Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

Clonal expansion within pneumococcal serotype 6C after use of seven-valent vaccine

Streptococcus pneumoniae causes invasive infections, primarily at the extremes of life. A seven-valent conjugate vaccine (PCV7) is used to protect against invasive pneumococcal disease in children. Within three years of PCV7 introduction, we observed a fourfold increase in serotype 6C carriage, predominantly due to a single clone. We determined the whole-genome sequences of nineteen S. pneumoniae serotype 6C isolates, from both carriage (n = 15) and disease (n = 4) states, to investigate the emergence of serotype 6C in our population, focusing on a single multi-locus sequence type (MLST) clonal complex 395 (CC395). A phylogenetic network was constructed to identify different lineages, followed by analysis of variability in gene sets and sequences. Serotype 6C isolates from this single geographical site fell into four broad phylogenetically distinct lineages. Variation was seen in the 6C capsular locus and in sequences of genes encoding surface proteins. The largest clonal complex was characterised by the presence of lantibiotic synthesis locus. In our population, the 6C capsular locus has been introduced into multiple lineages by independent capsular switching events. However, rapid clonal expansion has occurred within a single MLST clonal complex. Worryingly, plasticity exists within current and potential vaccine-associated loci, a consideration for future vaccine use, target selection and design

Materials modeling and development for use in double-exposure lithography applications

The current optical photolithography technology is approaching the physical barrier to the minimum achievable feature size. To produce smaller devices, new resolution enhancement technologies must be developed. Double-exposure lithography has shown promise as a potential pathway that is attractive because it is much cheaper than double-patterning lithography and can be deployed on existing imaging tools. However, this technology is not possible without the development of new materials with nonlinear response to exposure dose. The performance of existing materials such as reversible contrast enhancement layers (rCELs), and theoretical materials such as intermediate state two-photon (ISTP) and optical threshold layer (OTL) materials in double-exposure applications have been investigated through computer simulation. All three materials yielded process windows in double-exposure mode. OTL materials showed the largest process window (depth of focus (DOF) 0.14 µm, exposure latitude (EL) 5.1%). ISTP materials had the next-largest process window (DOF 0.12 µm, EL 3.2%), followed by the rCEL (0.11 µm, 0.58%). This study is an analysis of the feasibility of using the materials in double-exposure mode

Double Exposure Materials: Simulation Study of Feasibility

Double patterning and double exposure techniques have been proposed as possible methods for reducing half pitch resolution below k1=0.25. Both methods have the potential to reduce the theoretical lithographic half pitch to k1=0.125. Double patterning is a process-intensive method that requires multiple coat, develop, and etch steps to achieve the low k1 imaging. Double exposure processes have been proposed that do not require multiple coat, develop, or etch steps. Potentially, double exposure processes will have a lower cost of ownership that double patterning. However, double exposure materials have not yet been proven to work experimentally. Before applying significant effort to develop double exposure materials, their feasibility can be determined using rigorous simulation techniques. This work presents a feasibility study of four types of double exposure materials and their potential process windows

Polarized Redundant-Baseline Calibration for 21 cm Cosmology Without Adding Spectral Structure

21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly-constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally-smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degrees of freedom are not constrained by asserting internal consistency between redundant measurements. In this paper, we review the origin of these "degeneracies" of redundant-baseline calibration and demonstrate how they can source unwanted spectral structure in our measurement and show how to eliminate that additional, artificial structure. We also generalize redundant calibration to dual-polarization instruments, derive the degeneracy structure, and explore the unique challenges to calibration and preserving spectral smoothness presented by a polarized measurement.Comment: 12 pages, 3 figures, updated to match the published MNRAS versio

Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity

We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a non-spinning particle orbiting a Kerr black hole of mass M and spin S = -0.5 M^2, down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations.Comment: 18 pages, 12 figures; matches version to appear in Phys. Rev.

An analysis of double exposure lithography options

The current optical photolithography technology is approaching the physical barrier to the minimum achievable feature size. To produce smaller devices, new resolution enhancement technologies must be developed. Double exposure lithography has shown promise as potential pathway that is attractive because it is much cheaper than double patterning lithography and it can be deployed on existing imaging tools. However, this technology is not possible without the development of new materials with nonlinear response to exposure dose. The performance of existing materials such as reversible contrast enhancement layers (rCELs) and theoretical materials such as intermediate state two-photon (ISTP) and optical threshold layer (OTL) materials in double exposure applications was investigated through computer simulation. All three materials yielded process windows in double exposure mode. OTL materials showed the largest process window (DOF 0.137 µm, EL 5.06 %). ISTP materials had the next largest process window (DOF 0.124 µm, EL 3.22 %) followed by the rCEL (0.105 µm, 0.58 %). This study is an analysis of the feasibility of using the materials in double exposure mode