Two-tier femtocell networks is an efficient communication architecture that significantly improves throughput in indoor environments with low power consumption. Traditionally, a femtocell network is usually configured to be either completely open or
completely closed in that its channels are either made available to all users or used by its own users only. This may limit network flexibility and performance. It is desirable for owners of femtocell base stations if a femtocell can partially open its channels for external users access. In such scenarios, spectrum and energy efficiency becomes a critical issue in the design of femtocell network protocols and structure. In this paper, we conduct performance analysis for two-tier femtocell networks with partially open channels. In particular, we build a Markov chain to model the channel access in the femtocell network and then derive the performance metrics in terms of the blocking probabilities. Based on stationary state probabilities derived by Markov chain models, spectrum and energy efficiency are modeled and analyzed under different scenarios characterized by critical parameters, including number of femtocells in a macrocell, average number of users, and number of open channels in a femtocell. Numerical and Monte-Carlo (MC) simulation results indicate that the number of open channels in a femtocell has an adverse impact on the spectrum and energy efficiency of two-tier femtocell networks. Results in this paper provide guidelines for trading off spectrum and energy efficiency of two-tier femtocell networks by configuring different numbers of open channels in a femtocell.
We present a complete evaluation for the prompt $eta_c$ production at the LHC at next-to-leading order in $alpha_s$ in nonrelativistic QCD. By assuming heavy quark spin symmetry, the recently observed $eta_c$ production data by LHCb results in a very
strong constraint on the upper bound of the color-octet long distance matrix element $1S0$ of $J/psi$. We find this upper bound is consistent with our previous study of the $J/psi$ yield and polarization and can give good descriptions for the measurements, but inconsistent with some other theoretical estimates. This may provide important information for understanding the nonrelativistic QCD factorization formulism.
The search for new quantum phases, especially in frustrated magnets, is central to modern condensed matter physics. One of the most promising places to look is in rare-earth pyrochlore magnets with highly-anisotropic exchange interactions, materials
closely related to the spin ices Ho2Ti2O7 and Dy2Ti2O7. Here we establish a general theory of magnetic order in these materials. We find that many of their most interesting properties can be traced back to the accidental degeneracies where phases with different symmetry meet. These include the ordered ground state selection by fluctuations in Er2Ti2O7, the dimensional-reduction observed in Yb2Ti2O7, and the absence of magnetic order in Er2Sn2O7.
