery have a limited service life and need periodic maintenance due to the limitation of battery capacity. Fortunately, the development of environmental energy harvesting technology provides an effective way to eliminate the needs and the replacement of the batteries. Among the environmental stray energy, wind energy is rich, almost endless, widely distributed, and clean. Due to the advantages of simple structure, miniaturization, and high power density, wind energy harvesters using piezoelectric materials (PWEHs) have attracted much attention. By the ways of principal exploration, structure design, and performance optimization, great and steady progress has been made in the research of PWEH. This Review is focused on the review of PWEHs. After introducing the basic principle of PWEHs, the structural performance and research status of PWEHs based on different mechanisms, such as a rotating turbine, vortex-induced vibration, flutter, and galloping, are analyzed and summarized. Finally, the development trend of PWEHs has been prospected.
In this paper, the time-dependent invariant of the Dirac equation with time-dependent linear potential has been constructed in non-commutative phase space. The corresponding analytical solution of the Dirac equation is presented by Lewis-Riesenfield invariant method.
The Dbar dressing method is extended to study the focusing/defocusing nonlinear Schrödinger (NLS) equation with nonzero boundary condition. A special type of complex function is considered. The function is meromorphic outside an annulus with center 0 and satisfies a local Dbar problem inside the annulus. The theory of such function is extended to construct the Lax pair of the NLS equation with nonzero boundary condition. In this procedure, the relation between the NLS potential and the solution of the Dbar problem is established. A certain distribution for the Dbar problem is introduced to obtain the focusing/defocusing NLS equation and the conservation laws. The explicit solutions of the focusing/defocusing NLS equation with nonzero boundary condition are given from a special distribution.
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