Existence of Multistring Solutions of the Self-Gravitating Massive W−W-Boson

We consider a semilinear elliptic system which include the model system of the $W-$strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed in \cite{yan}Comment: 12 page

Activity Related Variations of High-Degree p-Mode Amplitude, Width and Energy in Solar Active Regions

We study the properties of high degree p-mode oscillations in flaring and dormant ARs and compare them with those in corresponding quiet regions (QRs) to find the association of mode parameters with magnetic and flare related activities. Our analysis of several flaring and dormant ARs, showed strong association of mode amplitude, width and energy with magnetic and flare activities although their changes are combined effects of foreshortening, filling factor, magnetic activity, flare activity, and measurement uncertainties. We find that the largest decrease in mode amplitude and background power of an AR are caused by the angular distance of the AR from the solar disc centre. After correcting the mode parameters for foreshortening and filling factor, we find that the mode amplitude of flaring and dormant ARs are smaller than in corresponding QRs, and decreases with increasing MAI suggesting a larger mode power suppression in ARs with stronger magnetic fields. The mode widths in ARs are larger than in corresponding QRs and increase with MAI, indicating shorter lifetimes of modes in ARs than in QRs. The largest decrease (increase) in mode amplitude (mode width) of dormant ARs is found in the five minute frequency band. The average mode energy of both the flaring and dormant ARs are smaller than in their corresponding QRs, decreasing with increasing MAI. But the average mode energy decrease rate in flaring ARs are smaller than in dormant ARs. Also, the increase in mode width rate in dormant (flaring) ARs is followed by decrease (increase) in amplitude variation rate. Furthermore, inclusion of mode corrections for MAI shows that mode amplitude and mode energy of flaring ARs increase with FI while mode width shows an opposite trend. The increase (decrease) in mode amplitude (width) is larger in the five minute and higher frequency band. Increase in width variation rate is ..

Explosive events associated with a surge

The solar atmosphere contains a wide variety of small-scale transient features. Here, we explore the inter-relation between some of them such as surges, explosive events and blinkers via simultaneous spectral and imaging data taken with the TRACE imager, the SUMER, and CDS spectrometers on board SoHO, and SVST La Palma. The alignment of all data both in time and solar XY shows that SUMER line profiles, which are attributed to explosive events, are due to a surge phenomenon. The surge is triggered, most probably, by one or more Elerman bombs which are best visible in Halpha +-350 A but were also registered by TRACE Fe IX/X 171 A and correspond to a strong radiance increase in the CDS Mg IX 368.07 A line. With the present study we demonstrate that the division of small-scale transient events into a number of different subgroups, for instance explosive events, blinkers, spicules, surges or just brightenings, is ambiguous, implying that the definition of a feature based only on either spectroscopic or imaging characteristics as well as insufficient spectral and spatial resolution can be incomplete.Comment: 17 pages, 7 figures, 1 tabl

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of compact support for the vorticit

The variation of relative magnetic helicity around major flares

We have investigated the variation of magnetic helicity over a span of several days around the times of 11 X-class flares which occurred in seven active regions (NOAA 9672, 10030, 10314, 10486, 10564, 10696, and 10720) using the magnetograms taken by the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO). As a major result we found that each of these major flares was preceded by a significant helicity accumulation over a long period (0.5 to a few days). Another finding is that the helicity accumulates at a nearly constant rate and then becomes nearly constant before the flares. This led us to distinguish the helicity variation into two phases: a phase of monotonically increasing helicity and the following phase of relatively constant helicity. As expected, the amount of helicity accumulated shows a modest correlation with time-integrated soft X-ray flux during flares. However, the average helicity change rate in the first phase shows even stronger correlation with the time-integrated soft X-ray flux. We discuss the physical implications of this result and the possibility that this characteristic helicity variation pattern can be used as an early warning sign for solar eruptions

The Cosmic Lens All-Sky Survey parent population - I. Sample selection and number counts

We present the selection of the Jodrell Bank Flat-spectrum (JBF) radio source sample, which is designed to reduce the uncertainties in the Cosmic Lens All-Sky Survey (CLASS) gravitational lensing statistics arising from the lack of knowledge about the parent population luminosity function. From observations at 4.86 GHz with the Very Large Array, we have selected a sample of 117 flat-spectrum radio sources with flux densities greater than 5 mJy. These sources were selected in a similar manner to the CLASS complete sample and are therefore representative of the parent population at low flux densities. The vast majority (~90 per cent) of the JBF sample are found to be compact on the arcsecond scales probed here and show little evidence of any extended radio jet emission. Using the JBF and CLASS complete samples we find the differential number counts slope of the parent population above and below the CLASS 30 mJy flux density limit to be -2.07+/-0.02 and -1.96+/-0.12, respectively.Comment: 10 pages, 4 figures, accepted for publication in MNRA

The Thermal Instability of Solar Prominence Threads

The fine structure of solar prominences and filaments appears as thin and long threads in high-resolution images. In H-alpha observations of filaments, some threads can be observed for only 5 - 20 minutes before they seem to fade and eventually disappear, suggesting that these threads may have very short lifetimes. The presence of an instability might be the cause of this quick disappearance. Here, we study the thermal instability of prominence threads as an explanation of their sudden disappearance from H-alpha observations. We model a prominence thread as a magnetic tube with prominence conditions embedded in a coronal environment. We assume a variation of the physical properties in the transverse direction, so that the temperature and density continuously change from internal to external values in an inhomogeneous transitional layer representing the particular prominence-corona transition region (PCTR) of the thread. We use the nonadiabatic and resistive magnetohydrodynamic equations, which include terms due to thermal conduction parallel and perpendicular to the magnetic field, radiative losses, heating, and magnetic diffusion. We combine both analytical and numerical methods to study linear perturbations from the equilibrium state, focusing on unstable thermal solutions. We find that thermal modes are unstable in the PCTR for temperatures higher than 80,000 K, approximately. These modes are related to temperature disturbances that can lead to changes in the equilibrium due to rapid plasma heating or cooling. For typical prominence parameters, the instability time scale is of the order of a few minutes and is independent of the form of the temperature profile within the PCTR of the thread. This result indicates that thermal instability may play an important role for the short lifetimes of threads in the observations.Comment: Accepted for publication in Ap

On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in \cite{Chae1}.Comment: 16page