1+1+2 Electromagnetic perturbations on non-vacuum LRS class II space-times: Decoupling scalar and 2-vector harmonic amplitudes

We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times. Ultimately, we show how to derive six real decoupled equations governing the total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new, and result from expanding the complex EM 2-vector which we defined in \cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then able to show that there are four precise combinations of the amplitudes that decouple, two of these are polar perturbations whereas the remaining two are axial. The remaining two decoupled equations are the generalized Regge-Wheeler equations which were developed previously in \cite{Betschart2004}, and these govern the two EM scalar harmonic amplitudes. However, our analysis generalizes this by including a full description and classification of energy-momentum sources, such as charges and currents.Comment: 9 page

SDO/HMI survey of emerging active regions for helioseismology

Observations from the Solar Dynamics Observatory (SDO) have the potential for allowing the helioseismic study of the formation of hundreds of active regions, which would enable us to perform statistical analyses. Our goal is to collate a uniform data set of emerging active regions observed by the SDO/HMI instrument suitable for helioseismic analysis up to seven days before emergence. We restricted the sample to active regions that were visible in the continuum and emerged into quiet Sun largely avoiding pre-existing magnetic regions. As a reference data set we paired a control region (CR), with the same latitude and distance from central meridian, with each emerging active region (EAR). We call this data set, which is currently comprised of 105 emerging active regions observed between May 2010 and November 2012, the SDO Helioseismic Emerging Active Region (SDO/HEAR) survey. To demonstrate the utility of a data set of a large number of emerging active regions, we measure the relative east-west velocity of the leading and trailing polarities from the line-of-sight magnetogram maps during the first day after emergence. The latitudinally averaged line-of-sight magnetic field of all the EARs shows that, on average, the leading (trailing) polarity moves in a prograde (retrograde) direction with a speed of 121 +/- 22 m/s (-70 +/- 13 m/s) relative to the Carrington rotation rate in the first day. However, relative to the differential rotation of the surface plasma, the east-west velocity is symmetric, with a mean of 95 +/- 13 m/s. The SDO/HEAR data set will not only be useful for helioseismic studies, but will also be useful to study other features such as the surface magnetic field evolution of a large sample of EARs.Comment: Accepted by Astronomy and Astrophysics, 11 figures, one longtable; update corrects units in Figure

1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations

We use the, covariant and gauge-invariant, 1+1+2 formalism developed by Clarkson and Barrett, and develop new techniques, to decouple electromagnetic (EM) perturbations on arbitrary locally rotationally symmetric (LRS) space-times. Ultimately, we derive 3 decoupled complex equations governing 3 complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized for LRS space-times, whereas the remaining two are new generalizations of the Bardeen-Press (BP) equations. This is achieved by first using linear algebra techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2 form which is conducive to decoupling. This new complex system immediately yields the generalized RW equation, and furthermore, we also derive a decoupled equation governing a newly defined complex EM 2-vector. Subsequently, a further decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed, allowing us to decompose the complex EM 2-vector, and its governing equations, into spin-weighted scalars, giving rise to the generalized BP equations

Average motion of emerging solar active region polarities I: Two phases of emergence

Our goal is to constrain models of active region formation by tracking the average motion of active region polarity pairs as they emerge onto the surface. We measured the motion of the two main opposite polarities in 153 emerging active regions (EARs) using line-of-sight magnetic field observations from the Solar Dynamics Observatory Helioseismic Emerging Active Region (SDO/HEAR) survey (Schunker et al. 2016). We first measured the position of each of the polarities eight hours after emergence and tracked their location forwards and backwards in time. We find that, on average, the polarities emerge with an east-west orientation and the separation speed between the polarities increases. At about 0.1 days after emergence, the average separation speed reaches a peak value of 229 +/- 11 m/s, and then starts to decrease, and about 2.5 days after emergence the polarities stop separating. We also find that the separation and the separation speed in the east-west direction are systematically larger for active regions with higher flux. Our results reveal two phases of the emergence process defined by the rate of change of the separation speed as the polarities move apart. Phase 1 begins when the opposite polarity pairs first appear at the surface, with an east-west alignment and an increasing separation speed. We define Phase 2 to begin when the separation speed starts to decrease, and ends when the polarities have stopped separating. This is consistent with the picture of Chen, Rempel, & Fan (2017): the peak of a flux tube breaks through the surface during Phase 1. During Phase 2 the magnetic field lines are straightened by magnetic tension, so that the polarities continue to move apart, until they eventually lie directly above their anchored subsurface footpoints.Comment: accepted A&

