Republication of: Black hole equilibrium states

This is a reprinting of Part 1 of Brandon Carter’s lectures given at the 1972 Les Houches school on black holes, first published in a book of proceedings of that school in 1973. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. The main value of this article is a comprehensive discussion of global properties of the Kerr solution, its maximal extension, its derivation from the separability of the Klein-Gordon equation and, most notably, its generalisation to nonzero cosmological constant. Numerous typos of the original text are corrected in this reprinting. The reprinted article is accompanied by an editorial note written by Niky Kamran and Andrzej Krasiński, and by B. Carter’s brief autobiography.     

Probabilistic modeling of forced ignition of alternative jet fuels

Fast and reliable high altitude re-ignition is a critical requirement for the development of alternative jet fuels (AJFs). To achieve stable combustion, a spark kernel needs to transit in a partially or fully extinguished flow to develop a flame front. Understanding the relight characteristics of the AJFs is complicated by the chaoticity of the turbulent flow and variations in the spark properties. The focus of this study is the prediction of such characteristics by high-fidelity simulations, with a specific focus on fuel composition effect on the ignition process. For this purpose, a previously developed computational framework is applied, which utilizes high-fidelity LES simulations, a hybrid tabulation approach for modeling forced ignition and detailed quantification of uncertainty resulting from initial and boundary conditions to predict ignition probability. The method is applied to two alternative fuels (named C1 and C5) and Jet-A fuel (named A2) under gaseous conditions. Results show that the mixing of kernel and fuel–air mixture is not affected by the ignition process, but chemistry effects strongly dominate ignition probability. In particular, C1 exhibits much lower ignition probability than the other two fuels, especially at lean operating conditions. More importantly, this behavior is contradictory to ignition delay experiments which predict longer delay times for C5 compared to C1. Comparisons with experiments show that the comprehensive modeling approach captures the ignition trends. Analysis of kernel trajectories in composition space shows that the variations are caused by the relative effects of kernel mixing, response to strain, and ignition properties of the fuel.     

Time-stretch oscilloscope with dual-channel differential detection front end for monitoring of 100 Gb/s return-to-zero differential quadrature phase-shift keying data

Optical performance monitoring of high-capacity networks is one of the enabling technologies of future reconfigurable optical switch networks. In such networks, rapid performance evaluation of data streams becomes challenging due to the use of advanced modulation formats and high data rates. The time-stretch enhanced recording oscilloscope offers a potential solution to monitoring high-rate data in a practical time scale. Here we demonstrate an architecture with a differential detection front end for simultaneous I/Q data monitoring of a 100 gigabits/s return-to-zero differential quadrature phase-shift keying signal. This demonstration shows the potential of this technology for rapid performance monitoring of high-rate optical data streams that employ advanced modulation formats.     

Electromagnetics via the Taylor-Galerkin Finite Element Method on Unstructured Grids

Traditional techniques for computing electromagnetic solutions in the time domain rely on finite differences. These so-called FDTD (finite-difference time-domain) methods are usually defined only on regular lattices of points and can be too restrictive for geometrically demanding problems. Great geometric flexibility can be achieved by abandoning the regular latticework of sample points and adopting an unstructured grid. An unstructured grid allows one to place the grid points anywhere one chooses, so that curved boundaries can be fit with ease and local regions in which the field gradients are steep can be selectively resolved with a fine mesh. In this paper we present a technique for solving Maxwell's equations on an unstructured grid based on the Taylor-Galerkin finite-element method. We present several numerical examples which reveal the fundamental accuracy and adaptability of the method. Although our examples are in two dimensions, the techniques and results generalize readily to 3D.     

An analytical prediction of sliding motions along discontinuous boundary in non-smooth dynamical systems

This paper presents a method for the analytical prediction of sliding motions along discontinuous boundaries in non-smooth dynamical systems. The methodology is demonstrated through investigation of a periodically forced linear oscillator with dry friction. The switching conditions for sliding motions in non-smooth dynamical systems are given. The generic mappings for the friction-induced oscillator are introduced. From the generic mappings, the corresponding criteria for the sliding motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the sliding motions is illustrated. Finally, numerical simulations of sliding motions are carried out to verify the analytical prediction. This analytical prediction provides an accurate prediction of sliding motions in non-smooth dynamical systems. The switching conditions developed in this paper are expressed by the total force of the oscillator, and the nonlinearity and linearity of the spring and viscous damping forces in the oscillator cannot change such switching conditions. Therefore, the achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces processing a C ⁰-discontinuity.     

