A new type of coupled Faraday wave appears in the system of two immiscible incompressible viscous liquid layers with a free surface filling in a Hele-Shaw cell under vertical oscillation [X. Li, X. Li, and S. Liao, “Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally,” Phys. Fluids, 30, 012108 (2018)]. The influence in terms of both depth of upper and lower liquids on these standing waves has been analyzed quantitatively by experiments, which can be understood in the form of the wave amplitudes, dispersion relation, and stability. It suggests that the depth of upper liquid plays a remarkable role, while the lower one does not seem to contribute significantly.
In this paper, we study efficient power control schemes for delay sensitive communication over fading channels. Our objective is to find a power control law that optimizes the link layer performance, specifically, minimizes the packet drop probability, subject to a long-term average power constraint.We assume the buffer at the transmitter is finite; hence packet drop happens when the buffer is full.The fading channel under our study has a continuous state, e.g., Rayleigh fading. Since the channel state space is continuous, dynamic programming is not applicable for power control. In this paper, we propose a sub-optimal power control law based on a parametric approach. The proposed power control scheme tries to minimize the packet drop probability by considering the queue length, i.e., reducing the probability of those queue-length states that will cause full buffer. Simulation results show that our proposed power control scheme reduces the packet drop probability by one or two orders of magnitude, compared to the time domain water filling and the truncated channel inversion power control.
We report a numerical study of the contact-line effect on the Faraday instability. A momentum balance model is implemented to simulate the hysteresis of the meniscus. By using this model, a stick-slip-motion of the contact line happens on the lateral wall when a vertical vibration is exerted to the container. The numerical result further supports that the contact-line hysteresis can increase the natural frequency by inference. Besides, it can largely delay the timing of the onset because of an extra dissipation provided by the capillary effect. The growth rate can also be affected by the meniscus but the impact of the hysteresis seems limited. The presence of the meniscus is the reason why Faraday instability occurs without any artificial disturbance. Finally, a linear relation between the contact-angle range and the contact-line position is observed from our computation.
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