Late time behaviour of the maximal slicing of the Schwarzschild black hole

A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be evolved into a foliation of the $r>3m/2$-region of the spacetime by maximal surfaces with the requirement that time runs equally fast at both spatial ends of the manifold. This paper studies the behaviour of these slices in the limit as proper time-at-infinity becomes arbitrarily large and gives an analytic expression for the collapse of the lapse.Comment: 18 pages, Latex, no figure

Lessons Learned in the First Year Operating Software Defined Radios in Space

Operating three unique software defined radios (SDRs) in a space environment aboard the Space Communications and Navigation (SCaN) Testbed for over one year has provided an opportunity to gather knowledge useful for future missions considering using software defined radios. This paper provides recommendations for the development and use of SDRs, and it considers the details of each SDR's approach to software upgrades and operation. After one year, the SCaN Testbed SDRs have operated for over 1000 hours. During this time, the waveforms launched with the SDR were tested on-orbit to assure that they operated in space at the same performance level as on the ground prior to launch to obtain an initial on-orbit performance baseline. A new waveform for each SDR has been developed, implemented, uploaded to the flight system, and tested in the flight environment. Recommendations for SDR-based missions have been gathered from early development through operations. These recommendations will aid future missions to reduce the cost, schedule, and risk of operating SDRs in a space environment. This paper considers the lessons learned as they apply to SDR pre-launch checkout, purchasing space-rated hardware, flexibility in command and telemetry methods, on-orbit diagnostics, use of engineering models to aid future development, and third-party software. Each SDR implements the SCaN Testbed flight computer command and telemetry interface uniquely, allowing comparisons to be drawn. The paper discusses the lessons learned from these three unique implementations, with suggestions on the preferred approach. Also, results are presented showing that it is important to have full system performance knowledge prior to launch to establish better performance baselines in space, requiring additional test applications to be developed pre-launch. Finally, the paper presents the issues encountered with the operation and implementation of new waveforms on each SDR and proposes recommendations to avoid these issues

Topology Change and Causal Continuity

The result that, for a scalar quantum field propagating on a ``trousers'' topology in 1+1 dimensions, the crotch singularity is a source for an infinite burst of energy has been used to argue against the occurrence of topology change in quantum gravity. We draw attention to a conjecture due to Sorkin that it may be the particular type of topology change involved in the trousers transition that is problematic and that other topology changes may not cause the same difficulties. The conjecture links the singular behaviour to the existence of ``causal discontinuities'' in the spacetime and relies on a classification of topology changes using Morse theory. We investigate various topology changing transitions, including the pair production of black holes and of topological geons, in the light of these ideas.Comment: Latex, 28 pages, 10 figures, small changes in text (one figure removed), conclusions remain unchanged. Accepted for publication in Physical Review

An Application of Physical Flexibility and Software Reconfigurability for the Automation of Battery Module Assembly

Batteries are a strategic technology to decarbonize conventional automotive powertrains and enable energy policy turnaround from fossil fuels to renewable energy. The demand for battery packs is rising, but they remain unable to compete with conventional technologies, primarily due to higher costs. Major sources of cost remain in manufacturing and assembly. These costs can be attributed to a need for high product quality, material handling complexity, uncertain and fluctuating production volumes, and an unpredictable breadth of product variants. This research paper applies the paradigms of flexibility from a mechanical engineering perspective, and reconfigurability from a software perspective to form a holistic, integrated manufacturing solution to better realize product variants. This allows manufacturers to de-risk investment as there is increased confidence that a facility can meet new requirements with reduced effort, and also shows how part of the vision of Industry 4.0 associated with the integration and exploitation of data can be fulfilled. A functional decomposition of battery packs is used to develop a foundational understanding of how changes in customer requirements can result in physical product changes. A Product, Process, and Resource (PPR) methodology is employed to link physical product characteristics to physical and logical characteristics of resources. This mapping is leveraged to enable the design of a gripper with focused flexibility by the Institute for Machine Tools and Industrial Management (iwb) at the Technical University of Munich, as it is acknowledged that mechanical changes are challenging to realize within industrial manufacturing facilities. Reconfigurability is realised through exploitation of data integration across the PPR domains, through the extension of the capabilities of a non-commercial virtual engineering toolset developed by the Automation Systems Group at the University of Warwick. The work shows an “end-to-end” approach that practically demonstrates the application of the flexibility and reconfigurability paradigms within an industrial engineering context

