Level Set Dynamics and the Non-blowup of the 2D Quasi-geostrophic Equation

In this article we apply the technique proposed in Deng-Hou-Yu (Comm. PDE, 2005) to study the level set dynamics of the 2D quasi-geostrophic equation. Under certain assumptions on the local geometric regularity of the level sets of $\theta$, we obtain global regularity results with improved growth estimate on $| \nabla^{\bot} \theta |$. We further perform numerical simulations to study the local geometric properties of the level sets near the region of maximum $| \nabla^{\bot} \theta |$. The numerical results indicate that the assumptions on the local geometric regularity of the level sets of $\theta$ in our theorems are satisfied. Therefore these theorems provide a good explanation of the double exponential growth of $| \nabla^{\bot} \theta |$ observed in this and past numerical simulations.Comment: 25 pages, 10 figures. Corrected a few typo

Jet-cloud/star interaction as an interpretation of neutrino outburst from the blazar TXS 0506+056

Recently, a high-energy neutrino event IceCube-170922A in the spatial and temporal coincidence with the flaring gamma-ray blazar TXS 0506+056 was reported. A neutrino outburst between September 2014 and March 2015 was discovered in the same direction by a further investigation of $9.5$ years of IceCube data, while the blazar is in a quiescent state during the outburst with a gamma-ray flux only about one-fifth of the neutrino flux. In this letter, we propose the neutrino outburst originates from the interaction between a relativistic jet and a dense gas cloud which may be formed via the tidally disrupted envelope of a red giant being blown by the impact of the jet. Gamma-ray photons and electron/positron pairs that are produced correspondingly will induce electromagnetic cascades. Comptonization of the cascade emission inside the cloud forms an X-ray photon field with Wien distribution. GeV flux is suppressed due to the absorption by the Comptonized photon field and, as a result, a hard spectrum above 10 GeV is formed. The gamma-ray spectrum predicted in our model is consistent with the Fermi-LAT data of TXS 0506+056.Comment: 6 pages, 3 figure

1,3-Diprop-2-ynyl-1H-imidazol-3-ium bromide

In the title salt, C9H9N2 +·Br−, the ethynyl groups are nearly anti­parallel to each other [the angle between the two ethynyl groups is179.7 (2)°]. No classical hydrogen bonds or π–π inter­actions are observed. The mol­ecules are linked by C—H⋯Br hydrogen bonds. The bromide anions are involved in inter­actions with three H atoms

On the Origin of Galactic Diffuse TeV-PeV Emission: Insight from LHAASO and IceCube

The high-energy diffuse gamma-ray emission and neutrino emission are expected from the Galactic plane, generated by hadronuclear interactions between cosmic rays (CR) and interstellar medium (ISM). Therefore, measurements of these diffuse emissions will provide important clues on the origin and nature of Galactic CRs. Comparing the latest observations of LHAASO and IceCube on the diffuse Galactic gamma-ray and neutrino emissions respectively, we suggest that the diffuse gamma-ray emission at multi-TeV energies contains a considerable contribution of a leptonic component. By modelling the gamma-ray halos powered by middle-aged pulsars in our Galaxy with taking into account the magnetic field configuration and the interstellar radiation field in the Galaxy, we demonstrate that the collective contribution of pulsar halos can account for the excess in the measured diffuse gamma-ray emission with respect to the predicted flux from CR-ISM interactions. The resulting one-dimensional profile along the Galactic longitude is also consistent with the observation.Comment: 24 pages, 11 figures; Comments are Welcom