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Vulnerability analysis is a key issue in power systems since power transmission grids play a crucial role as a critical infrastructure. The power grid structure (number of nodes and lines, their connections, and their physical properties and operational constraints) is one of the main factors to assure power system security. Complex network theory as a promising topological approach for the structural vulnerability analysis has been widely used in many different fields. Recently, many complex network metrics have been proposed to assess the topological vulnerability of power transmission grids. However, these approaches are purely topological and fail in capturing the specific features of power systems. In this paper, an extended topological approach which incorporates electrical features such as flow path, line flow limits, etc., is presented. Three new metrics, net-ability, electrical betweenness and entropy degree are provided and used to assess structural vulnerability in power transmission grids.

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Modified kaolin clay (MKC) was synthesized through ultrasound-assisted coprecipitation method, and its adsorption behaviors to Cr(VI) and phosphate (P) from single and binary solutions were investigated by batch and column experiments. The adsorption capacities of Cr(VI) and P in single-ion solutions were found to be 309.60 and 605.75 mmol/kg, respectively. Because of competition adsorption, the adsorption capacities in binary solutions were reduced to 145.38 and 461.61 mmol/kg, respectively. The single and binary adsorption data fitted the pseudo-second-order kinetic model and the Langmuir isotherm well. The simultaneous addition of the two adsorbates led to a decrease and an increase in adsorption rate of Cr(VI) and P onto MKC, respectively. Scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD), and Fourier transform infrared (FTIR) spectroscopy were performed to confirm the adsorption phenomenon. FTIR spectroscopy demonstrated that hydroxyl groups, NH 4 + , and NO 3 − ions on the adsorbent surface were responsible for Cr(VI) and P adsorption, and the adsorption mechanism involved anion exchange and surface complexation. Column experiments indicated that the breakthrough time and adsorption capacity of the fixed bed increased as the bed depth increased and decreased as the flow rate increased. The breakthrough curves were found to fit the Yoon−Nelson model well. Moreover, the feasibility of reusing MKC through three adsorption/desorption cycles in a fixed-bed column was studied. The column regeneration efficiency after the third cycle was 71.9% for Cr(VI) and 69.6% for P.

Based on the space curve meshing equation, in this article, a geometry design of a novel circular arc helical gear mechanism with pure rolling for parallel transmission was presented. Different from conventional circular arc gears, the meshing points of circular arc helical gears were limited at the instantaneous centre of rotation. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equation, and parameter equations of the concave-convex circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was presented, and the impact factors influencing the contact ratio were discussed. Then, the parameter design was presented for the geometry parameters of tooth profiles, such as normal pitch, tooth height and tooth thickness. Using the deduced equations, several numerical examples were then considered, and prototype samples were produced to experimentally validate the contact ratio equation and the theoretical kinematic performance. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance such as a pure rolling meshing, a high contact ratio and a large comprehensive strength, when considering engineering applications.

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