High P–T Raman study of transitions in relaxor multiferroic Pb(Fe0.5Nb0.5)O3

The vibrational and structural properties of Pb(Fe_0.5Nb_0.5)O₃ have been investigated using Raman spectroscopy up to 40 GPa at 300 K and from 300 to 415 K at selected pressures. The measurements reveal three phase transitions, at 5.5, 8.7, and 24 GPa at room temperature. The temperature dependences of the spectra indicate transitions at 1.5 GPa, at 335 and 365 K. The results are consistent with the appearance of an intermediate tetragonal P4mm phase between the ferroelectric R3m and paraelectric Pm‐3m phases. A P–T phase diagram is proposed that allows further insight into the magnetoelectric coupling present in this material. Copyright © 2015 John Wiley & Sons, Ltd.     

Automated solvent system screening for the preparative countercurrent chromatography of pharmaceutical discovery compounds

A fully automated countercurrent chromatography system has been constructed to rapidly screen the commonly used heptane/ethyl acetate/methanol/water solvent system series and translate the results to preparative scale separations. The system utilizes “on‐demand” preparation of the heptane/ethyl acetate/methanol/water solvent system upper and lower phases. Elution‐extrusion countercurrent chromatography was combined with non‐dynamic equilibrium injection reducing the screening time for each heptane/ethyl acetate/methanol/water system to 17 min. The result enabled solvent system development to be reduced to under 2 h. The countercurrent chromatography system was interfaced with a mass spectrometer to allow selective detection of target components in crude medicinal chemistry reaction mixtures. Mass‐directed preparative countercurrent chromatography purification was demonstrated for the first time using a synthetic tetrazole epoxide derived from a routine medicinal chemistry support workflow.     

Direct on-strip analysis of size- and time-resolved aerosol impactor samples using laser induced fluorescence spectra excited at 263 and 351 nm

We report a novel atmospheric aerosol characterization technique, in which dual wavelength UV laser induced fluorescence (LIF) spectrometry marries an eight-stage rotating drum impactor (RDI), namely UV-LIF-RDI, to achieve size- and time-resolved analysis of aerosol particles on-strip. The UV-LIF-RDI technique measured LIF spectra via direct laser beam illumination onto the particles that were impacted on a RDI strip with a spatial resolution of 1.2 mm, equivalent to an averaged time resolution in the aerosol sampling of 3.6 h. Excited by a 263 nm or 351 nm laser, more than 2000 LIF spectra within a 3-week aerosol collection time period were obtained from the eight individual RDI strips that collected particles in eight different sizes ranging from 0.09 to 10 μm in Djibouti. Based on the known fluorescence database from atmospheric aerosols in the US, the LIF spectra obtained from the Djibouti aerosol samples were found to be dominated by fluorescence clusters 2, 5, and 8 (peaked at 330, 370, and 475 nm) when excited at 263 nm and by fluorescence clusters 1, 2, 5, and 6 (peaked at 390 and 460 nm) when excited at 351 nm. Size- and time-dependent variations of the fluorescence spectra revealed some size and time evolution behavior of organic and biological aerosols from the atmosphere in Djibouti. Moreover, this analytical technique could locate the possible sources and chemical compositions contributing to these fluorescence clusters. Advantages, limitations, and future developments of this new aerosol analysis technique are also discussed.     

Tribological durability of silane monolayers on silicon

We report the frictional performance and long-term tribological stability of various alkyl silane monolayer films on silicon by using pin-on-disk tribometry at ambient conditions. We show that the durability of monolayers derived from n-alkyltrichlorosilanes on silicon increases exponentially with the chain length of the silane precursor, which we relate to the cohesive energy of these monolayers through molecular dynamics simulations. X-ray photoelectron spectroscopy (XPS) was used to show that tribological damage consisted of the loss of molecular components that could be partially replaced upon exposure to a solution containing perfluorinated silane precursors. For monolayers derived from n-octadecyltrichlorosilane, a critical load was identified to be approximately 250 mN (200 MPa), above which failure of films occurred within 100 cycles of testing. Monolayers with hydroxyl surfaces exhibited reduced stabilities due to stronger tip-surface interactions. Monolayers with the capability for cross-linking exhibited much greater stabilities than monolayers where cross-linking was limited or prevented. Collectively, these results demonstrate that the mechanical durability of monolayers when subjected to a tribological load is greatly enhanced by maximizing dispersional interactions and cross-linking and minimizing tip-surface interactions.