Formation of Five-Dimensional String Solutions from the Gravitational Collapse

We study the formation of five-dimensional string solutions including the Gregory-Laflamme (GL) black string, the Kaluza-Klein (KK) bubble, and the geometry with a naked singularity from the gravitational collapse. The interior solutions of five-dimensional Einstein equations describe collapsing non-isotropic matter clouds. It is shown that the matter cloud always forms the GL black string solution while the KK bubble solution cannot be formed. The numerical study seems to suggest that the collapsing matter forms the geometries with timelike naked curvature singularities, which should be taken cautiously as the general relativity is not reliable in the strong curvature regime.Comment: 17 pages, 10 figures, LaTeX, to appear in Class. Quant. Grav., a appendix and some discussions added, title change

Channel Assignment for Multiple Interface Nodes in Wireless Ad

In wireless networks, due to the broadcast property of the medium, nodes close to each other cannot simultaneously transmit over the same channel. One way to overcome this limitation is to use multiple independent channels available in the system. Although we can use a single wireless interface card to access multiple channels, such schemes can raise issues of compatibility (e.g., modication of the MAC protocol) and performance degradation (e.g., due to frequent channel switching). In this paper, we assume that nodes are equipped with multiple interface cards, and focus on the channel assignment problem for minimizing the total number of interferences among wireless links. We show that the problem is NP-hard and present distributed heuristics. We also present two centralized algorithms and show that the algorithms give constant factor approximation guarantees. We perform simulation experiments for the proposed distributed heuristic. The results show that compared to one-channel scenarios, our proposed algorithm can reduce the number of interferences by up to 85% when nodes are equipped with four interface cards. Through detailed packetlevel simulation experiments, we also show that depending on the scenario, the resulting channel assignment actually achieves up to seven times throughput improvement over the single-channel case