Spherically Symmetric Gravitational Collapse of Perfect Fluids

Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but also finds a new coordinate system for the Schwarzschild spacetime expressed in generalized Painleve-Gullstrand coordinates.Comment: 3 pages, To appear in the proceedings of the eleventh Marcel Grossmann meeting on general relativity (MGXI), 23-29 July, 2006, Berli

Identification of a carbohydrate-based endothelial ligand for a lymphocyte homing receptor.

Lymphocyte attachment to high endothelial venules within lymph nodes is mediated by the peripheral lymph node homing receptor (pnHR), originally defined on mouse lymphocytes by the MEL-14 mAb. The pnHR is a calcium-dependent lectin-like receptor, a member of the LEC-CAM family of adhesion proteins. Here, using a soluble recombinant form of the homing receptor, we have identified an endothelial ligand for the pnHR as an approximately 50-kD sulfated, fucosylated, and sialylated glycoprotein, which we designate Sgp50 (sulfated glycoprotein of 50 kD). Recombinant receptor binding to this lymph node-specific glycoprotein requires calcium and is inhibitable by specific carbohydrates and by MEL-14 mAb. Sialylation of the component is required for binding. Additionally, the glycoprotein is precipitated by MECA-79, an adhesion-blocking mAb reactive with lymph node HEV. A related glycoprotein of approximately 90 kD (designated as Sgp90) is also identified

Three-dimensional shapelets and an automated classification scheme for dark matter haloes

We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole moment and moment of inertia tensors. Using cosmological N-body simulations as an application domain, we show that three-dimensional shapelets can be used to replicate the complex sub-structure of dark matter halos and demonstrate the basis of an automated classification scheme for halo shapes. We investigate the shapelet decomposition process from an algorithmic viewpoint, and consider opportunities for accelerating the computation of shapelet-based representations using graphics processing units (GPUs).Comment: 19 pages, 11 figures, accepted for publication in MNRA

A homing receptor-IgG chimera as a probe for adhesive ligands of lymph node high endothelial venules.

The binding of lymphocytes to high endothelial venules (HEV) within peripheral lymph nodes (pln) is thought to be mediated by a lectinlike adhesion molecule termed the pln homing receptor (pln HR). The cloning and sequencing of cDNAs encoding both murine and human pln HR revealed that these adhesion molecules contain protein motifs that are homologous to C-type or calcium dependent lectin domains as well as to epidermal growth factor (egf) and complement-regulatory protein domains. We have produced a novel, antibody-like form of the murine HR by joining the extracellular region of the receptor to a human IgG heavy chain. This antibody-like molecule is capable of recognizing carbohydrates, blocking the binding of lymphocytes to pln HEV, and serving as a histochemical reagent for the staining of pln HEV. This murine HR-IgG chimera should prove useful in analyzing the distribution of the HR ligand(s) in normal as well as in inflammatory states

The complement binding-like domains of the murine homing receptor facilitate lectin activity.

The leukocyte homing receptor (HR), the endothelial leukocyte adhesion molecule, and gmp140/platelet activation-dependent granule membrane protein are members of a family of adhesion molecules, termed the lectin cell adhesion molecules (LEC-CAMS) which are unified by a multi-domain structure containing a lectin motif, an epidermal growth factor-like (egf) motif, and variable numbers of a complement binding-like (CB) motif. Previous data have indicated a predominant role for the lectin motif in cell adhesion directed by the LEC-CAMS, although the egf-like domain of the HR may also play a potential role in cell binding. While the role(s) of the CB domains in the LEC-CAMS is currently not understood, they have been hypothesized to act as rigid spacers or stalks for lectin and perhaps, egf domain presentation. In this paper, we analyze the functional characteristics of murine HR-IgG chimeras containing the lectin, lectin plus egf, and lectin plus egf plus CB domains. The Mel 14 mAb, an adhesion blocking antibody which recognizes a conformational determinant in the N-terminus of the HR lectin domain, shows a significantly decreased affinity for a HR construct which lacks the CB motifs, consistent with the possibility that the CB domains are involved with lectin domain structure. In agreement with this conjecture, HR mutants lacking the CB domains show a profound decrease in lectin-specific interaction with the carbohydrate polyphosphomannan ester, suggesting that the changes in Mel 14 affinity for the lectin domain are reflected in lectin functionality. Various assays investigating the interactions between the HR deletion mutants and the peripheral lymph node high endothelium, including cell blocking, immunohistochemical staining, and radioactively labeled ligand binding, all showed that removal of the CB domains results in a lack of HR adhesive function. These results imply that the CB domains of the HR, and, by analogy, the other members of the LEC-CAM family, may play important structural roles involving induction of lectin domain conformation and resultant functionality

Are gravitational waves from giant magnetar flares observable?

