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

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

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

Decay of weak solutions to the 2D dissipative quasi-geostrophic equation

We address the decay of the norm of weak solutions to the 2D dissipative quasi-geostrophic equation. When the initial data is in $L^2$ only, we prove that the $L^2$ norm tends to zero but with no uniform rate, that is, there are solutions with arbitrarily slow decay. For the initial data in $L^p \cap L^2$, with $1 \leq p < 2$, we are able to obtain a uniform decay rate in $L^2$. We also prove that when the $L^{\frac{2}{2 \alpha -1}}$ norm of the initial data is small enough, the $L^q$ norms, for $q > \frac{2}{2 \alpha -1}$ have uniform decay rates. This result allows us to prove decay for the $L^q$ norms, for $q \geq \frac{2}{2 \alpha -1}$, when the initial data is in $L^2 \cap L^{\frac{2}{2 \alpha -1}}$.Comment: A paragraph describing work by Carrillo and Ferreira proving results directly related to the ones in this paper is added in the Introduction. Rest of the article remains unchange

Small scale energy release driven by supergranular flows on the quiet Sun

In this article we present data and modelling for the quiet Sun that strongly suggest a ubiquitous small-scale atmospheric heating mechanism that is driven solely by converging supergranular flows. A possible energy source for such events is the power transfer to the plasma via the work done on the magnetic field by photospheric convective flows, which exert drag of the footpoints of magnetic structures. In this paper we present evidence of small scale energy release events driven directly by the hydrodynamic forces that act on the magnetic elements in the photosphere, as a result of supergranular scale flows. We show strong spatial and temporal correlation between quiet Sun soft X-ray emission (from &lt;i&gt;Yohkoh&lt;/i&gt; and &lt;i&gt;SOHO&lt;/i&gt; MDI-derived flux removal events driven by deduced photospheric flows. We also present a simple model of heating generated by flux submergence, based on particle acceleration by converging magnetic mirrors. In the near future, high resolution soft X-ray images from XRT on the &lt;i&gt;Hinode&lt;/i&gt; satellite will allow definitive, quantitative verification of our results

B0850+054: a new gravitational lens system from CLASS

We report the discovery of a new gravitational lens system from the CLASS survey. Radio observations with the VLA, the WSRT and MERLIN show that the radio source B0850+054 is comprised of two compact components with identical spectra, a separation of 0.7 arcsec and a flux density ratio of 6:1. VLBA observations at 5 GHz reveal structures that are consistent with the gravitational lens hypothesis. The brighter of the two images is resolved into a linear string of at least six sub-components whilst the weaker image is radially stretched towards the lens galaxy. UKIRT K-band imaging detects an 18.7 mag extended object, but the resolution of the observations is not sufficient to resolve the lensed images and the lens galaxy. Mass modelling has not been possible with the present data and the acquisition of high-resolution optical data is a priority for this system.Comment: 5 pages, 4 figures, accepted for publication in MNRA

Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Utilization of the Aspergillus nidulans pyrG gene as a selectable marker for transformation and electroporation of Neurospora crassa

We report the complementation of the Neurospora crassa pyr-4 mutation with the Aspergillus nidulans pyrG gene. The use of the pyrG gene as a selectable marker for N. crassa transformation offers several advantages: a non toxic nutritional selection, the ability to put single-copy transformants through a sexual cross without the occurrence of RIP (Repeat-Induced Point mutation) by alleles of the pyr-4 gene, and a relatively-high electroporation efficiency. These traits were exploited for targeted gene replacement in N. crassa. In addition, the high electroporation efficiency of pyrG achieved using supercoiled circular DNA renders it an ideal marker for random insertional mutagenesis studies in N. crassa

Strong polarization-induced reduction of addition energies in single-molecule nanojunctions

We address polarization-induced renormalization of molecular levels in solid-state based single-molecule transistors and focus on an organic conjugate molecule where a surprisingly large reduction of the addition energy has been observed. We have developed a scheme that combines a self-consistent solution of a quantum chemical calculation with a realistic description of the screening environment. Our results indeed show a large reduction, and we explain this to be a consequence of both (a) a reduction of the electrostatic molecular charging energy and (b) polarization induced level shifts of the HOMO and LUMO levels. Finally, we calculate the charge stability diagram and explain at a qualitative level general features observed experimentally.Comment: 9 pages, 5 figure