Schwarzschild-de Sitter Spacetimes, McVittie Coordinates, and Trumpet Geometries

Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated numerical studies of black holes in asymptotically de Sitter spacetimes. We derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter spacetimes by first generalizing the static maximal trumpet slicing of the Schwarzschild spacetime to static constant mean curvature trumpet slicings of Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic radial coordinate which results in a coordinate system analogous to McVittie coordinates. At large distances from the black hole the resulting metric asymptotes to a Friedmann-Lemaitre-Robertson-Walker metric with an exponentially-expanding scale factor. While McVittie coordinates have another asymptotically de Sitter end as the radial coordinate goes to zero, so that they generalize the notion of a "wormhole" geometry, our new coordinates approach a horizon-penetrating trumpet geometry in the same limit. Our analytical expressions clarify the role of time-dependence, boundary conditions and coordinate conditions for trumpet slices in a cosmological context, and provide a useful test for black hole simulations in asymptotically de Sitter spacetimes.Comment: 7 pages, 3 figures, added referenc

Approximate initial data for binary black holes

We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the presence of a binary companion. A superposition of these two perturbations then yields approximate, but fully analytic binary black hole initial data that are accurate to first order in the inverse of the binary separation and the square of the black holes' momenta.Comment: 13 pages, 4 figures, added comparison to numerical calculations, accepted to PR

Trumpet Slices in Kerr Spacetimes

We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.Comment: 5 pages, 2 figures; version published in PR

The role of C-terminal amidation in the membrane interactions of the anionic antimicrobial peptide, maximin H5

Maximin H5 is an anionic antimicrobial peptide from amphibians, which carries a C-terminal amide moiety, and was found to be moderately haemolytic (20%). The α-helicity of the peptide was 42% in the presence of lipid mimics of erythrocyte membranes and was found able to penetrate (10.8mNm(-1)) and lyse these model membranes (64 %). In contrast, the deaminated peptide exhibited lower levels of haemolysis (12%) and α-helicity (16%) along with a reduced ability to penetrate (7.8mNm(-1)) and lyse (55%) lipid mimics of erythrocyte membranes. Taken with molecular dynamic simulations and theoretical analysis, these data suggest that native maximin H5 primarily exerts its haemolytic action via the formation of an oblique orientated α-helical structure and tilted membrane insertion. However, the C-terminal deamination of maximin H5 induces a loss of tilted α-helical structure, which abolishes the ability of the peptide's N-terminal and C-terminal regions to H-bond and leads to a loss in haemolytic ability. Taken in combination, these observations strongly suggest that the C-terminal amide moiety carried by maximin H5 is required to stabilise the adoption of membrane interactive tilted structure by the peptide. Consistent with previous reports, these data show that the efficacy of interaction and specificity of maximin H5 for membranes can be attenuated by sequence modification and may assist in the development of variants of the peptide with the potential to serve as anti-infective

Internet Use Policies in the Public Schools of Nebraska: Implications for Health Education

Nebraska school board presidents (n=604) were asked to respond to a 36-item questionnaire that addressed the issues of health education and the Internet use policy regulating Internet use in the public schools. The response rate was 22.3 percent (n=135). Nebraska school board presidents reported that health education was not an important item to take into consideration when developing an Internet use policy, but reported that that sexual content, drug content, violence-related material and commercial content, respectively were very important items the Internet use policy should regulate. Thus, this study revealed that the school board presidents of Nebraska were not aware that sexual content, drug content, violence-related material and commercial content were components of health education. Nebraska school board presidents also reported that sexual content, drug content, violence-related material and commercial content were important issues that the Internet use policy should control and each were significantly different in the reported regulation importance. Chi-square analyses found that large school districts of Nebraska perceived importance of Internet regulation and a written Internet use policy significantly more than small school districts of Nebraska

A sequence related to the Stern sequence

In this dissertation we de???ne and study a two-parameter family of recursive sequences which we call the bow sequences. The general bow sequence is de???ned similarly to the Stern sequence, and many of the properties of the bow sequences are related to known properties of the Stern sequence. In particular, we derive the generating function for the general bow sequence, and give interpretations of the generating function for two basic cases. We also determine properties of the bow sequences modulo 2 and 3, and give conjectures for the behavior of the bow sequences modulo d for d ???4. Finally, we discuss ideas for future research

Trumpet slices of the Schwarzschild-Tangherlini spacetime

We study families of time-independent maximal and 1+log foliations of the Schwarzschild-Tangherlini spacetime, the spherically-symmetric vacuum black hole solution in D spacetime dimensions, for D >= 4. We identify special members of these families for which the spatial slices display a trumpet geometry. Using a generalization of the 1+log slicing condition that is parametrized by a constant n we recover the results of Nakao, Abe, Yoshino and Shibata in the limit of maximal slicing. We also construct a numerical code that evolves the BSSN equations for D=5 in spherical symmetry using moving-puncture coordinates, and demonstrate that these simulations settle down to the trumpet solutions.Comment: 11 pages, 6 figures, submitted to PR

Measurement of Conductivity and Charge Storage in Insulators Related to Spacecraft Charging

Improved experimental methods are discussed for laboratory measurement of conductivity and electric field in insulating spacecraft material intended for space radiation and plasma environments. These measurement techniques investigate the following features: 1) Measurements of conductivity are up to four orders of magnitude smaller than those determined by existing standard methods. 2) Conductivity is altered as radiation accumulates and trapping states fill with electrons. 3) With intense keV electron irradiation, electrons are continually emitted for hours from the irradiated surface after the irradiation ceases. 4) Charging induced by electron irradiation is strongly modified by the electron-hole pairs that the irradiation generates in the insulator. 5) High field effects at 106 V/cm act strongly on the electron-hole pairs and on electrons in shallow traps to provide extended conductivity. 6) The capacitance of the sample can be measured in the same apparatus along with the other testing. 7) Visible light can be used to investigate conduction by electrons (or holes) emitted from shallow trapping levels. The qualitative physics of such processes in solid dielectrics has long been known, and instrumentation is developed here for measuring the effects in practical spacecraft charging applications