Localised states in an extended Swift-Hohenberg equation

Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is variational in time and conservative in space. In this paper we investigate an extended Swift-Hohenberg equation in which non-variational and non-conservative effects play a key role. Our work concentrates on aspects of this much more complicated problem. Firstly we carry out the normal form analysis of the initial pattern forming instability that leads to small-amplitude localised states. Next we examine the bifurcation structure of the large-amplitude localised states. Finally we investigate the temporal stability of one-peak localised states. Throughout, we compare the localised states in the extended Swift-Hohenberg equation with the analogous solutions to the usual Swift-Hohenberg equation

Alien Registration- Burke, John H. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/25218/thumbnail.jp

A comparison of crossover control mechanisms within single-point selection hyper-heuristics using HyFlex

Hyper-heuristics are search methodologies which operate at a higher level of abstraction than traditional search and optimisation techniques. Rather than operating on a search space of solutions directly, a hyper-heuristic searches a space of low-level heuristics or heuristic components. An iterative selection hyper-heuristic operates on a single solution, selecting and applying a low-level heuristic at each step before deciding whether to accept the resulting solution. Crossover low-level heuristics are often included in modern selection hyper-heuristic frameworks, however as they require multiple solutions to operate, a strategy is required to manage potential solutions to use as input. In this paper we investigate the use of crossover control schemes within two existing selection hyper-heuristics and observe the difference in performance when the method for managing potential solutions for crossover is modified. Firstly, we use the crossover control scheme of AdapHH, the winner of an international competition in heuristic search, in a Modified Choice Function - All Moves selection hyper-heuristic. Secondly, we replace the crossover control scheme within AdapHH with another method taken from the literature. We observe that the performance of selection hyper-heuristics using crossover low level heuristics is not independent of the choice of strategy for managing input solutions to these operators

A modified choice function hyper-heuristic controlling unary and binary operators

Hyper-heuristics are a class of high-level search methodologies which operate on a search space of low-level heuristics or components, rather than on solutions directly. Traditional iterative selection hyper-heuristics rely on two key components, a heuristic selection method and a move acceptance criterion. Choice Function heuristic selection scores heuristics based on a combination of three measures, selecting the heuristic with the highest score. Modified Choice Function heuristic selection is a variant of the Choice Function which emphasises intensification over diversification within the heuristic search process. Previous work has shown that improved results are possible in some problem domains when using Modified Choice Function heuristic selection over the classic Choice Function, however in most of these cases crossover low-level heuristics (operators) are omitted. In this paper, we introduce crossover low-level heuristics into a Modified Choice Function selection hyper-heuristic and present results over six problem domains. It is observed that although on average there is an increase in performance when using crossover low-level heuristics, the benefit of using crossover can vary on a per-domain or per-instance basis

PhoSim-NIRCam: Photon-by-photon image simulations of the James Webb Space Telescope's Near-Infrared Camera

Recent instrumentation projects have allocated resources to develop codes for simulating astronomical images. Novel physics-based models are essential for understanding telescope, instrument, and environmental systematics in observations. A deep understanding of these systematics is especially important in the context of weak gravitational lensing, galaxy morphology, and other sensitive measurements. In this work, we present an adaptation of a physics-based ab initio image simulator: The Photon Simulator (PhoSim). We modify PhoSim for use with the Near-Infrared Camera (NIRCam) -- the primary imaging instrument aboard the James Webb Space Telescope (JWST). This photon Monte Carlo code replicates the observational catalog, telescope and camera optics, detector physics, and readout modes/electronics. Importantly, PhoSim-NIRCam simulates both geometric aberration and diffraction across the field of view. Full field- and wavelength-dependent point spread functions are presented. Simulated images of an extragalactic field are presented. Extensive validation is planned during in-orbit commissioning

Relevance of the slowly-varying electron gas to atoms, molecules, and solids

Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact to order $\nabla^2$. Neutral atoms of large $Z$ scale similarly, but a cusp correction at the nucleus requires generalizing the gradient expansion for exchange, producing the wrong gradient coefficient in the slowly-varying limit. Meta-generalized gradient approximations (meta-GGA's) recover both the slowly-varying and large-$Z$ limits. GGA correlation energies of large-Z atoms are found to be accurate.Comment: 5 pages, 4 figures, submitted at PR

Exact condition on the Kohn-Sham kinetic energy, and modern parametrization of the Thomas-Fermi density

We study the asymptotic expansion of the neutral-atom energy as the atomic number Z goes to infinity, presenting a new method to extract the coefficients from oscillating numerical data. We find that recovery of the correct expansion is an exact condition on the Kohn-Sham kinetic energy that is important for the accuracy of approximate kinetic energy functionals for atoms, molecules and solids, when evaluated on a Kohn-Sham density. For example, this determines the small gradient limit of any generalized gradient approximation, and conflicts somewhat with the standard gradient expansion. Tests are performed on atoms, molecules, and jellium clusters. We also give a modern, highly accurate parametrization of the Thomas-Fermi density of neutral atoms.Comment: 10 pages, 9 figures, submitted at JC

A target enrichment method for gathering phylogenetic information from hundreds of loci: An example from the Compositae.

UnlabelledPremise of the studyThe Compositae (Asteraceae) are a large and diverse family of plants, and the most comprehensive phylogeny to date is a meta-tree based on 10 chloroplast loci that has several major unresolved nodes. We describe the development of an approach that enables the rapid sequencing of large numbers of orthologous nuclear loci to facilitate efficient phylogenomic analyses. •Methods and resultsWe designed a set of sequence capture probes that target conserved orthologous sequences in the Compositae. We also developed a bioinformatic and phylogenetic workflow for processing and analyzing the resulting data. Application of our approach to 15 species from across the Compositae resulted in the production of phylogenetically informative sequence data from 763 loci and the successful reconstruction of known phylogenetic relationships across the family. •ConclusionsThese methods should be of great use to members of the broader Compositae community, and the general approach should also be of use to researchers studying other families

Longitudinal stability augmentation of seaplanes in planing

The towing tank experiments conducted at Yokohama National University from November 30 to December 9 in 2005 suggested a new way of suppressing a dangerous coupled motion between heave and pitch called porpoising. The research in this paper was developed on the observations made in the experiments and conducted numerical simulations to further investigate the parametric design space. Two linear-time-invariant models were developed: rigid-body planing craft (conventional float planes or flying boats), and flexibly supported planing craft. The latter could simulate the new method found in the experiments for suppressing porpoising. In this study, the stability of the oscillatory motions was analyzed to see the effect of design variables on the inception of porpoising. The parametric study of flexibly supported float planes in the context of porpoising was a new contribution in the conceptual design of seaplanes