Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.Comment: 50 pages;7 figure

Preventing pain on injection of propofol: A comparison between lignocaine pre-treatment and lignocaine added to propofol

Publisher's copy made available with the permission of the publisherA randomized double-blind study compared two methods of preventing the pain from injection of propofol, lignocaine pre-treatment followed by propofol and lignocaine added to propofol. One hundred patients received a 4 ml solution intravenously with a venous tourniquet for 1 minute, followed by propofol mixed with 2 ml of solution. Patients were divided into two treatment groups of 50 patients each: 4 ml 1% lignocaine pre-treatment followed by propofol and 2 ml saline, or 4 ml saline followed by propofol and 2 ml 2% lignocaine. Pain was assessed with a 100 mm visual analogue scale after induction and in recovery. The incidence of injection pain was 8% in the propofol mixed with lignocaine group, and 28% in the lignocaine pre-treatment group. This difference is statistically significant (P=0.017). For those patients who had pain, the mean pain score was 26.5 on induction for the propofol with lignocaine group (n=4), while the mean score was 44.4 for the pre-treatment group (n=13). The difference was not statistically significant (P=0.25). None of the propofol mixed with lignocaine group recalled pain, while 13 of the pre-treatment group did so. Lignocaine pre-treatment does not improve the immediate or the recalled comfort of patients during propofol induction when compared to lignocaine added to propofol. It is recommended that lignocaine should be added to propofol for induction rather than given before induction.P. Lee, W. J. Russellhttp://www.aaic.net.au/Article.asp?D=200339

The magnetic field topology associated to two M flares

On 27 October, 2003, two GOES M-class flares occurred in the lapse of three hours in active region NOAA 10486. The two flares were confined and their associated brightenings appeared at the same location, displaying a very similar shape both at the chromospheric and coronal levels. We focus on the analysis of magnetic field (SOHO/MDI), chromospheric (HASTA, Kanzelhoehe Solar Observatory, TRACE) and coronal (TRACE) observations. By combining our data analysis with a model of the coronal magnetic field, we compute the magnetic field topology associated to the two M flares. We find that both events can be explained in terms of a localized magnetic reconnection process occurring at a coronal magnetic null point. This null point is also present at the same location one day later, on 28 October, 2003. Magnetic energy release at this null point was proposed as the origin of a localized event that occurred independently with a large X17 flare on 28 October, 2003, at 11:01 UT. The three events, those on 27 October and the one on 28 October, are homologous. Our results show that coronal null points can be stable topological structures where energy release via magnetic reconnection can happen, as proposed by classical magnetic reconnection models.Comment: 14 pages, 7 figure

Evidence for charge localization in the ferromagnetic phase of La_(1-x)Ca_(x)MnO_3 from High real-space-resolution x-ray diffraction

High real-space-resolution atomic pair distribution functions of La_(1-x)Ca_(x)MnO_3 (x=0.12, 0.25 and 0.33) have been measured using high-energy x-ray powder diffraction to study the size and shape of the MnO_6 octahedron as a function of temperature and doping. In the paramagnetic insulating phase we find evidence for three distinct bond-lengths (~ 1.88, 1.95 and 2.15A) which we ascribe to Mn^{4+}-O, Mn^{3+}-O short and Mn^{3+}-O long bonds respectively. In the ferromagnetic metallic (FM) phase, for x=0.33 and T=20K, we find a single Mn-O bond-length; however, as the metal-insulator transition is approached either by increasing T or decreasing x, intensity progressively appears around r=2.15 and in the region 1.8 - 1.9A suggesting the appearance of Mn^{3+}-O long bonds and short Mn^{4+}-O bonds. This is strong evidence that charge localized and delocalized phases coexist close to the metal-insulator transition in the FM phase.Comment: 8 pages, 8 postscript figures, submitted to Phys. Rev.

Aspects of Two-Photon Physics at Linear e+e- Colliders

We discuss various reactions at future e+e- and gamma-gamma colliders involving real (beamstrahlung or backscattered laser) or quasi--real (bremsstrahlung) photons in the initial state and hadrons in the final state. The production of two central jets with large pT is described in some detail; we give distributions for the rapidity and pT of the jets as well as the di--jet invariant mass, and discuss the relative importance of various initial state configurations and the uncertainties in our predictions. We also present results for `mono--jet' production where one jet goes down a beam pipe, for the production of charm, bottom and top quarks, and for single production of W and Z bosons. Where appropriate, the two--photon processes are compared with annihilation reactions leading to similar final states. We also argue that the behaviour of the total inelastic gamma-gamma cross section at high energies will probably have little impact on the severity of background problems caused by soft and semi--hard (`minijet') two--photon reactions. We find very large differences in cross sections for all two--photon processes between existing designs for future e+e- colliders, due to the different beamstrahlung spectra; in particular, both designs with >1 events per bunch crossing exist.Comment: 51 pages, 13 figures(not included

A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

FGF receptor genes and breast cancer susceptibility: results from the Breast Cancer Association Consortium

