Self-regulated gravitational accretion in protostellar discs

We present a numerical model for the evolution of a protostellar disc that has formed self-consistently from the collapse of a molecular cloud core. The global evolution of the disc is followed for several million years after its formation. The capture of a wide range of spatial and temporal scales is made possible by use of the thin-disc approximation. We focus on the role of gravitational torques in transporting mass inward and angular momentum outward during different evolutionary phases of a protostellar disc with disc-to-star mass ratio of order 0.1. In the early phase, when the infall of matter from the surrounding envelope is substantial, mass is transported inward by the gravitational torques from spiral arms that are a manifestation of the envelope-induced gravitational instability in the disc. In the late phase, when the gas reservoir of the envelope is depleted, the distinct spiral structure is replaced by ongoing irregular nonaxisymmetric density perturbations. The amplitude of these density perturbations decreases with time, though this process is moderated by swing amplification aided by the existence of the disc's sharp outer edge. Our global modelling of the protostellar disc reveals that there is typically a residual nonzero gravitational torque from these density perturbations, i.e. their effects do not exactly cancel out in each region. In particular, the net gravitational torque in the inner disc tends to be negative during first several million years of the evolution, while the outer disc has a net positive gravitational torque. Our global model of a self-consistently formed disc shows that it is also self-regulated in the late phase, so that it is near the Toomre stability limit, with a near-uniform Toomre parameter Q\approx 1.5-2.0. (Abstract abridged).Comment: 9 pages, 9 figures, accepted for publication in MNRA

Third-order matching in λ→\lambda\rightarrow-Curry is undecidable

Given closed untyped $\lambda$-terms $\lambda x1... xk.s$ and $t$, which can be assigned some types $S1->...->Sk->T$ and $T$ respectively in the Curry-style systems of type assignment (essentially due to R.~Hindley) $\lambda->$-Curry [Barendregt 92], $\lambda^{->}_t$ [Mitchell 96], $TA_\lambda$ [Hindley97], it is undecidable whether there exist closed terms $s1,...,sk$ of types $S1,...,Sk$ such that $s[s1/x1,...,sk/xk]=_{\beta\eta}t$, even if the orders of $si$'s do not exceed 3. This undecidability result should be contrasted to the decidability of the third-order matching in the Church-style simply typed lambda calculus with a single constant base type [Dowek 92]. The proof is by reduction from the recursively inseparable sets of invalid and finitely satisfiable sentences of the first-order theory of binary relation [Trakhtenbrot 53, Vaught 60]

The Burst Mode of Accretion in Primordial Star Formation

We present simulation results for the formation and long-term evolution of a primordial protostellar disk harbored by a first star. Using a 2+1D nonaxisymmetric thin disk numerical simulation, together with a barotropic relation for the gas, we are able to probe ~20 kyr of the disk's evolution. During this time period we observe fragmentation leading to loosely bound gaseous clumps within the disk. These are then torqued inward and accreted onto the growing protostar, giving rise to a burst phenomenon. The luminous feedback produced by this mechanism may have important consequences for the subsequent growth of the protostar.Comment: 3 pages, 2 figures, to appear in proceedings of First Stars IV meeting (Kyoto, Japan; 2012

Precoder design for space-time coded systems over correlated Rayleigh fading channels using convex optimization

A class of computationally efficient linear precoders for space-time block coded multiple-input multiple-output wireless systems is derived based on the minimization of the exact symbol error rate (SER) and its upper bound. Both correlations at the transmitter and receiver are assumed to be present, and only statistical channel state information in the form of the transmit and receive correlation matrices is assumed to be available at the transmitter. The convexity of the design based on SER minimization is established and exploited. The advantage of the developed technique is its low complexity. We also find various relationships of the proposed designs to the existing precoding techniques, and derive very simple closed-form precoders for special cases such as two or three receive antennas and constant receive correlation. The numerical simulations illustrate the excellent SER performance of the proposed precoders

Robust Linear Receiver Design for Multi-Access Space-Time Block Coded MIMO Systems Using stochastic Optimization

Traditional receiver algorithms developed for multiple-input multiple-output (MIMO) wireless systems are based on the assumption that the channel state information (CSI) is precisely known at the receiver. However, in real environments the exact CSI may be unavailable. In this paper, we address the problem of robustness of multi-access spacetime block coded (STBC) MIMO systems against imperfect CSI. We propose a class of linear receivers which guarantee the robustness against CSI errors with a certain selected probability. The proposed formulations of robust receivers are given by probability-constrained optimization problems which can be simplified to convex forms. The latter convex problems can be efficiently solved using standard optimization methods. 1