An Imaging and Spectral Study of Ten X-Ray Filaments around the Galactic Center

We report the detection of 10 new X-ray filaments using the data from the {\sl Chandra} X-ray satellite for the inner $6^{\prime}$ ($\sim 15$ parsec) around the Galactic center (GC). All these X-ray filaments are characterized by non-thermal energy spectra, and most of them have point-like features at their heads that point inward. Fitted with the simple absorbed power-law model, the measured X-ray flux from an individual filament in the 2-10 keV band is $\sim 2.8\times10^{-14}$ to $10^{-13}$ ergs cm$^{-2}$ s$^{-1}$ and the absorption-corrected X-ray luminosity is $\sim 10^{32}-10^{33}$ ergs s$^{-1}$ at a presumed distance of 8 kpc to the GC. We speculate the origin(s) of these filaments by morphologies and by comparing their X-ray images with the corresponding radio and infrared images. On the basis of combined information available, we suspect that these X-ray filaments might be pulsar wind nebulae (PWNe) associated with pulsars of age $10^3 \sim 3\times 10^5$ yr. The fact that most of the filament tails point outward may further suggest a high velocity wind blowing away form the GC.Comment: 29 pages with 7 figures and 3 pages included. Accepted to Ap

Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Envelope Expansion with Core Collapse. III. Similarity Isothermal Shocks in a Magnetofluid

We explore MHD solutions for envelope expansions with core collapse (EECC) with isothermal MHD shocks in a quasi-spherical symmetry and outline potential astrophysical applications of such magnetized shock flows. MHD shock solutions are classified into three classes according to the downstream characteristics near the core. Class I solutions are those characterized by free-fall collapses towards the core downstream of an MHD shock, while Class II solutions are those characterized by Larson-Penston (LP) type near the core downstream of an MHD shock. Class III solutions are novel, sharing both features of Class I and II solutions with the presence of a sufficiently strong magnetic field as a prerequisite. Various MHD processes may occur within the regime of these isothermal MHD shock similarity solutions, such as sub-magnetosonic oscillations, free-fall core collapses, radial contractions and expansions. We can also construct families of twin MHD shock solutions as well as an `isothermal MHD shock' separating two magnetofluid regions of two different yet constant temperatures. The versatile behaviours of such MHD shock solutions may be utilized to model a wide range of astrophysical problems, including star formation in magnetized molecular clouds, MHD link between the asymptotic giant branch phase to the proto-planetary nebula phase with a hot central magnetized white dwarf, relativistic MHD pulsar winds in supernova remnants, radio afterglows of soft gamma-ray repeaters and so forth.Comment: 21 pages, 33 figures, accepted by MNRA

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Coupled KdV equations derived from atmospherical dynamics

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models are classified via Painlev\'e test. Three types of $\tau$-function solutions and multiple soliton solutions of the models are explicitly given by means of the exact solutions of the usual KdV equation. It is also interesting that for a non-Painlev\'e integrable coupled KdV system there may be multiple soliton solutions.Comment: 19 pages, 2 figure

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided

New variable separation approach: application to nonlinear diffusion equations

The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the derivative-dependent functional separable solutions is obtained and some exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig

Phase Separation of Bismuth Ferrite into Magnetite under Voltage Stressing

Micro-Raman studies show that under ~700 kV/cm of d.c. voltage stressing for a few seconds, thin-film bismuth ferrite BiFeO3 phase separates into magnetite Fe3O4. No evidence is found spectroscopically of hemite alpha-Fe2O3, maghemite gamma-Fe2O3, or of Bi2O3. This relates to the controversy regarding the magnitude of magnetization in BiFeO3.Comment: 9 pages and 2 figure