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Abstract

Many biological microswimmers locomote by periodically beating the densely packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the analytical and the numerical point of view, optimisation of the ciliary motion of microswimmers has received limited attention, especially for non-spherical shapes. In this paper, using an envelope model for the microswimmer, we numerically optimise the ciliary motion of a ciliate with an arbitrary axisymmetric shape. Forward solutions are found using a fast boundary-integral method, and the efficiency sensitivities are derived using an adjoint-based method. Our results show that a prolate microswimmer with a $2\,{:}\,1$ aspect ratio shares similar optimal ciliary motion as the spherical microswimmer, yet the swimming efficiency can increase two-fold. More interestingly, the optimal ciliary motion of a concave microswimmer can be qualitatively different from that of the spherical microswimmer, and adding a constraint to the cilia length is found to improve, on average, the efficiency for such swimmers.

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are derived. They involve evaluating physical variables (traction, pressure, etc.) on the boundary only. By employing these formulas in conjunction with a boundary integral approach for solving forward and adjoint problems, we completely avoid the issue of volume remeshing when updating the pump shape as the optimization proceeds. This leads to significant cost savings and we demonstrate the performance on several numerical examples.

China’s growing electricity consumption has become an important factor to improving socio-economic development, as well as aggravating environmental degradation. Based on the provincial level data in China for the entire period and every five years during 2000–2015, this paper used a spatial shift-share analysis (SSS) to detect the driving factors of electricity consumption changes in China, mainly focusing on the spatial spillover effects of electricity consumption which have been ignored by previous literature. Results show that economic growth and industry structure change have increased China’s electricity consumption by 8919 and 746 billion kWh, respectively, while the electricity efficiency improvement has reduced China’s electricity consumption by 5337 billion kWh for the entire period. Among the total decrease in China’s electricity consumption caused by electricity efficiency improvement, about 20% is caused by spatial spillover effects, which cannot be ignored. Moreover, there are great differences in electricity consumption changes’ components across China’s provinces. The results provide a quantitative and better understanding of the determinants of China’s electricity consumption changes, and practical implications for differentiated electricity consumption regulation policies and regional energy cooperation strategies for China, as well as for other similar countries.