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

Stabilization of Cascaded Two-Port Networked Systems Against Nonlinear Perturbations

A networked control system (NCS) consisting of cascaded two-port communication channels between the plant and controller is modeled and analyzed. Towards this end, the robust stability of a standard closed-loop system in the presence of conelike perturbations on the system graphs is investigated. The underlying geometric insights are then exploited to analyze the two-port NCS. It is shown that the robust stability of the two-port NCS can be guaranteed when the nonlinear uncertainties in the transmission matrices are sufficiently small in norm. The stability condition, given in the form of "arcsin" of the uncertainty bounds, is both necessary and sufficient.Comment: 8 pages, in preparation for journal submissio