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86 - Lizhao You , Zimu Yuan , Bin Tang 2013
We study the minimum latency broadcast scheduling (MLBS) problem in Single-Radio Multi-Channel (SR-MC) wireless ad-hoc networks (WANETs), which are modeled by Unit Disk Graphs. Nodes with this capability have their fixed reception channels, but can s witch their transmission channels to communicate with their neighbors. The single-radio and multi-channel model prevents existing algorithms for single-channel networks achieving good performance. First, the common assumption that one transmission reaches all the neighboring nodes does not hold naturally. Second, the multi-channel dimension provides new opportunities to schedule the broadcast transmissions in parallel. We show MLBS problem in SR-MC WANETs is NP-hard, and present a benchmark algorithm: Basic Transmission Scheduling (BTS), which has approximation ratio of 4k + 12. Here k is the number of orthogonal channels in SR-MC WANETs. Then we propose an Enhanced Transmission Scheduling (ETS) algorithm, improving the approximation ratio to k + 23. Simulation results show that ETS achieves better performance over BTS, and the performance of ETS approaches the lower bound.
We have successfully synthesized three quasi-2D geometrically frustrated magnetic compounds (alpha-MCr_2O_4, M=Ca, Sr, Ba) using the spark-plasma-sintering technique. All these members of the alpha-MCr_2O_4 family consist of the stacking planar trian gular lattices of Cr$^{3+}$ spins (${rm S}=3/2$), separated by non-magnetic alkaline earth ions. Their corresponding magnetic susceptibility, specific heat, dielectric permittivity and ferroelectric polarization are systematically investigated. A long-range magnetic ordering arises below the N{e}el temperature (around 40K) in each member of the alpha-MCr_2O_4 family, which changes to the quasi-120degree proper-screw-type helical spin structure at low temperature. A very small but confirmed spontaneous electric polarization emerges concomitantly with this magnetic ordering. The direction of electric polarization is found within the basal triangular plane. The multiferroicity in alpha-MCr_2O_4 can not be explained within the frameworks of the magnetic exchange striction or the inverse Dzyaloshinskii-Moriya interaction. The observed results are more compatible with the newly proposed Arima mechanism that is associated the d-p hybridization between the ligand and transition metal ions, modified by the spin-orbit coupling. The evolution of multiferroic properties with the increasing inter-planar spacing (as M changes from Ca to Ba) reveals the importance of interlayer interaction in this new family of frustrated magnetic systems.
LiCu2O2 is the first multiferroic cuprate to be reported and its ferroelectricity is induced by complex magnetic ordering in ground state, which is still in controversy today. Herein, we have grown nearly untwinned LiCu2O2 single crystals of high qua lity and systematically investigated their dielectric and ferroelectric behaviours in external magnetic fields. The highly anisotropic response observed in different magnetic fields apparently contradicts the prevalent bc- or ab- plane cycloidal spin model. Our observations give strong evidence supporting a new helimagnetic picture in which the normal of the spin helix plane is along the diagonal of CuO4 squares which form the quasi-1D spin chains by edge-sharing. Further analysis suggests that the spin helix in the ground state is elliptical and in the intermediate state the present c-axis collinear SDW model is applicable with some appropriate modifications. In addition, our studies show that the dielectric and ferroelectric measurements could be used as probes for the characterization of the complex spin structures in multiferroic materials due to the close tie between their magnetic and electric orderings.
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