Background:Breast cancer is one of the most common malignancies in women. Genome-wide association studies have identified FGFR2 as a breast cancer susceptibility gene. Common variation in other fibroblast growth factor (FGF) receptors might also modify risk. We tested this hypothesis by studying genotyped single-nucleotide polymorphisms (SNPs) and imputed SNPs in FGFR1, FGFR3, FGFR4 and FGFRL1 in the Breast Cancer Association Consortium. Methods:Data were combined from 49 studies, including 53 835 cases and 50 156 controls, of which 89 050 (46 450 cases and 42 600 controls) were of European ancestry, 12 893 (6269 cases and 6624 controls) of Asian and 2048 (1116 cases and 932 controls) of African ancestry. Associations with risk of breast cancer, overall and by disease sub-type, were assessed using unconditional logistic regression. Results:Little evidence of association with breast cancer risk was observed for SNPs in the FGF receptor genes. The strongest evidence in European women was for rs743682 in FGFR3; the estimated per-allele odds ratio was 1.05 (95 confidence interval=1.02-1.09, P=0.0020), which is substantially lower than that observed for SNPs in FGFR2. Conclusion:Our results suggest that common variants in the other FGF receptors are not associated with risk of breast cancer to the degree observed for FGFR2. © 2014 Cancer Research UK

All-particle cosmic ray energy spectrum measured with 26 IceTop stations

We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array, the surface component of the IceCube Neutrino Observatory at the South Pole. The data used in this analysis were taken between June and October, 2007, with 26 surface stations operational at that time, corresponding to about one third of the final array. The fiducial area used in this analysis was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV measured for three different zenith angle ranges between 0{\deg} and 46{\deg}. Because of the isotropy of cosmic rays in this energy range the spectra from all zenith angle intervals have to agree. The cosmic-ray energy spectrum was determined under different assumptions on the primary mass composition. Good agreement of spectra in the three zenith angle ranges was found for the assumption of pure proton and a simple two-component model. For zenith angles {\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on composition assumption. Spectral indices above the knee range from -3.08 to -3.11 depending on primary mass composition assumption. Moreover, an indication of a flattening of the spectrum above 22 PeV were observed.Comment: 38 pages, 17 figure

Imaging Observations of Quasi-Periodic Pulsatory Non-Thermal Emission in Ribbon Solar Flares

Using RHESSI and some auxiliary observations we examine possible connections between spatial and temporal morphology of the sources of non-thermal hard X-ray (HXR) emission which revealed minute quasi-periodic pulsations (QPPs) during the two-ribbon flares on 2003 May 29 and 2005 January 19. Microwave emission also reveals the same quasi-periodicity. The sources of non-thermal HXR emission are situated mainly inside the footpoints of the flare arcade loops observed by the TRACE and SOHO instruments. At least one of the sources moves systematically both during the QPP-phase and after it in each flare that allows to examine the sources velocities and the energy release rate via the process of magnetic reconnection. The sources move predominantly parallel to the magnetic inversion line or the appropriate flare ribbon during the QPP-phase whereas the movement slightly changes to more perpendicular regime after the QPPs. Each QPP is emitted from its own position. It is also seen that the velocity and the energy release rate don't correlate well with the flux of the HXR emission calculated from the sources. The sources of microwaves and thermal HXRs are situated near the apex of the loop arcade and are not stationary either. Almost all QPPs and some spikes of HXR emission during the post-QPP-phase reveal the soft-hard-soft spectral behavior indicating separate acts of electrons acceleration and injection, rather than modulation of emission flux by some kinds of magnetohydrodynamic (MHD) oscillations of coronal loops. In all likelihood, the flare scenarios based on the successively firing arcade loops are more preferable to interpret the observations, although we can not conclude exactly what mechanism forces these loops to flare up.Comment: 22 pages, 10 figure

Origin of the submillimeter radio emission during the time-extended phase of a solar flare

Solar flares observed in the 200-400 GHz radio domain may exhibit a slowly varying and time-extended component which follows a short (few minutes) impulsive phase and which lasts for a few tens of minutes to more than one hour. The few examples discussed in the literature indicate that such long-lasting submillimeter emission is most likely thermal bremsstrahlung. We present a detailed analysis of the time-extended phase of the 2003 October 27 (M6.7) flare, combining 1-345 GHz total-flux radio measurements with X-ray, EUV, and H{\alpha} observations. We find that the time-extended radio emission is, as expected, radiated by thermal bremsstrahlung. Up to 230 GHz, it is entirely produced in the corona by hot and cool materials at 7-16 MK and 1-3 MK, respectively. At 345 GHz, there is an additional contribution from chromospheric material at a few 10^4 K. These results, which may also apply to other millimeter-submillimeter radio events, are not consistent with the expectations from standard semi-empirical models of the chromosphere and transition region during flares, which predict observable radio emission from the chromosphere at all frequencies where the corona is transparent.Comment: 27 pages, 7 figure