Human osteoblast growth and maturation in response to metformin and the thienopyridone, A769662

Metformin (Met) is a biguanide drug widely used in the treatment and management of non insulin-dependent diabetes mellitus. In recent years it has emerged that Met, by stimulating adenosine monophosphate-activated protein kinase (AMPK), can promote the maturation of osteoblasts, albeit cells sourced from rodent and murine calvaria. Finding novel uses for existing drugs is especially appealing, primarily from the fiscal and time constraints posed in developing new products. Identifying agents capable of supporting human osteoblast growth and differentiation are attractive in a bone regenerative context. Since studies using Met are invariably restricted to rodent and murine osteoblasts we sought to investigate whether this biguanide might have a positive influence upon human osteoblast growth and maturation. To this end we examined the effect of Met on two osteoblast-like cell lines, MG63 and Saos-2, and compared the responses to primary human osteoblasts and their bone marrow-derived stem cell progeny. Furthermore we examined the effect of a cell permeable Met surrogate, A769662, which is a potent and far more selective activator of AMPK. Herein we report that Met is without influence on cell growth. Furthermore the application of Met, albeit in the millimolar range, actually inhibited osteoblast maturation. Conversely A769662 was toxic to the osteosarcoma-derived cell lines, MG63 and Saos-2, but without effect on the growth of primary cells or their stem cell progenitors. Since the cell lines are known to be p53 deficient we propose that activation of AMPK by A769662 could form part of the arsenal in the fight against osteosarcoma

Children with lesbian parents: A community study

Existing research on children with lesbian parents is limited by reliance on volunteer or convenience samples. The present study examined the quality of parent-child relationships and the socio-emotional and gender development of a community sample of 7-year-old children with lesbian parents. Families were recruited through the Avon Longitudinal Study of Parents and Children, a geographic population study of 14,000 mothers and their children. Thirty-nine lesbian-mother families, 74 two-parent heterosexual families, and 60 families headed by single heterosexual mothers were compared on standardized interview and questionnaire measures administered to mothers, co-mothers/fathers, children, and teachers. Findings are in line with those of earlier investigations showing positive mother-child relationships and well-adjusted children

Covariant perturbations of f(R) black holes: the Weyl terms

In this paper we revisit non-spherical perturbations of the Schwarzschild black hole in the context of f(R) gravity. Previous studies were able to demonstrate the stability of the f(R) Schwarzschild black hole against gravitational perturbations in both the even and odd parity sectors. In particular, it was seen that the Regge-Wheeler and Zerilli equations in f(R) gravity obey the same equations as their General Relativity counterparts. More recently, the 1+1+2 semi-tetrad formalism has been used to derive a set of two wave equations: one for transverse, trace-free (tensor) perturbations and one for the additional scalar modes that characterise fourth-order theories of gravitation. The master variable governing tensor perturbations was shown to be a modified Regge-Wheeler tensor obeying the same equation as in General Relativity. However, it is well known that there is a non-uniqueness in the definition of the master variable. In this paper we derive a set of two perturbation variables and their concomitant wave equations that describe gravitational perturbations in a covariant and gauge invariant manner. These variables can be related to the Newman-Penrose (NP) Weyl scalars as well as the master variables from the 2+2 formalism

Therapeutic approach to Gradenigo's syndrome: a case report

Abstract Introduction Traditional management of Gradenigo's syndrome requires aggressive and radical surgery without any attempt to preserve hearing. Recent reports, however, describe a successful outcome after conservative surgical intervention without labyrinthectomy. A similar outcome has also been reported in patients who were only prescribed with antibiotics and did not undergo myringotomy. Case presentation We report the case of a 24-year-old Caucasian Greek woman with Gradenigo's syndrome who was treated by draining her petrous apex via an infralabyrithine approach between her posterior semicircular canal and the jugular bulb. Her inner ear was not sacrificed during the procedure. She presented pre-operatively with ipsilateral conductive hearing loss, which recovered completely four weeks after the surgery. Conclusions Patients with Gradenigo's syndrome may be successfully treated with a combination of long-term permanent drainage and ventilation of the apical cells with corresponding hearing preservation. This can be achieved via a combination of transmastoid, infralabyrinthine and suprajugular approaches, if such would be allowed by the anatomy of the region or if there is enough space between the posterior semicircular canal and the jugular bulb.</p