A method to calculate correlation functions for β=1\beta=1 random matrices of odd size

The calculation of correlation functions for $\beta=1$ random matrix ensembles, which can be carried out using Pfaffians, has the peculiar feature of requiring a separate calculation depending on the parity of the matrix size N. This same complication is present in the calculation of the correlations for the Ginibre Orthogonal Ensemble of real Gaussian matrices. In fact the methods used to compute the $\beta=1$, N odd, correlations break down in the case of N odd real Ginibre matrices, necessitating a new approach to both problems. The new approach taken in this work is to deduce the $\beta=1$, N odd correlations as limiting cases of their N even counterparts, when one of the particles is removed towards infinity. This method is shown to yield the correlations for N odd real Gaussian matrices.Comment: 20 pages, corrected typo

A real quaternion spherical ensemble of random matrices

One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with truncations of unitary matrices. This paper focusses on an ensemble corresponding to the sphere: matrices of the form \bY= \bA^{-1} \bB, where \bA and \bB are independent $N\times N$ matrices with iid standard Gaussian real quaternion entries. By applying techniques similar to those used for the analogous complex and real spherical ensembles, the eigenvalue jpdf and correlation functions are calculated. This completes the exploration of spherical matrices using the traditional Dyson indices $\beta=1,2,4$. We find that the eigenvalue density (after stereographic projection onto the sphere) has a depletion of eigenvalues along a ring corresponding to the real axis, with reflective symmetry about this ring. However, in the limit of large matrix dimension, this eigenvalue density approaches that of the corresponding complex ensemble, a density which is uniform on the sphere. This result is in keeping with the spherical law (analogous to the circular law for iid matrices), which states that for matrices having the spherical structure \bY= \bA^{-1} \bB, where \bA and \bB are independent, iid matrices the (stereographically projected) eigenvalue density tends to uniformity on the sphere.Comment: 25 pages, 3 figures. Added another citation in version

Deflection and Rotation of CMEs from Active Region 11158

Between the 13 and 16 of February 2011 a series of coronal mass ejections (CMEs) erupted from multiple polarity inversion lines within active region 11158. For seven of these CMEs we use the Graduated Cylindrical Shell (GCS) flux rope model to determine the CME trajectory using both Solar Terrestrial Relations Observatory (STEREO) extreme ultraviolet (EUV) and coronagraph images. We then use the Forecasting a CME's Altered Trajectory (ForeCAT) model for nonradial CME dynamics driven by magnetic forces, to simulate the deflection and rotation of the seven CMEs. We find good agreement between the ForeCAT results and the reconstructed CME positions and orientations. The CME deflections range in magnitude between 10 degrees and 30 degrees. All CMEs deflect to the north but we find variations in the direction of the longitudinal deflection. The rotations range between 5\mydeg and 50\mydeg with both clockwise and counterclockwise rotations occurring. Three of the CMEs begin with initial positions within 2 degrees of one another. These three CMEs all deflect primarily northward, with some minor eastward deflection, and rotate counterclockwise. Their final positions and orientations, however, respectively differ by 20 degrees and 30 degrees. This variation in deflection and rotation results from differences in the CME expansion and radial propagation close to the Sun, as well as the CME mass. Ultimately, only one of these seven CMEs yielded discernible in situ signatures near Earth, despite the active region facing near Earth throughout the eruptions. We suggest that the differences in the deflection and rotation of the CMEs can explain whether each CME impacted or missed the Earth.Comment: 18 pages, 6 figures, accepted in Solar Physic

The Physical Processes of CME/ICME Evolution

As observed in Thomson-scattered white light, coronal mass ejections (CMEs) are manifest as large-scale expulsions of plasma magnetically driven from the corona in the most energetic eruptions from the Sun. It remains a tantalizing mystery as to how these erupting magnetic fields evolve to form the complex structures we observe in the solar wind at Earth. Here, we strive to provide a fresh perspective on the post-eruption and interplanetary evolution of CMEs, focusing on the physical processes that define the many complex interactions of the ejected plasma with its surroundings as it departs the corona and propagates through the heliosphere. We summarize the ways CMEs and their interplanetary CMEs (ICMEs) are rotated, reconfigured, deformed, deflected, decelerated and disguised during their journey through the solar wind. This study then leads to consideration of how structures originating in coronal eruptions can be connected to their far removed interplanetary counterparts. Given that ICMEs are the drivers of most geomagnetic storms (and the sole driver of extreme storms), this work provides a guide to the processes that must be considered in making space weather forecasts from remote observations of the corona.Peer reviewe

Origin and ion charge state evolution of solar wind transients during 4 - 7 August 2011

