The rapid development of economy has led to an increase of acid rain that can react with the bitumen physically and chemically, causing further damage to the bitumen properties. Therefore, the effects of acid rain on the chemical composition and rheological properties of bitumen at different depths were investigated in this study. Fourier transform infrared spectroscopy and dynamic shear rheometer tests were performed on the bitumen samples after immersion in acid rain. The results show that in the early stage of immersion, acid rain leads to carbonyl dissolution, reduction of complex modulus, increase of phase angle, and softening of bitumen, thus improving the fatigue cracking resistance. In the late stage of immersion, bitumen is gradually oxidized to form carbonyl group. The change degree of complex modulus and phase angle decreases, and the fatigue cracking resistance is weakened with time. The effect of acid rain on the fatigue cracking resistance fluctuates more for bitumen at 0~50 μm and is more stable for bitumen at 50~100 μm. ... Read more

Network recoverability refers to the ability of a network to recover to a desired performance level after suffering topological perturbations such as link failures. The minimum number of driver nodes is a typical metric to denote the network controllability. In this paper, we propose closed-form analytic approximations for the minimum number of driver nodes to investigate the recoverability of network controllability under link-based perturbations in two scenarios: 1) only the links which are damaged in the failure process can be recovered and 2) links can be established between any pair of nodes that have no link between them after the failure process. Results show that our approximations fit well with simulation results both in synthetic networks and real-world networks, such as swarm signaling networks and some communication networks. ... Read more