Coordinated Multicasting with Opportunistic User Selection in Multicell Wireless Systems

Physical layer multicasting with opportunistic user selection (OUS) is examined for multicell multi-antenna wireless systems. By adopting a two-layer encoding scheme, a rate-adaptive channel code is applied in each fading block to enable successful decoding by a chosen subset of users (which varies over different blocks) and an application layer erasure code is employed across multiple blocks to ensure that every user is able to recover the message after decoding successfully in a sufficient number of blocks. The transmit signal and code-rate in each block determine opportunistically the subset of users that are able to successfully decode and can be chosen to maximize the long-term multicast efficiency. The employment of OUS not only helps avoid rate-limitations caused by the user with the worst channel, but also helps coordinate interference among different cells and multicast groups. In this work, efficient algorithms are proposed for the design of the transmit covariance matrices, the physical layer code-rates, and the target user subsets in each block. In the single group scenario, the system parameters are determined by maximizing the group-rate, defined as the physical layer code-rate times the fraction of users that can successfully decode in each block. In the multi-group scenario, the system parameters are determined by considering a group-rate balancing optimization problem, which is solved by a successive convex approximation (SCA) approach. To further reduce the feedback overhead, we also consider the case where only part of the users feed back their channel vectors in each block and propose a design based on the balancing of the expected group-rates. In addition to SCA, a sample average approximation technique is also introduced to handle the probabilistic terms arising in this problem. The effectiveness of the proposed schemes is demonstrated by computer simulations.Comment: Accepted by IEEE Transactions on Signal Processin

Fluctuations of Entropy Production in Partially Masked Electric Circuits: Theoretical Analysis

In this work we perform theoretical analysis about a coupled RC circuit with constant driven currents. Starting from stochastic differential equations, where voltages are subject to thermal noises, we derive time-correlation functions, steady-state distributions and transition probabilities of the system. The validity of the fluctuation theorem (FT) is examined for scenarios with complete and incomplete descriptions.Comment: 4 pages, 1 figur

A Balanced Budget View on Forming Giant Planets by Pebble Accretion

Pebble accretion refers to the assembly of rocky planet cores from particles whose velocity dispersions are damped by drag from circumstellar disc gas. Accretion cross-sections can approach maximal Hill-sphere scales for particles whose Stokes numbers approach unity. While fast, pebble accretion is also lossy. Gas drag brings pebbles to protocores but also sweeps them past; those particles with the largest accretion cross-sections also have the fastest radial drift speeds and are the most easily drained out of discs. We present a global model of planet formation by pebble accretion that keeps track of the disc's mass budget. Cores, each initialized with a lunar mass, grow from discs whose finite stores of mm-cm sized pebbles drift inward across all radii in viscously accreting gas. For every 1 $M_\oplus$ netted by a core, at least 10 $M_\oplus$ and possibly much more are lost to radial drift. Core growth rates are typically exponentially sensitive to particle Stokes number, turbulent Mach number, and solid surface density. This exponential sensitivity, when combined with disc migration, tends to generate binary outcomes from 0.1-30 AU: either sub-Earth cores remain sub-Earth, or explode into Jupiters, with the latter migrating inward to varying degrees. When Jupiter-breeding cores assemble from mm-cm sized pebbles, they do so in discs where such particles drain out in $\sim$10$^5$ yr or less; such fast-draining discs do not fit mm-wave observations.Comment: Accepted to MNRA

Resolved Depletion Zones and Spatial Differentiation of N2H+ and N2D+

We present a study on the spatial distribution of N2D+ and N2H+ in thirteen protostellar systems. Eight of thirteen objects observed with the IRAM 30m telescope show relative offsets between the peak N2D+ (J=2-1) and N2H+ (J=1-0) emission. We highlight the case of L1157 using interferometric observations from the Submillimeter Array and Plateau de Bure Interferometer of the N2D+ (J=3-2) and N2H+ (J=1-0) transitions respectively. Depletion of N2D+ in L1157 is clearly observed inside a radius of ~2000 AU (7") and the N2H+ emission is resolved into two peaks at radii of ~1000 AU (3.5"), inside the depletion region of N2D+. Chemical models predict a depletion zone in N2H+ and N2D+ due to destruction of H2D+ at T ~ 20 K and the evaporation of CO off dust grains at the same temperature. However, the abundance offsets of 1000 AU between the two species are not reproduced by chemical models, including a model that follows the infall of the protostellar envelope. The average abundance ratios of N2D+ to N2H+ have been shown to decrease as protostars evolve by Emprechtinger et al., but this is the first time depletion zones of N2D+ have been spatially resolved. We suggest that the difference in depletion zone radii for N2H+ and N2D+ is caused by either the CO evaporation temperature being above 20 K or an H2 ortho-to-para ratio gradient in the inner envelope.Comment: Accepted to ApJ. 44 pages 13 Figure