Event horizons and apparent horizons in spherically symmetric geometries

Spherical configurations that are very massive must be surrounded by apparent horizons. These in turn, when placed outside a collapsing body, must propagate outward with a velocity equal to the velocity of radially outgoing photons. That proves, within the framework of (1+3) formalism and without resorting to the Birkhoff theorem, that apparent horizons coincide with event horizons.Comment: 5 pages, plainte

Some Curvature Problems in Semi-Riemannian Geometry

In this survey article we review several results on the curvature of semi-Riemannian metrics which are motivated by the positive mass theorem. The main themes are estimates of the Riemann tensor of an asymptotically flat manifold and the construction of Lorentzian metrics which satisfy the dominant energy condition.Comment: 25 pages, LaTeX, 4 figure

Force balance and membrane shedding at the Red Blood Cell surface

During the aging of the red-blood cell, or under conditions of extreme echinocytosis, membrane is shed from the cell plasma membrane in the form of nano-vesicles. We propose that this process is the result of the self-adaptation of the membrane surface area to the elastic stress imposed by the spectrin cytoskeleton, via the local buckling of membrane under increasing cytoskeleton stiffness. This model introduces the concept of force balance as a regulatory process at the cell membrane, and quantitatively reproduces the rate of area loss in aging red-blood cells.Comment: 4 pages, 3 figure

Vacuum Spacetimes with Future Trapped Surfaces

In this article we show that one can construct initial data for the Einstein equations which satisfy the vacuum constraints. This initial data is defined on a manifold with topology $R^3$ with a regular center and is asymptotically flat. Further, this initial data will contain an annular region which is foliated by two-surfaces of topology $S^2$. These two-surfaces are future trapped in the language of Penrose. The Penrose singularity theorem guarantees that the vacuum spacetime which evolves from this initial data is future null incomplete.Comment: 19 page

Peptide Sequence and Conformation Strongly Influence Tryptophan Fluorescence

AbstractThis article probes the denatured state ensemble of ribonuclease Sa (RNase Sa) using fluorescence. To interpret the results obtained with RNase Sa, it is essential that we gain a better understanding of the fluorescence properties of tryptophan (Trp) in peptides. We describe studies of N-acetyl-L-tryptophanamide (NATA), a tripeptide: AWA, and six pentapeptides: AAWAA, WVSGT, GYWHE, HEWTV, EAWQE, and DYWTG. The latter five peptides have the same sequence as those surrounding the Trp residues studied in RNase Sa. The fluorescence emission spectra, the fluorescence lifetimes, and the fluorescence quenching by acrylamide and iodide were measured in concentrated solutions of urea and guanidine hydrochloride. Excited-state electron transfer from the indole ring of Trp to the carbonyl groups of peptide bonds is thought to be the most important mechanism for intramolecular quenching of Trp fluorescence. We find the maximum fluorescence intensities vary from 49,000 for NATA with two carbonyls, to 24,400 for AWA with four carbonyls, to 28,500 for AAWAA with six carbonyls. This suggests that the four carbonyls of AWA are better able to quench Trp fluorescence than the six carbonyls of AAWAA, and this must reflect a difference in the conformations of the peptides. For the pentapeptides, EAWQE has a fluorescence intensity that is more than 50% greater than DYWTG, showing that the amino acid sequence influences the fluorescence intensity either directly through side-chain quenching and/or indirectly through an influence on the conformational ensemble of the peptides. Our results show that peptides are generally better models for the Trp residues in proteins than NATA. Finally, our results emphasize that we have much to learn about Trp fluorescence even in simple compounds