## 6 Conclusions  
In this paper, for the first time, we present a three dimensional network deployment algorithm inspired by physical dusty plasma crystallization theory in large scale WSN applications. We summarize our main conclusions and contributions as follows:  
(1) The 3D node deployment algorithm (VFA-DP-3D) and corresponding equations developed from the dusty plasma theory are presented. We also introduced four kinds of performance evaluation methods in 3D space, such as the moving distance, the spatial distribution diversion, system coverage rate, and the system utilization. The SDD parameter is compared with the truncated octahedron distribution to intuitively characterize the quality of the whole network. Based on the detailed analysis, our virtual force algorithm can work well in a 3D space for large scale WSN applications, which has good system coverage and small energy cost (moving distance). According to the SDD value, we observe that our algorithm can quickly deploy the scattered sensor nodes to a relatively regular state in the first 200 steps. However, due to the influence of the algorithm formulae, most of the nodes will have slight fluctuations because of the reverse distribution of acceleration during the 500-1000 steps. However, after 1500 steps, the node deployment tends to be stable and reaches a good convergence state. (2) Since the Debye length is the most important parameter in a dusty plasma algorithm, we further discussed the parameter effect of \(\lambda_{D}\) on the 3D deployment performance. Figure 9: **(a)** The variation of coverage rate and the system utilization depending on different \(\lambda_{D}\). **(b)** optimal \(R_{S}\) for different \(\lambda_{D}\). A larger \(\lambda_{D}\) corresponds to the wider final deployment range and the sparser distribution. It should also be noticed that, when \(\lambda_{D}\) is larger, the SDD value has a faster convergence speed, which means that the whole network takes less time to reach a better deployment state. Besides, the corresponding moving distance becomes smaller and has less variance, which also indicates less system energy consumption. After \(\lambda_{D}\) is fixed, the density state of the distribution needs to be further determined. We can then evaluate the whole system performances of the final network state, such as the coverage rate \(C\) and utilization \(U\), by artificially varying \(R_{S}\). When \(\lambda_{D}\) is smaller, the energy consumption is larger and the convergence speed is slower, so that a larger \(R_{S}\) is required to achieve the ideal coverage effect. When we look at the final performance of WSN deployment by combining the system coverage rate and the system utilization, it suggests that our algorithm can make WSN obtain a greater coverage rate at a certain point with a higher utilization. After finding the corresponding optimal sensing radius at that point, we can also use this value to adjust network settings in the practical applications. In a summary, our 3D-VFA-DP algorithm can quickly complete an overall 3D network deployment and then dynamically adjust some parameters to achieve a better distribution. In our opinion, there are two ways to use our method in the practical applications: (1) If the users need to deploy a very large-scale sensor network in a real 3D application, our method can quickly calculate the exact positions for all nodes. All four evaluation methods can be combined to give the convergence and the whole performance of the calculated 3D UAV-assisted wireless sensor network before the actual deployment process. After obtaining the network topology and those positions, all UAVs can fly to their given positions to achieve the sensor network and collect information. In such a case, our method provides a possible virtual force algorithm derived from the physical dusty plasma theory, which can indeed form a good spherical stack of truncated octahedrons. (2) On the other hand, the users can randomly spread all sensor nodes (sensors carried by UAVs) in a target region at the beginning.