A conserved variable in the perturbed hydrodynamic world model

We introduce a scalar-type perturbation variable $\Phi$ which is conserved in the large-scale limit considering general sign of three-space curvature ($K$), the cosmological constant ($\Lambda$), and time varying equation of state. In a pressureless medium $\Phi$ is {\it exactly conserved} in all scales.Comment: 4 pages, no figure, To appear in Phys. Rev.

Exploring the Physics of Type Ia Supernovae Through the X-ray Spectra of their Remnants

We present the results of an ongoing project to use the X-ray observations of Type Ia Supernova Remnants to constrain the physical processes involved in Type Ia Supernova explosions. We use the Tycho Supernova Remnant (SN 1572) as a benchmark case, comparing its observed spectrum with models for the X-ray emission from the shocked ejecta generated from different kinds of Type Ia explosions. Both the integrated spectrum of Tycho and the spatial distribution of the Fe and Si emission in the remnant are well reproduced by delayed detonation models with stratified ejecta. All the other Type Ia explosion models fail, including well-mixed deflagrations calculated in three dimensions.Comment: 5 pages, 3 figures, to appear in the proceedings of the "Stellar end products" workshop, 13-15 April 2005, Granada, Spain, ed. M.A. Perez-Torres, Vol. 77 (Jan 2006) of MmSA

Spatial Distribution of Metal Emissions in SNR 3C 397 Viewed with Chandra and XMM

We present X-ray equivalent width imaging of the supernova remnant (SNR) 3C 397 for Mg He\alpha, Si He\alpha, S He\alpha, and Fe K\alpha complex lines with the Chandra and XMM-Newton observations. The images reveal that the heavier the element is, the smaller the extent of the element distribution is. The Mg emission is evidently enhanced in the southeastern blow-out region, well along the radio boundary there, and appears to partially envelope the eastern Fe knot. Two bilateral hat-like Si line-emitting structures are along the northern and southern borders, roughly symmetric with respect to the southeast-northwest elongation axis. An S line-emitting shell is located just inner to the northern radio and IR shell, indicating of a layer of reversely shocked sulphur in the ejecta. A few enhanced Fe features are basically aligned along the diagonal of the rectangular shape of the SNR, which implicates an early asymmetric SN explosion.Comment: 4 pages, 4 figures, appears in Science China Physics, Mechanics & Astronomy, 2010, 53 (Suppl.1), 267-27

Narrow Band Chandra X-ray Analysis of Supernova Remnant 3C391

We present the narrow-band and the equivalent width (EW) images of the thermal composite supernova remnant (SNR) 3C391 for the X-ray emission lines of elements Mg, Si, & S using the Chandra ACIS Observational data. These EW images reveal the spatial distribution of the emission of the metal species Mg, Si, & S in the remnant. They have clumpy structure similar to that seen from the broadband diffuse emission, suggesting that they are largely of interstellar origin. We find an interesting finger-like feature protruding outside the southwestern radio border of the remnant, which is somewhat similar to the jet-like Si structure found in the famous SNR Cas A. This feature may possibly be the debris of the jet of ejecta which implies an asymmetrical supernova explosion of a massive progenitor star.Comment: 9 pages, 4 embedded figures, Chinese Journal of Astronomy and Astrophysics (ChJAA), in pres

Far-infrared spectroscopy of spin excitations and Dzyaloshinskii-Moriya interactions in a Shastry-Sutherland compound SrCu2_2(BO3_3)$_2

We have studied spin excitation spectra in the Shastry-Sutherland model compound SrCu$_2$(BO$_3$)$_2$ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at 24 cm$^{-1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in SrCu$_2$(BO$_3$)$_2$. One is $a$-polarized and creates an intra-dimer dynamic DM along the c axis. The other is $c$-polarized and creates an intra-dimer dynamic DM interaction, it is in the $(ab)$ plane and perpendicular to the dimer axis. Singlet levels at 21.5 and 28.6 cm$^{-1}$ anti-cross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and inter-dimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static inter-dimer DM in the c-direction $d_1=0.7$ cm$^{-1}$ splits the triplet state sub-levels in zero field [C\'{e}pas et al., Phys. Rev. Lett. \textbf{87}, 167205 (2001)]. The static intra-dimer DM in the $(ab)$ plane (perpendicular to the dimer axis) $d_2=1.8$ cm$^{-1}$, allowed by the buckling of CuBO$_3$ planes, couples the triplet state to the 28.6 cm$^{-1}$ singlet as is seen from the avoided crossing.Comment: 12 pages with 7 figures, some references correcte

