Numerical study of ergodicity for the overdamped Generalized Langevin Equation with fractional noise

The Generalized Langevin Equation, in history, arises as a natural fix for the rather traditional Langevin equation when the random force is no longer memoryless. It has been proved that with fractional Gaussian noise (fGn) mostly considered by biologists, the overdamped Generalized Langevin equation satisfying fluctuation-dissipation theorem can be written as a fractional stochastic differential equation (FSDE). While the ergodicity is clear for linear forces, it remains less transparent for nonlinear forces. In this work, we present both a direct and a fast algorithm respectively to this FSDE model. The strong orders of convergence are proved for both schemes, where the role of the memory effects can be clearly observed. We verify the convergence theorems using linear forces, and then present the ergodicity study of the double well potentials in both 1D and 2D setups

Is the Taurus B213 Region a True Filament?: Observations of Multiple Cyanoacetylene Transitions

We have obtained spectra of the J=2-1 and J=10-9 transitions of cyanoacetylene (\hc3n) toward a collection of positions in the most prominent filament, B213, in the Taurus molecular cloud. The analysis of the excitation conditions of these transitions reveals an average gas H$_2$ volume density of $(1.8\pm 0.7) \times10^{4}$ \cc. Based on column density derived from 2MASS and this volume density, the line of sight dimension of the high density portion of B213 is found to be $\simeq$ 0.12 pc, which is comparable to the smaller projected dimension and much smaller than the elongated dimension of B213 ($\sim$2.4 pc). B213 is thus likely a true cylinder--like filament rather than a sheet seen edge-on. The line width and velocity gradient seen in \hc3n are also consistent with Taurus B213 being a self-gravitating filament in the early stage of either fragmentation and/or collape.Comment: Accepted for publication by Ap

The Five-hundred-meter Aperture Spherical Radio Telescope Project and its Early Science Opportunities

The National Astronomical Observatories, Chinese Academy of Science (NAOC), has started building the largest antenna in the world. Known as FAST, the Five-hundred-meter Aperture Spherical radio Telescope is a Chinese mega-science project funded by the National Development and Reform Commission (NDRC). FAST also represents part of Chinese contribution to the international efforts to build the square kilometer array (SKA). Upon its finishing around September of 2016, FAST will be the most sensitive single-dish radio telescope in the low frequency radio bands between 70 MHz and 3 GHz. The design specifications of FAST, its expected capabilities, and its main scientific aspirations were described in an overview paper by Nan et al. (2011). In this paper, we briefly review the design and the key science goals of FAST, speculate the likely limitations at the initial stages of FAST operation, and discuss the opportunities for astronomical discoveries in the so-called early science phase.Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 6 pages, 2 figure