Droplet impacting on solid or liquid interfaces is a ubiquitous phenomenon in nature. Although complete rebound of droplets is widely observed on superhydrophobic surfaces, the bouncing of droplets on liquid is usually vulnerable due to easy collapse of entrapped air pocket underneath the impinging droplet. Here, we report a superhydrophobic-like bouncing regime on thin liquid film, characterized by the contact time, the spreading dynamics, and the restitution coefficient independent of underlying liquid film. Through experimental exploration and theoretical analysis, we demonstrate that the manifestation of such a superhydrophobic-like bouncing necessitates an intricate interplay between the Weber number, the thickness and viscosity of liquid film. Such insights allow us to tune the droplet behaviours in a well-controlled fashion. We anticipate that the combination of superhydrophobic-like bouncing with inherent advantages of emerging slippery liquid interfaces will find a wide range of applications.

When a fast-moving drop impacts onto a smooth substrate, splashing will be produced at the edge of the expanding liquid sheet. This ubiquitous phenomenon lacks a fundamental understanding. Combining experiment with model, we illustrate that the ultrathin air film trapped under the expanding liquid front triggers splashing. Because this film is thinner than the mean free path of air molecules, the interior airflow transfers momentum with an unusually high velocity comparable to the speed of sound and generates a stress 10 times stronger than the airflow in common situations. Such a large stress initiates Kelvin-Helmholtz instabilities at small length scales and effectively produces splashing. Our model agrees quantitatively with experimental verifications and brings a fundamental understanding to the ubiquitous phenomenon of drop splashing on smooth surfaces.T he common phenomenon of drop splashing on smooth surfaces may seem simple and natural to most people; however, its understanding is surprisingly lacking. Splashing is crucial in many important fields, such as the sprinkler irrigation and pesticide application in agriculture, ink-jet printing and plasma spraying in printing and coating industries, and spray cooling in various cooling systems; therefore its better understanding and effective control may make a far-reaching impact on our daily life. Starting in the 19th century, extensive studies on drop impact and splashing have covered a wide range of control parameters, including the impact velocity, drop size, surface tension, viscosity, and substrate properties (1-12), and various splashing criteria have been proposed and debated (13)(14)(15)(16)(17)(18). Nevertheless, at the most fundamental level the generation mechanism of splashing remains a big mystery.Recently a breakthrough has surprisingly revealed the importance of surrounding air and suggested the interaction between air and liquid as the origin of splashing (15,19,20). However, this interaction is highly complex: Below the drop air is trapped at both the impact center and the expanding front (21-34), and above it the atmosphere constantly interacts with its top surface. As a result, even the very basic question of which part of air plays the essential role is completely unknown. Moreover, the analysis from classical aerodynamics (18) indicates that the viscous effect from air totally dominates any pressure influence, whereas the experiment contradictorily revealed a strong pressure dependence (15). Even more puzzling, it was revealed that the speed of sound in air plays an important role in splashing generation (15), although the impact speed is typically 10-100 times slower! Therefore, an entirely new and nonclassical interaction, which can directly connect these two distinct timescales, is required to solve this puzzle. Due to the poor understanding of underlying interaction, the fundamental instability that produces splashing is unclear: The prevailing model of Rayleigh-Taylor (RT) instability (35) contradicts the pressure-dependent observat...

In this paper, we study simultaneous wireless information and power transfer (SWIPT) in orthogonal frequency division multiple access (OFDMA) systems with the coexistence of information receivers (IRs) and energy receivers (ERs). The IRs are served with best-effort secrecy data and the ERs harvest energy with minimum required harvested power. To enhance the physical layer security for IRs and yet satisfy energy harvesting requirements for ERs, we propose a new frequencydomain artificial noise (AN) aided transmission strategy. With the new strategy, we study the optimal resource allocation for the weighted sum secrecy rate maximization for IRs by power and subcarrier allocation at the transmitter. The studied problem is shown to be a mixed integer programming problem and thus non-convex, while we propose an efficient algorithm for solving it based on the Lagrange duality method. To further reduce the computational complexity, we also propose a suboptimal algorithm of lower complexity. The simulation results illustrate the effectiveness of proposed algorithms as compared against other heuristic schemes.Index Terms-Physical layer security, simultaneous wireless information and power transfer (SWIPT), artificial noise (AN), orthogonal frequency-division multiple access (OFDMA), resource allocation.

This paper studies the secure beamforming design in a multiple-antenna three-node system where two source nodes exchange messages with the help of an untrusted relay node. The relay acts as both an essential signal forwarder and a potential eavesdropper. Both two-phase and three-phase two-way relay strategies are considered. Our goal is to jointly optimize the source and relay beamformers for maximizing the secrecy sum rate of the two-way communications. We first derive the optimal relay beamformer structures. Then, iterative algorithms are proposed to find source and relay beamformers jointly based on alternating optimization. Furthermore, we conduct asymptotic analysis on the maximum secrecy sum-rate. Our analysis shows that when all transmit powers approach infinity, the two-phase two-way relay scheme achieves the maximum secrecy sum rate if the source beamformers are designed such that the received signals at the relay align in the same direction. This reveals an important advantage of signal alignment technique in against eavesdropping. It is also shown that if the source powers approach zero, the three-phase scheme performs the best while the two-phase scheme is even worse than direct transmission. Simulation results have verified the efficiency of the proposed secure beamforming algorithms as well as the analytical findings.

Abstract-Integrating power transfer into wireless communications for supporting simultaneous wireless information and power transfer (SWIPT) is a promising technique in energy-constrained wireless networks. While most existing work on SWIPT focuses on capacity-energy characterization, the benefits of cooperative transmission for SWIPT are much less investigated. In this paper, we consider SWIPT in an orthogonal frequency-division multiplexing (OFDM) relaying system, where a source node transfers information and a fraction of power simultaneously to a relay node, and the relay node uses the harvested power from the source node to forward the source information to the destination. To support the simultaneous information and energy cooperation, we first propose a transmission protocol assuming that the direct link between the source and destination does not exist, namely power splitting (PS) relaying protocol, where the relay node splits the received signal power in the first hop into two separate parts, one for information decoding and the other for energy harvesting. Then, we consider the case that the direct link between the source and destination is available, and the transmission mode adaptation (TMA) protocol is proposed, where the transmission can be completed by cooperative mode and direct mode simultaneously (over different subcarriers). In direct mode, when the source transmits signal to the destination, the destination receives the signal as information and the relay node concurrently receives the signal for energy harvesting. Joint resource allocation problems are formulated to maximize the system throughput. By using the Lagrangian dual method, we develop efficient algorithms to solve the nonconvex optimization problems.Index Terms-Simultaneous wireless information and power transfer (SWIPT), orthogonal frequency-division multiplexing (OFDM), cooperative relay, resource allocation.