Nearest Neighbor and Contact Distance Distribution for Binomial Point Process on Spherical Surfaces

This letter characterizes the statistics of the contact distance and the nearest neighbor (NN) distance for binomial point processes (BPP) spatially-distributed on spherical surfaces. We consider a setup of $n$ concentric spheres, with each sphere $S_k$ has a radius $r_k$ and $N_k$ points that are uniformly distributed on its surface. For that setup, we obtain the cumulative distribution function (CDF) of the distance to the nearest point from two types o observation points: (i) the observation point is not a part of the point process and located on a concentric sphere with a radius $r_e<r_k\forall k$, which corresponds to the contact distance distribution, and (ii) the observation point belongs to the point process, which corresponds to the nearest-neighbor (NN) distance distribution

Stochastic Geometry-Based Low Latency Routing in Massive LEO Satellite Networks

In this paper, the routing in massive low earth orbit (LEO) satellite networks is studied. When the satellite-to-satellite communication distance is limited, we choose different relay satellites to minimize the latency in a constellation at a constant altitude. Firstly, the global optimum solution is obtained in the ideal scenario when there are available satellites at all the ideal locations. Next, we propose a nearest neighbor search algorithm for realistic (non-ideal) scenarios with a limited number of satellites. The proposed algorithm can approach the global optimum solution under an ideal scenario through a finite number of iterations and a tiny range of searches. Compared with other routing strategies, the proposed algorithm shows significant advantages in terms of latency. Furthermore, we provide two approximation techniques that can give tight lower and upper bounds for the latency of the proposed algorithm, respectively. Finally, the relationships between latency and constellation height, satellites' number, and communication distance are investigated

Coverage Analysis of Dynamic Coordinated Beamforming for LEO Satellite Downlink Networks

In this paper, we investigate the coverage performance of downlink satellite networks employing dynamic coordinated beamforming. Our approach involves modeling the spatial arrangement of satellites and users using Poisson point processes situated on concentric spheres. We derive analytical expressions for the coverage probability, which take into account the in-cluster geometry of the coordinated satellite set. These expressions are formulated in terms of various parameters, including the number of antennas per satellite, satellite density, fading characteristics, and path-loss exponent. To offer a more intuitive understanding, we also develop an approximation for the coverage probability. Furthermore, by considering the distribution of normalized distances, we derive the spatially averaged coverage probability, thereby validating the advantages of coordinated beamforming from a spatial average perspective. Our primary finding is that dynamic coordinated beamforming significantly improves coverage compared to the absence of satellite coordination, in direct proportion to the number of antennas on each satellite. Moreover, we observe that the optimal cluster size, which maximizes the ergodic spectral efficiency, increases with higher satellite density, provided that the number of antennas on the satellites is sufficiently large. Our findings are corroborated by simulation results, confirming the accuracy of the derived expressions

Conditional Contact Angle Distribution in LEO Satellite-Relayed Transmission

This letter characterizes the contact angle distribution based on the condition that the relay low earth orbit (LEO) satellite is in the communication range of both the ground transmitter and the ground receiver. As one of the core distributions in stochastic geometry-based routing analysis, the analytical expression of the \ac{CDF} of the conditional contact angle is derived. Furthermore, the conditional contact angle is applied to analyze the inaccessibility of common satellites between the ground transmitter and receiver. Finally, with the help of the conditional contact angle, coverage probability and achievable data rate in LEO satellite-relayed transmission are studied

Test and evaluation of Apollo 14 composite casting demonstration specimens and flight and control samples

The results of experiments 1, 2, and 10 of the Apollo 14 composite casting demonstration are discussed. The purpose of the demonstration, with regard to samples 1 and 2, was to obtain preliminary data on the liquid phase sintering process in a weightless environment. With regard to sample 10, the purpose was to obtain preliminary information on how to achieve uniform dispersion of dense particles on a metal matrix by employing shaking modes or forces in the system when the metal matrix is molten. Results of the demonstrations were interpreted in a quantitative and qualitative manner. For experiment 1 it was found that the tungsten particles were redistributed more uniformly in the flight sample than in the control sample. Experiment 2 results indicate that complete melting may not have occured and thus a high degree of significance cannot be associated with the qualitative results relating to particle redistribution data. The particle-matrix system of experiment 10 was found to be nonwetting