Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Korteweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the complex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.Comment: 12 figure

catena-Poly[[bis­(1-methyl-1H-imidazole-κN 3)zinc]-μ-3-nitro­phthalato-κ2 O 1:O2]

In the title complex, [Zn(C8H3NO6)(C4H6N2)2]n, the carboxyl­ate groups of the 3-nitro­phthalate dianion ligand coordinate the ZnII ion in a bis-monodentate mode. The ZnII ion shows distorted tetra­hedral coordination as it is bonded to two O atoms from the carboxyl­ate groups of symmetry-related 3-nitro­phthalate anions and two N atoms of two independent 1-methyl­imidazole mol­ecules. The bridging 3-nitro­phthalate ligand allows the formation of one-dimensional chains in the c direction. The crystal structure is further stabilized by weak inter­molecular C—H⋯O hydrogen bonds

Phenol Adsorption on Nitrogen-Enriched Activated Carbon from Wood Fiberboard Waste

Nitrogen-enriched activated carbons were prepared from wood fiberboard waste using 50% potassium hydroxide solution. Activated carbons were obtained with an impregnation ratio (gram chemical agent/gram wood fiberboard waste) of 3 in 850°C activation temperature carbonized for 60 min. Nitrogen content in activated carbon was 1.33% by analysis. Effects of contact time, pH, adsorbent dosage level, and temperature on phenol adsorption capacity of activated carbons were investigated. Adsorption equilibrium was achieved within 100 min at the given phenol concentration of 250 mg/L. When 0.1 g of the carbon absorbent and 100 mL of phenol solution at 250 mg/L were used, maximum adsorption capacity of phenol on activated carbon can reach 207 mg/g. The kinetics of phenol adsorption followed nicely the pseudo-second-order rate expression. In the adsorption isotherm, the Langmuir model fit better than the Freundlich model in phenol adsorption. This study suggests that nitrogen-enriched activated carbon prepared from wood fiberboard waste can be used effectively for removal of phenol compounds from aqueous solutions

Discriminating different scenarios to account for the cosmic e±e^\pm excess by synchrotron and inverse Compton radiation

The excesses of the cosmic positron fraction recently measured by PAMELA and the electron spectra by ATIC, PPB-BETS, Fermi and H.E.S.S. indicate the existence of primary electron and positron sources. The possible explanations include dark matter annihilation, decay, and astrophysical origin, like pulsars. In this work we show that these three scenarios can all explain the experimental results of the cosmic $e^\pm$ excess. However, it may be difficult to discriminate these different scenarios by the local measurements of electrons and positrons. We propose possible discriminations among these scenarios through the synchrotron and inverse Compton radiation of the primary electrons/positrons from the region close to the Galactic center. Taking typical configurations, we find the three scenarios predict quite different spectra and skymaps of the synchrotron and inverse Compton radiation, though there are relatively large uncertainties. The most prominent differences come from the energy band $10^4\sim 10^9$ MHz for synchrotron emission and $\gtrsim 10$ GeV for inverse Compton emission. It might be able to discriminate at least the annihilating dark matter scenario from the other two given the high precision synchrotron and diffuse $\gamma$-ray skymaps in the future.Comment: published in Pr

Galactic Disk Bulk Motions as Revealed by the LSS-GAC DR2

We report a detailed investigation of the bulk motions of the nearby Galactic stellar disk, based on three samples selected from the LSS-GAC DR2: a global sample containing 0.57 million FGK dwarfs out to $\sim$ 2 kpc, a local subset of the global sample consisting $\sim$ 5,400 stars within 150 pc, and an anti-center sample containing $\sim$ 4,400 AFGK dwarfs and red clump stars within windows of a few degree wide centered on the Galactic anti-center. The global sample is used to construct a three-dimensional map of bulk motions of the Galactic disk from the solar vicinity out to $\sim$ 2 kpc with a spatial resolution of $\sim$ 250 pc. Typical values of the radial and vertical components of bulk motion range from $-$15 km s$^{-1}$ to 15 km s$^{-1}$, while the lag behind the circular speed dominates the azimuthal component by up to $\sim$ 15 km s$^{-1}$. The map reveals spatially coherent, kpc-scale stellar flows in the disk, with typical velocities of a few tens km s$^{-1}$. Bending- and breathing-mode perturbations are clearly visible, and vary smoothly across the disk plane. Our data also reveal higher-order perturbations, such as breaks and ripples, in the profiles of vertical motion versus height. From the local sample, we find that stars of different populations exhibit very different patterns of bulk motion. Finally, the anti-center sample reveals a number of peaks in stellar number density in the line-of-sight velocity versus distance distribution, with the nearer ones apparently related to the known moving groups. The "velocity bifurcation" reported by Liu et al. (2012) at Galactocentric radii 10--11 kpc is confirmed. However, just beyond this distance, our data also reveal a new triple-peaked structure.Comment: 27 pages, 17 figures, Accepted for publication in a special issue of Research in Astronomy and Astrophysics on LAMOST science