Are giant flares in magnetars viable sources of gravitational radiation? Few theoretical studies have been concerned with this problem, with the small number using either highly idealized models or assuming a magnetic field orders of magnitude beyond what is supported by observations. We perform nonlinear general-relativistic magnetohydrodynamics simulations of large-scale hydromagnetic instabilities in magnetar models. We utilise these models to find gravitational wave emissions over a wide range of energies, from 10^40 to 10^47 erg. This allows us to derive a systematic relationship between the surface field strength and the gravitational wave strain, which we find to be highly nonlinear. In particular, for typical magnetar fields of a few times 10^15 G, we conclude that a direct observation of f-modes excited by global magnetic field reconfigurations is unlikely with present or near-future gravitational wave observatories, though we also discuss the possibility that modes in a low-frequency band up to 100 Hz could be sufficiently excited to be relevant for observation.Comment: 4 pages, 3 figures. Further information can be found at http://www.physik.uni-tuebingen.de/institute/astronomie-astrophysik/institut/theoretische-astrophysik/forschung.htm

Implementing and Sustaining Science Curriculum Reform: A Study of Leadership Practices Among Teachers within a High School Science Department

This study presents a description and analysis of a ninth-grade integrated science curriculum developed and implemented by teachers within a high school science department and subsequently sustained for over 25 years. The Integrated Science Program (ISP) at Lakeside Southwest High School depicted here offers a unique example of longitudinal science education reform. In this study, we examined ISP as an artifact of teacher leadership. Findings affirmed the importance of shared philosophical purpose among teachers, attention to public perceptions, staff stability, the distribution of responsibilities, and instructional coherence. This study also demonstrated how curricular reforms might change over time in response to contextual pressures as was the case with the equity challenges faced by the current teachers of ISP

Stability and Quasinormal Modes of Black holes in Tensor-Vector-Scalar theory: Scalar Field Perturbations

The imminent detection of gravitational waves will trigger precision tests of gravity through observations of quasinormal ringing of black holes. While General Relativity predicts just two polarizations of gravitational waves, the so-called plus and cross polarizations, numerous alternative theories of gravity predict up to six different polarizations which will potentially be observed in current and future generations of gravitational wave detectors. Bekenstein's Tensor-Vector-Scalar (TeVeS) theory and its generalization fall into one such class of theory that predict the full gamut of six polarizations of gravitational waves. In this paper we begin the study of quasinormal modes (QNMs) in TeVeS by studying perturbations of the scalar field in a spherically symmetric background. We show that, at least in the case where superluminal propagation of perturbations is not present, black holes are generically stable to this kind of perturbation. We also make a unique prediction that, as the limit of the various coupling parameters of the theory tend to zero, the QNM spectrum tends to $1/\sqrt{2}$ times the QNM spectrum induced by scalar perturbations of a Schwarzschild black hole in General Relativity due to the intrinsic presence of the background vector field. We further show that the QNM spectrum does not vary significantly from this value for small values of the theory's coupling parameters, however can vary by as much as a few percent for larger, but still physically relevant parameters.Comment: Published in Physical Review

Spherically Symmetric Gravitational Collapse of General Fluids

We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null radiation such that a region of Vaidya spacetime develops. Therefore, on any subsequent spacelike slice there exists three regions; general fluid, Vaidya and Schwarzschild, all expressed in a single coordinate patch with two free-boundaries determined by the equations. This implies complicated matching schemes are not required at the interfaces between the regions, instead, one simply requires the matter variables tend to the appropriate equations of state. We also show the reduction of the system of equations to the static cases, and show staticity necessarily implies zero ``heat flux''. Furthermore, the static equations include a generalization of the Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium to include anisotropic stresses in general coordinates.Comment: 11 pages, 3 figures, submitted to Phys. Rev.

Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes

We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of electromagnetic matter. We show the system reduces to the Reissner-Nordstrom spacetime in general, spherically symmetric coordinates in the vacuum limit. Furthermore, we show reduction to the charged Vaidya spacetime in non-null coordinates when certain equations of states are chosen. A model of gravitational collapse is discussed whereby a charged fluid resides within a boundary of finite radial extent on the initial hypersurface, and is allowed to radiate charged particles. Our formalism allows for the discussion of all regions in this model without the need for complicated matching schemes at the interfaces between successive regions. As further examples we consider the collapse of a thin shell of charged matter onto a Reissner-Nordstrom black hole. Finally, we reduce the entire system of equations to the static case such that we have the equations for hydrostatic equilibrium of a charged fluid.Comment: Accepted for publication in Phys. Rev.