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214). The computational work for this article was carried out on the joint STFC and SFC (SRIF) funded clusters at the University of St Andrews (Scotland, UK). The work is partially supported by RFBR grants 17-02-00787, 14-02-00945 and the P7 Program of the Russian Academy of Sciences.We present a study of the complex event consisting of several solar wind transients detected by the Advanced Composition Explorer (ACE) on 4 - 7 August 2011, which caused a geomagnetic storm with Dst=-110 nT. The supposed coronal sources, three flares and coronal mass ejections (CMEs), occurred on 2 - 4 August 2011 in active region (AR) 11261. To investigate the solar origin and formation of these transients, we study the kinematic and thermodynamic properties of the expanding coronal structures using the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) EUV images and differential emission measure (DEM) diagnostics. The Helioseismic and Magnetic Imager (HMI) magnetic field maps were used as the input data for the 3D magnetohydrodynamic (MHD) model to describe the flux rope ejection (Pagano, Mackay, and Poedts, 2013b). We characterize the early phase of the flux rope ejection in the corona, where the usual three-component CME structure formed. The fluxrope was ejected with a speed of about 200 km s-1 to the height of 0.25 R⊙. The kinematics of the modeled CME front agrees well with the Solar Terrestrial Relations Observatory (STEREO) EUV measurements. Using the results of the plasma diagnostics and MHD modeling, we calculate the ion charge ratios of carbon and oxygen as well as the mean charge state of iron ions of the 2 August 2011 CME, taking into account the processes of heating, cooling, expansion, ionization, and recombination of the moving plasma in the corona up to the frozen-in region. We estimate a probable heating rate of the CME plasma in the low corona by matching the calculated ion composition parameters of the CME with those measured in situ for the solar wind transients. We also consider the similarities and discrepancies between the results of the MHD simulation and the observations.PostprintPeer reviewe

An Attempt to Detect Coronal Mass Ejections in Lyman- α Using SOHO Swan

In this study, the possibility that coronal mass ejections (CMEs) may be observed in neutral Lyman-α emission was investigated. An observing campaign was initiated for SWAN (Solar Wind ANisotropies), a Lyman-α scanning photometer on board the Solar and Heliospheric Observatory (SOHO) dedicated to monitoring the latitude distribution of the solar wind from its imprints on the interstellar sky background. This was part of SOHO Joint Observing Program (JOP) 159 and was an exploratory investigation as it was not known how, or even if, CMEs interact with the solar wind and interstellar neutral hydrogen at this distance (≈60 and 120 R S). The study addresses the lack of methods for tracking CMEs beyond the field-of-view of current coronagraphs (30 R S). In our first method we used LASCO, white-light coronagraphs on SOHO, and EIT, an extreme ultraviolet imaging telescope also on SOHO, to identify CME candidates which, subject to certain criteria, should have been observable in SWAN. The criteria included SWAN observation time and location, CME position angle, and extrapolated speed. None of the CME candidates that we discuss were identified in the SWAN data. For our second method we analyzed all of the SWAN data for 184 runs of the observing campaign, and this has yielded one candidate CME detection. The candidate CME appears as a dimming of the background Lyman-α intensity representing ≈10% of the original intensity, moving radially away from the Sun. Multiple candidate CMEs observed by LASCO and EIT were found which may have caused this dimming. Here we discuss the campaign, data analysis technique and statistics, and the results

Claudin-5 Levels Are Reduced in Human End-Stage Cardiomyopathy

Claudin-5 is a transmembrane cell junction protein that is a component of tight junctions in endothelial cell layers. We have previously shown that claudin-5 also localizes to lateral membranes of murine cardiomyocytes at their junction with the extracellular matrix. Claudin-5 levels are specifically reduced in myocytes from a mouse model of muscular dystrophy with cardiomyopathy. To establish whether claudin-5 is similarly specifically reduced in human cardiomyopathy, we compared the levels of claudin-5 with other cell junction proteins in 62 cardiomyopathic end-stage explant samples. We show that claudin-5 levels are reduced in at least 60% of patient samples compared with non-failing controls. Importantly, claudin-5 reductions can be independent of connexin-43, a gap junction protein previously reported to be reduced in failing heart samples. Other cell junction proteins including α-catenin, β-catenin, γ-catenin, desmoplakin, and N-cadherin are reduced in only a small number of failing samples and only in combination with reduced claudin-5 or connexin-43 levels. We also show that reduced claudin-5 levels can be present independently from dystrophin alterations, which are known to be capable of causing and resulting from cardiomyopathy. These data are the first to show alterations of a tight junction protein in human cardiomyopathy samples and suggest that claudin-5 may participate in novel mechanisms in the pathway to end-stage heart failure