Supernova Ejecta in the Youngest Galactic Supernova Remnant G1.9+0.3

G1.9+0.3 is the youngest known Galactic supernova remnant (SNR), with an estimated supernova (SN) explosion date of about 1900, and most likely located near the Galactic Center. Only the outermost ejecta layers with free-expansion velocities larger than about 18,000 km/s have been shocked so far in this dynamically young, likely Type Ia SNR. A long (980 ks) Chandra observation in 2011 allowed spatially-resolved spectroscopy of heavy-element ejecta. We denoised Chandra data with the spatio-spectral method of Krishnamurthy et al., and used a wavelet-based technique to spatially localize thermal emission produced by intermediate-mass elements (IMEs: Si and S) and iron. The spatial distribution of both IMEs and Fe is extremely asymmetric, with the strongest ejecta emission in the northern rim. Fe Kalpha emission is particularly prominent there, and fits with thermal models indicate strongly oversolar Fe abundances. In a localized, outlying region in the northern rim, IMEs are less abundant than Fe, indicating that undiluted Fe-group elements (including 56Ni) with velocities larger than 18,000 km/s were ejected by this SN. But in the inner west rim, we find Si- and S-rich ejecta without any traces of Fe, so high-velocity products of O-burning were also ejected. G1.9+0.3 appears similar to energetic Type Ia SNe such as SN 2010jn where iron-group elements at such high free-expansion velocities have been recently detected. The pronounced asymmetry in the ejecta distribution and abundance inhomogeneities are best explained by a strongly asymmetric SN explosion, similar to those produced in some recent 3D delayed-detonation Type Ia models.Comment: 6 pages, 3 figures, submitted to ApJ Letter

Nonuniform Expansion of the Youngest Galactic Supernova Remnant G1.9+0.3

We report measurements of X-ray expansion of the youngest Galactic supernova remnant, G1.9+0.3, using Chandra observations in 2007, 2009, and 2011. The measured rates strongly deviate from uniform expansion, decreasing radially by about 60% along the X-ray bright SE-NW axis from 0.84% +/- 0.06% per yr to 0.52% +/- 0.03% per yr. This corresponds to undecelerated ages of 120-190 yr, confirming the young age of G1.9+0.3, and implying a significant deceleration of the blast wave. The synchrotron-dominated X-ray emission brightens at a rate of 1.9% +/- 0.4% per yr. We identify bright outer and inner rims with the blast wave and reverse shock, respectively. Sharp density gradients in either ejecta or ambient medium are required to produce the sudden deceleration of the reverse shock or the blast wave implied by the large spread in expansion ages. The blast wave could have been decelerated recently by an encounter with a modest density discontinuity in the ambient medium, such as found at a wind termination shock, requiring strong mass loss in the progenitor. Alternatively, the reverse shock might have encountered an order-of-magnitude density discontinuity within the ejecta, such as found in pulsating delayed-detonation Type Ia models. We demonstrate that the blast wave is much more decelerated than the reverse shock in these models for remnants at ages similar to G1.9+0.3. Similar effects may also be produced by dense shells possibly associated with high-velocity features in Type Ia spectra. Accounting for the asymmetry of G1.9+0.3 will require more realistic 3D Type Ia models.Comment: 6 pages, 4 figures, accepted for publication in ApJ Letters, minor revision

THE DEVELOPMENT OF A ROBOTIC TRAINER FOR THE CORRECTION OF ABNORMAL HUMAN GAIT

In this study, we developed a robotic gait trainer which induces the gait training based on predefined continuous proper lower extremity joint movements for the paralysis. AC servo motors and linear actuators were used to control hip and knee joints of patients and the weight support system was used to support the patient's weight during the gait training. We also implemented a GUI program to set the gait training pattern with several training parameters and to confirm states of patients and the system through the visual feedback. The effectiveness of the gait trainer will be determined by the long-term clinical experiments in the future. We expect that the developed robotic gait trainer could be applied very practically to recover gait abilities for persons with gait disorder

A physical interpretation of the jet-like X-ray emission from supernova remnant W49B

In the framework of the study of supernova remnants and their complex interaction with the interstellar medium and the circumstellar material, we focus on the galactic supernova remnant W49B. Its morphology exhibits an X-ray bright elongated nebula, terminated on its eastern end by a sharp perpendicular structure aligned with the radio shell. The X-ray spectrum of W49B is characterized by strong K emission lines from Si, S, Ar, Ca, and Fe. There is a variation of the temperature in the remnant with the highest temperature found in the eastern side and the lowest one in the western side. The analysis of the recent observations of W49B indicates that the remnant may be the result of an asymmetric bipolar explosion where the ejecta are collimated along a jet-like structure and the eastern jet is hotter and more Fe-rich than the western one. Another possible scenario associates the X-ray emission with a spherical explosion where parts of the ejecta are interacting with a dense belt of ambient material. To overcome this ambiguity we present new results of the analysis of an XMM-Newton observation and we perform estimates of the mass and energy of the remnant. We conclude that the scenario of an anisotropic jet-like explosion explains quite naturally our observation results, but the association of W49B with a hypernova and a gamma-ray burst, although still possible, is not directly supported by any evidence.Comment: 7 pages, 5 figures, accepted for publication in Advances in Space Researc